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Takeaways:

• Causal inference is crucial for understanding the impact of interventions in various fields.
• ChiRho is a causal probabilistic programming language that bridges mechanistic and data-driven models.
• ChiRho allows for easy manipulation of causal models and counterfactual reasoning.
• The design of ChiRho emphasizes modularity and extensibility for diverse applications.
• Causal inference requires careful consideration of assumptions and model structures.
• Real-world applications of causal inference can lead to significant insights in science and engineering.
• Collaboration and communication are key in translating causal questions into actionable models.
• The future of causal inference lies in integrating probabilistic programming with scientific discovery.

Chapters:

05:53 Bridging Mechanistic and Data-Driven Models

09:13 Understanding Causal Probabilistic Programming

12:10 ChiRho and Its Design Principles

15:03 ChiRho’s Functionality and Use Cases

17:55 Counterfactual Worlds and Mediation Analysis

20:47 Efficient Estimation in ChiRho

24:08 Future Directions for Causal AI

50:21 Understanding the Do-Operator in Causal Inference

56:45 ChiRho’s Role in Causal Inference and Bayesian Modeling

01:01:36 Roadmap and Future Developments for ChiRho

01:05:29 Real-World Applications of Causal Probabilistic Programming

01:10:51 Challenges in Causal Inference Adoption

01:11:50 The Importance of Causal Claims in Research

01:18:11 Bayesian Approaches to Causal Inference

01:22:08 Combining Gaussian Processes with Causal Inference

01:28:27 Future Directions in Probabilistic Programming and Causal Inference

Thank you to my Patrons for making this episode possible!

Yusuke Saito, Avi Bryant, Ero Carrera, Giuliano Cruz, James Wade, Tradd Salvo, William Benton, James Ahloy, Robin Taylor,, Chad Scherrer, Zwelithini Tunyiswa, Bertrand Wilden, James Thompson, Stephen Oates, Gian Luca Di Tanna, Jack Wells, Matthew Maldonado, Ian Costley, Ally Salim, Larry Gill, Ian Moran, Paul Oreto, Colin Caprani, Colin Carroll, Nathaniel Burbank, Michael Osthege, Rémi Louf, Clive Edelsten, Henri Wallen, Hugo Botha, Vinh Nguyen, Marcin Elantkowski, Adam C. Smith, Will Kurt, Andrew Moskowitz, Hector Munoz, Marco Gorelli, Simon Kessell, Bradley Rode, Patrick Kelley, Rick Anderson, Casper de Bruin, Philippe Labonde, Michael Hankin, Cameron Smith, Tomáš Frýda, Ryan Wesslen, Andreas Netti, Riley King, Yoshiyuki Hamajima, Sven De Maeyer, Michael DeCrescenzo, Fergal M, Mason Yahr, Naoya Kanai, Aubrey Clayton, Jeannine Sue, Omri Har Shemesh, Scott Anthony Robson, Robert Yolken, Or Duek, Pavel Dusek, Paul Cox, Andreas Kröpelin, Raphaël R, Nicolas Rode, Gabriel Stechschulte, Arkady, Kurt TeKolste, Marcus Nölke, Maggi Mackintosh, Grant Pezzolesi, Joshua Meehl, Javier Sabio, Kristian Higgins, Matt Rosinski, Bart Trudeau, Luis Fonseca, Dante Gates, Matt Niccolls, Maksim Kuznecov, Michael Thomas, Luke Gorrie, Cory Kiser, Julio, Edvin Saveljev, Frederick Ayala, Jeffrey Powell, Gal Kampel, Adan Romero, Will Geary, Blake Walters, Jonathan Morgan, Francesco Madrisotti, Ivy Huang, Gary Clarke, Robert Flannery, Rasmus Hindström, Stefan, Corey Abshire, Mike Loncaric, David McCormick, Ronald Legere, Sergio Dolia, Michael Cao, Yiğit Aşık, Suyog Chandramouli and Adam Tilmar Jakobsen.

• Intro to Bayes Course (first 2 lessons free)
• Advanced Regression Course (first 2 lessons free)

Links from the show:

• Sam’s website: https://samwitty.github.io/
• Sam on LinkedIn: https://www.linkedin.com/in/sam-witty-46708572/
• Sam on GitHub: https://github.com/SamWitty
• ChiRho docs: https://basisresearch.github.io/chirho/getting_started.html
• Causal Inference using Gaussian Processes with Structured Latent Confounders: https://proceedings.mlr.press/v119/witty20a/witty20a.pdf
• Automated Efficient Estimation using Monte Carlo Efficient Influence Functions: https://proceedings.neurips.cc/paper_files/paper/2024/file/1d10fe211f5139de49f94c6f0c7cecbe-Paper-Conference.pdf
• PhD Thesis: https://samwitty.github.io/papers/Witty_Dissertation.pdf
• LBS #137 Causal AI & Generative Models, with Robert Ness: https://learnbayesstats.com/episode/137-causal-ai-generative-models-robert-ness

Transcript

This is an automatic transcript and may therefore contain errors. Please get in touch if you're willing to correct them.

In this episode, I am joined by Sam Witte, founder of Cerberus AI.

2

Sam is the driving force behind Pyro, an open-source framework that extends Pyro with

causal capabilities, giving scientists and engineers a way to run counterfactuals, analyze

3

path-specific effects, and build hybrid models that combine machine learning with domain

knowledge.

4

We talk about the challenges of translating causal questions for clients, the importance

of Bayesian thinking for scrutinizing assumptions, and the real-world impact of causal

5

probabilistic programming, from sustainable energy to preemptive health.

6

This is Learning Bayesian Statistics, recorded July 31, 2025.

7

Welcome Bayesian Statistics, a podcast about Bayesian inference, the methods, the

projects, and the people who make it possible.

8

I'm your host, Alex Andorra.

9

You can follow me on Twitter at alex-underscore-andorra.

10

like the country.

11

For any info about the show, learnbasedats.com is Laplace to be.

12

Show notes, becoming a corporate sponsor, unlocking Bayesian Merge, supporting the show on

Patreon, everything is in there.

13

That's learnbasedats.com.

14

If you're interested in one-on-one mentorship, online courses, or statistical consulting,

feel free to reach out and book a call at topmate.io slash alex underscore and dora.

15

See you around, folks.

16

and best patient wishes to you all.

17

And if today's discussion sparked ideas for your business, well, our team at Pimc Labs can

help bring them to life.

18

Check us out at pimc-labs.com.

19

Hello my dear Baysians!

20

Big news!

21

I am considering running a 6-week, more or less, live cohort of my Advanced Baysian

Regression course from Intuitive Bays that I wrote with the brilliant Robin Coomer and

22

Tommy Capretto.

23

Think weekly live sessions, projects, office hours, community...

24

So if you are into practical Bays and want to see how it's done in the wild, in practice

and

25

learned that, well, that sounds interesting to you, feel free to answer the short Google

form in the show notes to help me scope demand and logistics, and of course also to get

26

the early bird access and discount.

27

Thank you so much for your help and for being such a good patient.

28

I'm Witty, welcome to Learning Vision Statistics.

29

Thank you.

30

Glad to be here.

31

Yeah, I am super excited to have you on the show because, well, you're doing things I'm

very interested in, especially uh these days where I'm ramping up my causal inference,

32

intersecting with uh generative AI modeling skills.

33

I discovered your work through

34

Robert Ness's episode with us and also his great book called the Lay-A-Aye where he uses

Cairo and you are of course one of the developers of his great package.

35

So we'll talk about all that today.

36

um And if you have some stuff by the way you want to share on your screen, know, demo

stuff, live or else, let me know you can share your screen and that will be then on the

37

YouTube channel for people who want to follow along.

38

But first, as usual, we're going to dive into your origin story, So what are you doing

nowadays and how did you end up working on that?

39

So right now I'm a founder and principal consultant at a company I founded called Sorbus

AI.

40

um We do consulting on probabilistic and causal AI, mostly for engineering and scientific

clients.

41

um I'll talk a little later about why I think that's a really sweet spot for this

technology right now.

42

But at a high level, it's a boutique consultancy where I sit very closely with clients and

help them um kind of bridge the gap between what I call uh mechanistic and kind of

43

data-driven modeling workflows.

44

um So the story that got me there, um in undergrad I was a mechanical engineer.

45

I actually don't have uh you know, undergrad

46

computer science or statistics background, and I came into this world sort of by accident.

47

um I was a working mechanical engineer.

48

I worked for a small consulting firm that was doing energy efficiency consulting.

49

um Actually, uh a fun aside, I was doing causal inference without knowing it was causal

inference.

50

We were evaluating uh public policy programs m that give money for energy efficiency

projects.

51

and they wanted to know what the causal impact of those programs were.

52

um So at that job, I spent a lot of time doing kind of engineering first um modeling,

building models of fluid dynamics or heat transfer, these sorts of things.

53

um But I felt like very quickly that wasn't really able to keep up with the data we would

gather in the real world.

54

um So that naturally brought me to statistics and machine learning.

55

um which at the same time felt like I had to throw away all of the mechanistic knowledge I

had learned in engineering school.

56

um So with that kind of tension in mind, I went to grad school, studied a bunch of things

we'll talk about today, and now this consulting work is kind of coming full circle.

57

I'm trying to bridge the world between engineering first, modeling where you think hard

about the physics, think hard about the mechanisms in the world.

58

and the kind of probabilistic and causal AI that's made a lot of technical progress in the

last several years.

59

Yeah, definitely.

60

And I really like how you're blending all these different experiences into what you're

doing today.

61

And I'm actually also wondering, you did your PhD at UMass Amherst.

62

You did a visiting at MIT.

63

And if I understood correctly, both of those

64

revolved around some kind of probabilistic programming.

65

So was there a particular moment that turned that academic work into a career focus?

66

And where you knew you wanted to focus on that for at least the coming years because you

thought it was really interesting.

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Yeah, I've always been academically minded.

68

um

69

For any of your listeners who went to engineering school, uh you'll remember a common

phrase that professors make, is, uh I'm sorry for all the math, but we'll get to the cool

70

stuff soon.

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And that was never me.

72

I liked the math.

73

um So, you know, doing a PhD was a pretty natural progression for me.

74

But at the same time, I think that the career focus has been kind of driven by my past

engineering experience.

75

And then I see the computer science

76

um academic background is developing the schools to kind of meet that end.

77

Whereas other people might have started with a set of tools and then later developed those

tools into application areas for their career.

78

I see.

79

That's interesting.

80

I didn't know the like the engineering professors were like, okay, let's, let's get the

math out of the way and then focus on the cool stuff.

81

Yeah, it's it's often a lot of car nerds.

82

they want to build engines or design circuits and some, not all, certainly not all

engineers see math as an impediment to doing the cool physical things they want to do.

83

um It's obviously, it's a broad sweeping statement.

84

Many engineers are as math-nerdy as I am.

85

Right, Now that reminds me of em the TV series Big Bang Theory where

86

course Howard is the only the only member of the team who is an engineer and always get

teased by by Sheldon because first he doesn't have a PhD and second uh he's an engineer

87

saying that that made me think about that ah and which is of course not not true uh the

proof is that you're here you are on on this podcast ah which is very academic something

88

also I was I was um

89

interested in when preparing for your episode was that on your homepage, that's in the

show notes, by the way, folks, you say that you help teams combine mechanistic knowledge

90

with data driven machine learning.

91

From where you're coming from and the answers you just gave, I really understand now why

you're saying that on your website.

92

um But I'm also wondering

93

when you first realized that that marriage was a missing ingredient for many heartache

problems?

94

Yeah, yeah, it's a great question.

95

one of the core things about engineering models is that you can extrapolate with them,

right?

96

For a lot of models, they're derived from very simple concepts, right?

97

You might look at Newton's laws, for example.

98

And a lot of engineering modeling is about uh seeing the

99

natural consequences of those very simple laws.

100

so for example you can derive things about uh about objects colliding or rotation, uh

leverage, inertia, um conservation of energy, all from these kind of basic fundamental uh

101

laws of the world.

102

um and so the most part those laws generalize, right?

103

if i

104

If I imagine a bridge that I've never built before uh using these kind of mechanistic

laws, I can be pretty confident that if I've been careful about the math, that the bridge

105

is going to work the way I would expect it to work.

106

Now there are some caveats.

107

Of course, some materials behave in somewhat unsuspecting ways, but with a large asterisk,

that is generally true.

108

We expect engineering kind of mechanistic models first to generalize to unforeseen worlds.

109

um

110

And that matters, right?

111

People want to build systems.

112

They want to um make predictions outside of the realm of the data that they've gathered.

113

They want to be able to explain what would have happened had something been different to

inform policy decisions.

114

So people care about causality, um but they also care about learning from data, right?

115

Our knowledge of the world is fundamentally incomplete.

116

um And if you

117

If all you ever did was sat down, wrote down a model by hand, and then probed it for its

logical implications, the model would likely not represent the world very well.

118

It's just too complicated to try to model everything by hand.

119

I past waves of AI research have kind of taught us this.

120

um So the key point is that we should learn something from those mechanistic models of the

world, try to get some of that extrapolative capabilities, but not

121

lose all of kind of data-based machine learning approaches or statistical approaches that

have seen a lot of progress.

122

And I happen to think that probabilistic programming, in particular causal probabilistic

programming, is an extremely natural way to kind of bridge these two worlds.

123

Yeah, actually, that's a good segue into trying and defining all that.

124

Can you define those terms?

125

How do you differentiate them?

126

And why do you think?

127

that causal probabilistic programming has.

128

um Why do you have such hope for it to be able to bridge that gap?

129

Yeah, so when you say define those terms, you mean causal probabilistic programming?

130

Yes, exactly.

131

And the difference with the classic data-driven machine learning.

132

Sure.

133

So um it's worth zooming out a little bit.

134

um Maybe we could start by talking about

135

what is probabilistic programming before adding the causal part.

136

um So probabilistic programming ah in its most simplest form is just programs with

randomness.

137

um You can think of it essentially as writing simulation models that uh have special

syntax for denoting random variables and distributions.

138

um Now that's kind of a simplified representation because it doesn't tell you what they

do.

139

right?

140

and what you do with probabilistic programs is to automate or semi-automate uh a process

known as inference, which is about manipulating uh distributions to answer questions.

141

so some manipulations look like marginalization, uh what would happen if i were to sort of

uh average over a particular variable in my model, or conditioning where you

142

hold some variable fixed at some data and then update your distribution over all of the

other random variables.

143

um And these reasoning operations, these core reasoning operations of marginalization and

conditioning can be very computationally challenging.

144

So probabilistic programming languages often come with a set of inference algorithms that

either exactly or approximately solve um those reasoning steps.

145

So that's purely probabilistic.

146

Imagine uh coin flips or dice rolls or things like that.

147

um At this point, no causality is kind of imbued in these systems.

148

You can ask them about what is likely to occur when other events happen.

149

um But causal probabilistic programs give this kind of idea of taking action or

intervention in your system.

150

And they let you answer questions like,

151

would my distributions change if I were to hit my system with a hammer in some way?

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if I were to intervene?

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um and ah how would those changing distributions ah propagate into the things I care

about?

154

so causal probabilistic programming systems are systems that, uh similar to how

probabilistic programming systems help to automate probabilistic reasoning, causal

155

probabilistic programming systems like Cairo help to automate causal reasoning.

156

asking these kind of what if questions um that, as I said, many scientists and engineers

and policymakers care a lot about.

157

Yeah, yeah, yeah.

158

And I'm actually super grateful that you developed that whole package because it's

definitely something I'm going to use a lot.

159

And mainly because it's built on top of a probabilistic programming package, is amazing

because you get to keep all

160

goodies of Bayesian models basically where you have already the generative structure and

you can do forward and backward sampling but then you add the causal structure the ability

161

to intervene on your causal graph to do counterfactuals uh and stuff like that so I find

this is extremely helpful um and actually that's a good point now for us to turn

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and talk about Cairo in particular.

163

I'm curious first what design principles of Cairo you are particularly happy with and also

why was Pyro the right backend in your mind to do that?

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Yeah, so maybe I explain what causal probabilistic programming was.

165

general, but maybe I could just take a few minutes to explain what Cairo is.

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specifically.

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forgot my own question.

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Thanks for doing that, Sam.

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That's okay.

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You can do my job later too, if you want.

171

No, that's way harder.

172

I uh prefer it like that.

173

Well, we'll see.

174

So Cairo is a causal extension to the Pyro probabilistic programming language, which is

built on top of PyTorch.

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um So Pyro was one of the

176

earlier probabilistic programming languages to um really take deep learning and kind of

differential programming um as kind of a core building block.

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um So Pyro is built on top of PyTorch.

178

um Pyro programs are essentially collections of PyTorch operations with special, as I

said, special syntax for defining random variables.

179

um So Kyro um

180

in a certain sense, is just a wrapper around pyro programs.

181

uh You write your probabilistic causal models as you would any other probabilistic

program.

182

It's just that when you're writing it, you have to kind of imbue it with a little bit more

meaning than you would an ordinary probabilistic program.

183

You're making a kind of implicit assertion that the order of variables that you write

represents like the causal ordering of things unfolding in the world.

184

Whereas

185

This is not something you need to do explicitly if all you care about is estimating um

marginal and conditional probabilities, as in Pyro.

186

um So with that kind of conceptual difference, um Cairo provides two main uh pieces of

functionality above what Pyro does.

187

um One is, as we said, an intervention operator.

188

So this takes a probabilistic program

189

and transforms it where some intervention has been applied.

190

ah You can think of this intervention like ah forcing some variable in your system to take

a particular value or to be generated by some function that is not the normal mechanisms

191

in your probabilistic program.

192

uh And the other thing that Cairo does, which as far as I can tell no other systems yet

support, is to

193

provide sort of bookkeeping for managing what we call counterfactual worlds.

194

um And this is important because lots of really rich causal questions involve um

combinations of outputs from different worlds with different interventions applied that

195

are interacting with each other.

196

And without this kind of support in Cairo, that kind of reasoning is really, really

difficult.

197

um I can give an example of that.

198

um

199

If you'd like.

200

OK.

201

So um a common thing you might want to do with your model is understand what are called

path-specific effects.

202

um So for those familiar with the jargon, this is called mediation analysis.

203

And the idea is that if I have a large and complicated model, I might want to isolate the

effect of one variable on another variable only through a particular pathway.

204

um I don't want to know the total effect of treatment on outcome.

205

I only want to know the effects mediated through something I particularly care about.

206

Yeah.

207

Yeah.

208

So that'd be like, maybe to give an example to people, it's like, if you have a

confounder, so common cause of the treatment and the outcome, you obviously have two uh

209

causal paths here from the treatment to the outcome.

210

but you only had one direct path, which is the one.

211

So this is actually a subtlety.

212

Treatment to the error.

213

The confounding relationship.

214

uh for those who are unfamiliar, confounding, I never know how far to back up the jargon,

but I'll just go far up.

215

So confounding is when you have a variable that influences both the thing you're

interested in intervening on and the thing you're interested in measuring the outcome.

216

uh

217

So in this setting, actually confounding is not the issue.

218

The issue is that between my treatment and my outcome, there are many different paths, all

pointing the same direction.

219

OK, so that'd be more like if you had a direct path and then a path that's mediated?

220

Yeah, exactly.

221

OK.

222

Exactly.

223

And you want to be able to isolate how much of the total effect is going through each of

these different paths.

224

OK.

225

So one way to codify this.

226

is using what are called nested counterfactuals.

227

So you can reframe this question of ah what is the path-specific effect of treatment on

outcome as, let me make sure I get this right, ah what would the outcome be if I

228

intervened on treatment and intervened on the mediator to be what it would have been had I

not intervened on treatment?

229

Right.

230

So that long convoluted sentence involves

231

intervening in two different ways in two different places with values sampled from a

different counterfactual world and kind of interweaving with each other.

232

That sentence is very difficult to codify unless you have the counterfactual worlds that

that Cairo provides.

233

And with Cairo it's four lines of code.

234

And we actually have some tutorials that show exactly how to do that.

235

If you go you'll see a mediation analysis tutorial on the docs page.

236

Yeah, and the docs page is in the show notes.

237

I highly encourage people to check it out.

238

Yeah.

239

mediation analysis is one example.

240

But it turns out that these uh manipulating counterfactual worlds is necessary for

answering other questions, like the ambiguous question, like, why did something happen?

241

It turns out to represent that, you need to do a search over possible counterfactual

worlds.

242

um

243

and optimize that search for outcomes where the thing you're trying to explain is likely

to happen and some other conditions are unlikely to happen.

244

um So doing that kind of search over counterfactual worlds is again not easy, that's kind

of stretching Cairo as far as it can go, um but at least it can be mechanized in Cairo um

245

and it's very difficult otherwise without these utilities.

246

Yeah, I can.

247

I can attest to that.

248

And that's why the work you're doing on Cairo uh is very important to help practitioners

focus on what is actually the most interesting things to them and the most important and

249

the thing that is actually customized to their use case.

250

Whereas what Cairo is doing is

251

trying and abstracting away the math, which is basically the thing that's generalizable.

252

So like in all cases, you're gonna need uh to calculate, you're gonna need to analyze your

counterfactual graphs.

253

And so Cairo is doing that for you.

254

then you can just focus on, what are the DAGs I'm focused on?

255

What are the counterfactual queries I'm actually after?

256

So.

257

Yeah, yeah, think this is this absolutely awesome for people

258

Hello my dear Bajans, just a short break to let you know of a very exciting opportunity I

have for you.

259

Learning Bajan statistics friend of the show Robert Osasu-Hernes has just opened a new

cohort of his causal AI online course and you know what?

260

I personally will be part of this cohort, so if you want to come learn with me, make sure

to enroll at the link in the show notes by Sunday September…

261

First, of course, you have a 50 % discount if you're a patron of the show.

262

I already shared the magic code with you on Discord and Patreon.

263

In this course, we're going to see how to merge the power of deep learning, causal

inference and probabilistic programming all in the same models.

264

And honestly, as a lifelong learner, I am beyond excited to add these causal arrows to my

statistical quiver.

265

So if you need more details, can listen to Robert's latest appearance on the show, which

is episode 137.

266

You can check out the workshop's page in the show notes, or you can just launch a

discussion on Discord if you're a patron.

267

Hope to see you in the workshop, folks.

268

And well, I hope that I will learn with you and with Robert.

269

And now, let's get back to my interview with Sam Waity.

270

So one point of clarification there, because it's a little subtle, is that Cairo doesn't

actually use the do calculus.

271

um for...

272

I thought you guys were.

273

So yeah, how do you do that?

274

Yeah, I could explain.

275

um So the do calculus ah is a set of symbolic rules developed by Pearl and students

several years ago that translate causal questions into probabilistic questions.

276

for what are called nonparametric structural causal models.

277

So the idea is that if all I have is a graph, um which denotes the structure of causal

relationships between my variables, um then the Do Calculus gives me a sound and complete

278

algorithm for translating that into probabilistic expressions that I can estimate from

data.

279

um One of the limitations of the Do Calculus um

280

It's a great tool, and I think the symbolic approaches are awesome.

281

I see what we do in Cairo as supplementary.

282

um One of the limitations of the do calculus is uh there's a key word I said in the

definition, is nonparametric.

283

And a lot of the times, the models we write about the world include parametric assumptions

that actually make it really much easier to do puzzle inference, generally.

284

um

285

So an example of this is, uh if you're familiar with regression discontinuity designs, uh

this is what's called the quasi-experimental design, where you have observational data,

286

where you have a continuous covariate.

287

So for example, um a classic example is the test scores a student get uh on an exam.

288

And you have a treatment, which is

289

in this example, whether they are admitted into the next grade or not, or whether they're

held back, and then an outcome which is uh their education outcomes in the long term.

290

So a regression discontinuity design ah takes advantage of the fact that we know that

there's a fixed threshold in this test score where if you're to the left of this

291

threshold, you get held back a grade, and if you are to the right of this threshold, you

advance to the next grade.

292

A key idea, a key conclusion of this is that you can look at individuals who are very,

close to that threshold on the left and the right and kind of intuit that because they

293

have such similar values of test scores, which may confound the relationship between

whether they um get held back and how their education outcomes are.

294

um You can assume that they're basically the same, because they're infinitesimally close

to each other, uh but they have this kind of differentiated treatment.

295

So it turns out that if you're willing to make these parametric assumptions about uh

smoothness of the functions, or even just this discontinuity existing at all, you can

296

estimate what's called the conditional average treatment effect arbitrarily close to that

discontinuity.

297

That kind of assumption is really easy to write as a program.

298

um You can't, as far as I know, write it directly as a graphical model.

299

The structure of the variables influencing each other doesn't tell you enough to encode

that.

300

So we use a different way of thinking about causal inference, um which I call, in my

thesis, uh Bayesian structural causal inference.

301

So the idea, actually I

302

Is it okay if I share some some figures?

303

Yeah, yeah, for sure.

304

That's gonna be that's gonna be Yeah, and actually that's where so people listening you

might want to switch to the to YouTube channel and you'll have the chapters in the

305

description so you can jump right into that moment in the in the episode.

306

Okay, so this is a uh kind of a cartoonish view of

307

what a structural causal model does in what we call the factual world.

308

So you can think of this space on the left as the sort of space of all the causal models

in the world that you're considering.

309

And the space on the right is um the data that you would observe.

310

So here you can see it's, again, kind of cartoonish, but you can imagine a single

structural causal model inducing a distribution over data.

311

So being a

312

Being good Bayesians, we can put probability distributions on these things.

313

And again, quite cartoonish.

314

But now, if you imagine a distribution over structural causal models, that induces a much

broader distribution over the data you would see.

315

Oh, yeah.

316

That makes sense.

317

Great.

318

So then, hopefully this is all very intuitive.

319

If you start with a distribution over structural causal models, and then you observe

factual data,

320

you can propagate, ah you can condition on that data and propagate that into posterior

distribution over these structural causal models.

321

And so far this is nothing but ordinary Bayesian inference.

322

There's really nothing new here.

323

um But interesting things happen when you start to add these intervention transformations.

324

So you can think of an intervention as a kind of function between models.

325

It takes a structural causal model,

326

and turn that into a different structural causal model, which, as you can see here, is

kind of at a different point in structural causal model space.

327

So the original structural causal model induces a distribution over data.

328

And the intervened structural causal model induces a different distribution over data.

329

And uh you can construct what we call a causal query, which is some function of your

distribution over data and counterfactual data.

330

So this might be like,

331

uh the average difference between outcomes under intervention and under your original

world.

332

So again, the story is similar.

333

If we induce a distribution over structural causal models, that propagates to a

distribution over intervened structural causal models, which then propagate to

334

distributions over factual data and counterfactual data, and then a distribution over the

causal query.

335

um

336

And it turns out that if you've uh set up these interventions in a certain way,

essentially you just need to preserve measurability, um then the whole thing can just be

337

treated as one big probabilistic inference problem.

338

So now rather than having just a joint distribution over models and data, you have a joint

distribution over models, data, intervened models, counterfactual data, and counterfactual

339

queries.

340

that's just a joint distribution.

341

and the machinery of probabilistic modeling and inference tells us how we can manipulate

these joint distributions and get posterior distributions over all the things we care

342

about.

343

so your factual data propagates to the posterior over structural causal models, which then

gives you a push forward distribution onto intervened structural causal models, which then

344

pushes forward into a distribution over counterfactual data.

345

And then you get a sort of posterior distribution over answers to your causal query.

346

Yeah, this is great.

347

Yeah.

348

this is this idea of just like taking causal models and turning them into probabilistic

models um is not unique to um to Cairo or this or my thesis.

349

um But I think in in Cairo, we really codified this.

350

and made it very explicit.

351

um So one way of thinking about what Cairo is doing is it's automating this edge here,

intervening from a structural causal model to a different structural causal model.

352

And it's automating, constructing all these different parallel worlds that construct this

big joint distribution over different worlds.

353

But then once you have that, like I said, it's just probability.

354

Once you get to this space,

355

And then you can use all of Pyro's existing inference tools to approximate inference

however you'd like.

356

Yeah, this is amazing.

357

Thanks a lot for sharing that.

358

Yeah, no problem.

359

Makes me want to try this right now.

360

I need a use case.

361

Spin up a record.

362

Let's go.

363

Yeah.

364

Man, yeah.

365

I'm going to use that very soon.

366

I have some.

367

some ideas of projects I can apply that to.

368

that sounds, yeah, I think it's super interesting.

369

And I do think, you know, it's feeling the need we have right now with the generative AI,

well, in making sure we can harness this power in a more structured way.

370

So it's not gonna be helpful for every problems, but I'm guessing there is a lot of...

371

problems for which is going to be extremely helpful.

372

Yeah.

373

Yeah.

374

And that's great.

375

realized I kind of skipped your actual question.

376

You asked me about Cairo's design and I talked about what Cairo is.

377

Yeah, that's fine.

378

I was gonna I was gonna ask you again that.

379

Okay.

380

And then maybe we can walk through a do a period to

381

Concrete concrete example after that, but yeah first if you can come back to the yeah the

designing of Cairo Yeah I think you answered the pyro part, you know why you based it on

382

pyro, but Mainly the the main philosophy if you want the Zen of Cairo, let's say yeah

Yeah, so it's worth saying the caveat which is that one reason we designed it off of pyro

383

is because

384

Eli Bingham, uh was another core developer of Pyro, arguably the lead developer uh and

architect, was also a core developer of the Pyro probabilistic programming language.

385

So there's a certain practical element of just familiarity.

386

That helps.

387

It helps, uh At the same time, I think there are some interesting things about Pyro's

design that made it uh easy to build off of.

388

um

389

The main goal with Cairo was to make the causal probabilistic programming language uh

modular and extensible.

390

So modular meaning that it could be decomposed into kind of atomic parts that can be

combined at will to solve all sorts of different problems.

391

So that means users can write models in a modular fashion and combine it with many

different questions.

392

They can take

393

many different questions and reduce them to probabilistic inference and then have modular

choices about what probabilistic inference algorithms they use.

394

um So that combination of freely being able to mix and match models, questions, and

algorithms um gives you this common tutorial explosion of choices as a modeler.

395

And they're choices you can enumerate um pretty quickly.

396

Right, moving from an average treatment effect to a conditional average treatment effect

is again, just a few lines of code.

397

Going from a conditional average treatment effect to mediation analysis is another few

lines of uh Modeling non-compliance in your treatment assignment is another single line of

398

code.

399

You just add a distribution to your intervened treatment assignment.

400

And because this is all just code, uh all the kind of composability you would normally get

from software follows in CHIRO programs as well.

401

You're not really...

402

uh

403

constrained to just thinking of causal inference questions ah as a kind of catalog of

different things to choose from.

404

It really is a programming experience, um which we were really intentional about.

405

uh The other thing we were trying to achieve, which I think we have, is to make Cairo

extensible.

406

um So it was pretty clear when first building Cairo that we weren't going to build in all

of the capabilities that we wanted from the get-go.

407

um

408

The literature is too large and complicated.

409

Research continues and progresses the field.

410

So we wanted to design it in a way that as new research was developed, it could be tightly

integrated into Cairo without kind of uprooting the whole system.

411

um So there are two ways that we've seen that happen already, um which we could nerd out

about for a very long time, but maybe we can delay for later.

412

um

413

One is extending Cairo's modeling language to support continuous time dynamical systems.

414

um And we have a paper that's currently in review and will be coming out soon kind of

describing all the math of what's going on there.

415

Yeah, what do you mean by that?

416

It's easy.

417

Yeah, what's the problem right now?

418

And what would that solve?

419

Yeah, so the problem is that um by default,

420

Intervention semantics for probabilistic programs don't tell you how to deal with

continuous time.

421

um And they don't tell you how to deal with models written as differential equations.

422

So that means, does that mean when you have, so for instance, time series, or is it also a

problem if you have continuous um variables?

423

do you mean that your outcome and treatment always have to be binary?

424

Or can they be continuous?

425

Yeah, variables can be continuous in Cairo.

426

That's really no problem.

427

um Defining an intervention on a continuous variable is just as easy as defining an

intervention on a binary variable.

428

Estimating can be harder, but that's kind of a separate question.

429

What I mean is that uh if you have a time series model, like a differential equation, that

um

430

describes the behavior of the system at every point in continuous time, um a key challenge

is that when you're simulating the system, you don't actually visit every point in time.

431

You would approximate this continuous time system with a collection of finite time points.

432

And if you did the naive thing of just applying an intervention to any of those finite

time points, you might miss the time where you want to apply an intervention.

433

um

434

And sometimes you might want to have an intervention where you don't know in advance when

it's going to occur.

435

So for example, if you're modeling a control system that turns on an HVAC controller when

the temperature of some room gets above some threshold, you kind of need to wait until you

436

see what the temperature of the room is before you can decide when to intervene.

437

um And that kind of representation of an intervention just wasn't covered by the existing

438

uh existing literature.

439

Okay, okay.

440

Yeah.

441

Yeah, that sounds hard.

442

That definitely sounds harder.

443

It's harder.

444

But at the same time, one of the really cool things about Cairo is uh if you define what

it means to intervene in such a system, which is work, I mean, it there's a fair amount of

445

math to make sure that that works out correctly.

446

But once you've done that work, you get all the other thing Cairo provides to you for

free.

447

So now all of a sudden, you can ask

448

mediation analysis questions of differential equations models.

449

You can ask attribution questions.

450

You can ask about probability of necessity or probability of sufficiency.

451

um And this works because, like I said, Cairo is modular.

452

We have this abstract notion of an intervention.

453

We define what that means on any given modeling system.

454

And then we have queries that combine these abstract interventions um in a way that's...

455

So the query model agnostic, even though it's implemented concretely on any given model.

456

um So that's very exciting.

457

I happen to like those kind of models, but also I just think it's a really interesting

demonstration of how far we might be able to take causal reasoning into different modeling

458

families that people don't normally think of as causal.

459

sounds super exciting, honestly.

460

Can't wait to see that.

461

Yeah, I'll hold off on the other thing because I think

462

We're going to talk about it later.

463

we've also been able to extend Cairo to support what's called efficient estimation.

464

um So now with more or less the click of a button, Cairo provides efficient estimators for

more or less any probabilistic program in any query you write in Cairo, which is very

465

exciting.

466

Yeah, I mean, we can talk about that now.

467

That sounds interesting.

468

So yeah, maybe define what you mean by.

469

efficient estimators, why that's useful and in which cases, like, why would people use

that concretely?

470

Yeah, okay.

471

So em when solving causal inference problems, you inevitably have to solve uh some

estimation task, right?

472

So if I'm interested in the effect of some treatment on some outcome, and there are

confounders, I need to adjust for all the potential confounders.

473

I'm observing.

474

uh One way of doing that is to build a regression model of the outcome given all the other

things.

475

So essentially, uh fit uh some distribution p of y given this huge vector of covariance

and one individual treatment.

476

um And without even going Bayesian, even just from a frequentist perspective, you can show

that

477

as the number of covariates gets very, large, m even though you're only trying to estimate

a single treatment outcome relationship, um your error rate, like the ability to get

478

closer and closer to the truth, um doesn't decay that fast.

479

Essentially, you have what are called a lot of these nuisance parameters, a lot of

parameters that are necessary to fit the model that don't really matter for the question

480

you're trying to answer.

481

that you'd like to kind of ignore.

482

You can think of it as a kind of like statistical budgeting.

483

I've got a finite amount of data.

484

I want to allocate the statistical juice I get out of that data towards the questions I

care about and not all these other nuisances that don't really matter.

485

em So an efficient estimator is an estimator that behaves as if you were only estimating a

single variable in this regression.

486

single parameter.

487

Okay.

488

Okay.

489

So it gets uh it approaches the truth as fast as if it were just a one D regression

problem with some constants thrown in.

490

But that's the general idea.

491

Okay.

492

Okay.

493

Okay.

494

Yeah.

495

So it's gonna make like, ideally, this is something that users wouldn't even really need

to be conscious about.

496

right?

497

That's something that's probably would do under the hood for them.

498

Yeah, so they it's much faster to have their analysis run.

499

But like, the normal user wouldn't even need to worry about that.

500

Yeah, that's right.

501

So right now, it's quite computationally intensive.

502

So we leave it as a separate module that you can either use or not use.

503

um But yeah, that's that's the general idea is that um systems like Cairo should automate

the hard math of finding these efficient estimators.

504

Yeah.

505

So that you can focus on modeling and asking questions.

506

And you don't need to have a PhD and a lot of expertise in functional analysis, for

example.

507

Yeah.

508

Yeah, that makes sense.

509

That's also what we try to always optimize for in PMC, for instance.

510

And so it makes sense that you guys are doing the same thing.

511

Yeah.

512

Do you have anything to add on that or should we try and go through a um concrete

do-operator example for listeners to make sure the idea clicks?

513

Maybe I'll add a little bit of detail for the really interested listeners.

514

The way that algorithm works is there's a paper led by Raj Agrawal.

515

is a spotlight at NeurIPS last year.

516

um

517

where we show how to estimate what's called an efficient influence function.

518

um And maybe all I'll say is that ah there's been a lot of literature in um the

semi-parametric statistics literature that shows that if you were able to find an

519

efficient influence function, you can get these efficient estimators ah for free.

520

There are a number of general recipes for using this efficient influence function object

to build efficient estimators.

521

um

522

The challenge before our paper was that finding an efficient influence function required a

lot of handcrafted math.

523

And what our paper shows is how to approximate the efficient influence function using only

quantities that an ordinary probabilistic programming system can give you.

524

You need uh derivatives of probability densities.

525

You need to approximate the inverse Fisher information matrix.

526

um But that's something you can do using an AD system.

527

and a probabilistic programming system.

528

um So we show in the paper that using this technique, even though it's an approximation,

you get arbitrarily close to um what the efficient estimators would be.

529

There's a number of experiments.

530

Check out the paper for the cool math.

531

um Yeah.

532

Yeah.

533

And make sure to add the paper in the show notes if that's not done already, because I'm

sure interested listeners will go and check that out.

534

um

535

Cool.

536

Do you want to go through a do-operator example, then?

537

Sure.

538

Yeah, sounds great.

539

Fantastic.

540

Do you want to share your screen again, or do you want to do that, I don't have a visual

explanation.

541

I was hoping we could just talk about it.

542

Yeah, that works.

543

I was just curious how you wanted to do that.

544

Well, um Yeah.

545

OK, so uh maybe this isn't what you were looking for, but I think you can.

546

You can think of a do operator as modeling uh a kind of thought experiment where you force

something to be true or not true or a particular value.

547

So you could imagine a model relating um medication that patients take um and their health

outcomes and some variables describing their behavior.

548

uh

549

And in your original model, em all of these things are connected.

550

The way people behave in the world, their diet, their exercise, may causally influence the

medications they take em and may also causally influence their health outcomes.

551

This is what we would call a confounding variable, as we said before.

552

And if you want to ask the question, does this medication influence cardiovascular

disease, for example,

553

You can model that by uh instantiating a kind of thought experiment where you've forced

some people either to take the medication or not take the medication, regardless of what

554

their ordinary data generating mechanism would be.

555

And that act of forcing someone to do something is modeled in Cairo using this do

operator.

556

So the way you would do that mechanically is you write a probabilistic program describing

the way people,

557

the way you think people choose to uh take medication or not.

558

And again, this can be kind of a statistical model or machine learning model with many

free parameters you learn from data.

559

That's all fine.

560

And then in asking your question, what is the effect of medication on cardiovascular

disease, you would instantiate two counterfactual worlds and intervene to set one world

561

where the

562

Patients are forced not to take the disease.

563

One world where the patients are forced to take the disease and then compute their

difference in outcomes.

564

To see this concretely in code, maybe I'll share after some specific pointers to Cairo's

documentation where you can kind of walk through similar examples where the actual syntax

565

for the due operator is being used.

566

Yeah, for sure.

567

I mean, I've looked into those before the show also for people who've listened to a

568

Robert Ness episode here.

569

Well, I recommend to go through it.

570

And if you have his book also, he goes into a lot of details about the two operator.

571

Yes, it's good that you mentioned Robert.

572

it's a lot of the ideas I'm talking about, I like to try to be careful with credit

assignment.

573

So I'm not claiming that I invented any of the kind of general ideas of sort of causal

probabilistic programming stuff, I think.

574

um Robert, me, uh Alex Lev, Eli Bingham, Zena Tavares, and Jeremy Zucker um all wrote this

kind of opinion article maybe four or five years ago together, kind of outlining this

575

general kind of approach to thinking about causality and probabilistic programming.

576

um So just quickly wanted to give credit where credit is due, and I know Robert pretty

well, and we've chatted about a lot of these ideas for a long time.

577

Yeah, yeah, yeah.

578

And I've added so he was on episode 137 of the show and it's in the show notes already

folks.

579

So definitely recommend giving that a listen.

580

That was his second appearance actually on the show.

581

um Maybe a more general question for you about Cairo Sam that I have is what would you say

are the best use cases for it and when would you recommend listeners to give it a go?

582

So I think it's

583

quite a general purpose tool.

584

um If you're um interested in purely statistical forward causal inference workflows, you

can uh represent a lot of common assumptions as probabilistic programs in Cairo.

585

And we have a number of tutorials that show how to do that.

586

m For example, we have a synthetic difference in differences tutorial for uh causal

inference in panel data.

587

We've got uh some models about um proxy variables where you have a latent confounder and

some measured proxy of that confounder.

588

um So a lot of the kind of core kind of statistical econometric social science um models

and assumptions can be pretty easily represented in Cairo.

589

um

590

What I'm most excited about are these kind of hybrid models where part of your model is

like physical equations, like I said before, like mechanistic models.

591

And part of the model is kind of filled in with machine learning where you may assume a

causal structure, but you don't know much about the particular functions relating

592

variables.

593

And you just kind of hot swap in a machine learning component in your probabilistic

program um to represent that.

594

kind of broad uncertainty.

595

So I think either of those two camps would get a lot of value out of Cairo.

596

um It's also worth mentioning that Cairo provides some interesting capabilities even if

you don't have data and you just want to probe your model.

597

um So asking these kind mediation analysis questions or attribution questions, even just

from a probabilistic program you write from hand, can be really insightful.

598

It can tell you a lot about what the implicit assumptions you're making about your model

are.

599

it's nice that it happens to work well with conditioning on data and then doing posterior

inference over parameters.

600

Yeah, yeah, exactly.

601

mean, it's, it's also something that you get from, from Bayesian modeling, right, where

you have to, explicit your priors and your structure of the model, then if you add the

602

causal structure on top of that, it also makes your real modeling assumption in

assumptions even clearer and, and, and you get to know whether you can actually answer the

603

where is your actual curse about or if you need uh to refine your graph, your causal

graph, or if you need to um refine your data, if you can.

604

Yeah, it's actually, it's a great point.

605

So I think another audience who might get a lot of value out of looking at Cairo are data

scientists who are familiar with Bayesian modeling, but maybe less familiar with causal

606

inference.

607

Cause I happen to think that this view of causal inference as

608

writing probabilistic programs and then transforming them um is fairly intuitive for

people who already used to writing probabilistic programs.

609

And to me, it makes the assumptions seem much more clear.

610

uh Often the causal inference literature can be very verbose and complicated.

611

And I've always found it much more clear to look at a program and to kind of try to tease

apart what assumptions are being made in that program.

612

Yeah, completely agree.

613

I'm the same.

614

I'm also a very...

615

practical and visual learner.

616

So looking at the code and the programs and playing with it is actually a much better way

for me to learn.

617

I also get lost in the terminology.

618

actually seeing what the different objects represent is much more efficient for me.

619

Yeah, it's also unfortunate that there's so much terminology because the ideas are so

universal.

620

these different camps um actually are quite intimately connected.

621

I you can translate between them.

622

If you know the language, you can translate between them.

623

But from someone who's just getting into causal inference and looking at this kind of

literature, it's very confusing, unfortunately.

624

Yeah, for sure.

625

That's why I also have these podcasts in trying to be a

626

trying to be a bit helping people about, it's like out of the terminology, what are we

talking about here?

627

And how can we actually use that on, you know, on real models and use cases?

628

Yeah, I think it's great that you're talking to people and kind of cutting through the

jargon and the papers and the software.

629

I find just, like I said, talking or just listening to people talk, very clarifying.

630

Yeah.

631

Yeah, exactly.

632

And that's also why I keep doing this show, that like personally I learn a lot by talking

to people like you.

633

uh And that also makes the papers more uh incarnated, whereas creating a paper can be very

cold.

634

Yeah, it's sort of unfortunate that in an academic setting you write papers almost

defensively to prevent other reviewers from...

635

penalizing you too hard.

636

But that trend, I think, pushes papers to be less accessible for people who would actually

get value out of them.

637

ah So now that I'm out of my PhD a few years now, I'm sort of inclined to just write blog

posts.

638

That seems a bit nicer than still writing some papers.

639

But yeah, it's not as obviously the best communication medium to me anymore.

640

Yeah, I completely agree with you in

641

Yeah, I'm always, I always say that I read papers because I have to, but not because I

want to.

642

It's like, reading paper is never fun, honestly, for me.

643

Reading blog posts, reading package documentations as you have on Cairo, reading books,

know, like Robert's books or, you know, this is much, much more entertaining to me.

644

Also, because here, I didn't hear what you're trying to

645

uh optimize is not whether you're going to pass the threshold for peer reviewed

publication, but it's mainly just, well, I want people to enjoy what they are going to

646

read and remember what they're going to read and be interested in it.

647

And so that's a much better function to optimize than the first one.

648

Yeah.

649

And ultimately, if I want, you know, these tools to be useful to people, you have to have

people use them.

650

And I have a pleasure to use and understand, as you know.

651

That's a good point.

652

I will say, when I'm learning a new field or a new subfield, I actually like to read PhD

dissertations.

653

find that when you write a thesis, you have to write all this background and scaffolding,

if you do a good job.

654

And that provides a lot of context, which is hard to find otherwise.

655

Yeah.

656

Yeah, I see what you mean.

657

Yes, I mean, a thesis is almost like a book, right?

658

I think it's basically the same.

659

Right.

660

Could be a book most of the time.

661

So, right.

662

That's true.

663

Yeah, that helps.

664

em In well, actually, I'm curious, you know, talking about Cairo, what do you have in mind

on the roadmap for for the coming month?

665

Is there anything you are especially looking forward to adding to making better?

666

Do you need any help on that?

667

The links are in the show notes.

668

So people interested in making some PRs for that, they can look into that.

669

Yeah, what's the state of Cairo?

670

Yeah, so me personally, I'm doing a little bit less core development work now that I've

picked up more of this consulting work.

671

em But there are some things I'm excited about.

672

em So one is extending some of the dynamical systems work I talked about before.

673

um The landscape of dynamical systems models is very broad.

674

um So far we've gotten support for ordinary differential equations, but you might also

want to model stochastic differential equations, differential algebraic equations, VDE's,

675

those sorts of things.

676

um And that's going to take a lot of development work.

677

um As far as how people can get involved, know, Cairo, we try to maintain a um

678

the issues and pull requests as best you can.

679

And if you browse the issues and see any tagged help wanted, just jump right in or

discussion, anything like that.

680

em It's totally open source.

681

We welcome uh pull requests from the community.

682

em Just ask that you write tests and engage in conversation.

683

Yeah.

684

Well, that sounds great.

685

So folks, if you want to get in there, ah please do.

686

And I'm sure it will be received very well.

687

thing that's always useful for a system like Cairo is more examples.

688

So we have a number of examples and tutorials, but we're really only scratching the

surface of the kinds of things you can do with Cairo.

689

um So if you think of interesting causal machine learning methods or models you want to

implement and share with the world, that's a really good avenue to contribute to open

690

source software.

691

And I think it teaches a lot.

692

Yeah, yeah, it's also about how I how I learn about a new method, It's diving into an

example, trying to find your use case, and then just, you know, trying it and see what

693

doesn't work, what I didn't understand yet.

694

And that really makes me understand way better than than just passively consuming content.

695

um On the on the roadmap, though.

696

um Yeah, do you know, do you know if

697

if the other devs have something in particular they want to develop in the coming month?

698

is it pretty much open right now?

699

think Cairo is pretty open.

700

that some context um Cairo is uh built by a number of researchers at a nonprofit research

institute that I used to be a research scientist at named basis, constantly hiring great

701

people doing very interesting work.

702

So um

703

Cairo was developed uh as a part of Basis.

704

Again, like I said, it's fully open source.

705

And there are a number of other open source technologies that people at Basis are working

on.

706

um I think the plan right now, I'd have to check in with some of the other um Cairo

developers, but I think the plan right now is to kind of rebuild kind of the foundation of

707

probabilistic programming systems from the ground up.

708

So for now, don't take this with a grain of salt.

709

But my understanding is that Cairo is fairly stable um and that there are more kind of

larger scale visions on the research pipeline there.

710

Yeah.

711

I see.

712

So actually, let's talk a bit about your service AI uh company.

713

Because now that's your main gig, as you were saying.

714

That's right.

715

Yeah, okay.

716

I'm curious.

717

Of course, I'm very curious about it because this is what I used to do.

718

This is uh I've been in the exact same place as you are right now with the last but in

719

So yeah, like, how is it going?

720

What has been your uh your biggest surprises?

721

uh Currently, it's been on the three months you've told me but I'm also wondering, you

know, what are the toughest real world scientific question?

722

uh a client has thrown at you so far, and how did causal probabilistic programming help

with it?

723

Yeah, yeah.

724

So um I can't say that much about what I'm working on.

725

But from a high level, I have a few clients now who are in the kind of science and

engineering or health space.

726

um So one is working on uh

727

materials for sustainable energy products, and another is working on preemptive health.

728

And both of these settings care about m probability and causality um and machine learning

and learning from data.

729

um So I've been able to kind of insert myself into their teams and support them in

building models, understanding ah cause and effect relationships.

730

Um, and it's a lot, a lot of the work is translation.

731

Um, I think because causal probabilistic programming or causal inference is still a fairly

niche topic.

732

Um, I'd say the largest challenge for me is not just jumping right out the door with a lot

of jargon, um, and trying to meet people where they're at and do this kind kind of

733

translation into causal and probabilistic assumptions in my own head.

734

so it's, fairly common that I'll sit down and

735

and meet with engineers and kind of um in trying to probe causal questions for them, ask

it in several different ways.

736

um Often the questions that I thought they wanted to ask were not exactly the questions

they were asking.

737

um And actually, systems like Cairo in those settings make it uh really, really easy to

iterate on those workflows.

738

So I can sit down with an engineer and say, okay, well,

739

You have this kind of vague causal question you're interested about this domain.

740

ah Here's one proposed way of codifying that ah concretely, looking at the implications

together in the span of a few minutes, and then having them say, well, no, that's not

741

quite what I wanted.

742

Could we think about this other kind of causal question?

743

And then with just a few lines of code, changing the question and getting answers right

there in a live environment, that's turned out to be really powerful.

744

as kind of a modeling workflow.

745

um I think the biggest challenge, this is not specific to clients I have now, but the

biggest challenge I see in getting broader adoption out into the world is that for some

746

reason, it seems like people forget that when you have high dimensional data, correlation

still does not equal causation.

747

um I don't know why that is.

748

I think that there's just this really strong tendency to anthropomorphize

749

machine learning models to doing what they're not doing, especially given all the kind of

hype around agentic systems, LLMs, reasoning models, these kinds of things.

750

um It's very tempting for everyone to kind of say, well, let's just throw AI at it without

really knowing what that is or knowing what the implications are.

751

And in trying to be rigorous and precise, that's kind of an uphill battle.

752

You can find yourself battling.

753

That said, think my current clients, I'm very lucky to have collaborators who are uh

careful, thoughtful, measured, em maybe don't have as much expertise in the specific

754

things that I'm offering, but in general are kind of critical enough of hype cycles that

em they're not just buying all into LLMs as a kind of one-stop shop for all your AI needs.

755

Yeah, yeah, that makes a ton of sense.

756

I definitely resonate with that.

757

um And of course, I have uh delivery that's coming in.

758

So I'll come back in like five minutes stops.

759

And then we'll but we'll we'll get back to that.

760

Basically, I'll pick up on that and talk about what we're talking before uh recording, you

know, uh we're with like the adoption of causal inference and stuff like that.

761

And yeah, sounds great.

762

Yeah, awesome.

763

I'll be back in just a few minutes.

764

you soon.

765

That's good.

766

Yeah, actually, I actually have a similar experience and something I was always very

curious about this net, you often have to justify that you want to take the causal path.

767

And I'll always, you know, surprised by that because it was like, it feels like the burden

of proof should be reversed.

768

You know, you should

769

want, especially if you want scientific answers, you want reproducible results.

770

So I'm always thinking, well, why would you not want causal results should be the default.

771

uh But yeah, somehow, it's not really I have different uh speculations on why that is.

772

But I'm curious what your experience and thoughts are on on that.

773

Yeah, do you want my to have my hot take?

774

Or do you want my measured?

775

Diplomatic response.

776

Both, think both are going to be interesting.

777

I feel comfortable.

778

Let's go with the hot take.

779

So I think one of the major reasons why people are hesitant to go for causal inference is

because there's an academic tradition of um being almost curmudgeonly when people make

780

causal claims.

781

It's just

782

Because causal inference is hard, it's very easy to criticize.

783

I you need to make a number of assumptions, and um the conclusions often depend strongly

on the assumptions that you make, which is, good to know.

784

I mean, it's worth being critical.

785

um But I think, unfortunately, what this means is that people often are so afraid of being

criticized for overstepping in their causal claims that they don't even make an attempt.

786

the first place, and instead use kind of hosel-ish language with associational methods,

but never actually go out there and say anything about causality because they're kind of

787

afraid.

788

uh so let me give you an example.

789

several years ago i worked on a problem called genome-wide association studies, which is

about trying to understand the association between ah

790

single nucleotide polymorphisms, like the positions in your gene sequence um in your DNA,

um with various health outcomes.

791

So if you have this single nucleotide polymorphism, you're more likely to get, I don't

know, cardiovascular disease before you're 60 years old, something like that.

792

And if you look at a lot of the methods in...

793

genome-wide association studies.

794

They look like causal inference methods.

795

So you adjust for potential latent confounders.

796

You even do this kind um of latent PCA um correction step that looks like some causal

inference methods that have come out in the last several years on, it's called multi-cause

797

confounding.

798

um

799

But the methods are called association studies.

800

Again, I think because it's very risky to say that a particular single nucleotide

polymorphism is a cause for a particular phenotype.

801

And it's good to be hesitant, I think, again.

802

The problem with that kind cautious worldview, I think, is that you have to make

decisions.

803

And if you have to make decisions one way or another,

804

implicitly you need to reason about causality.

805

So if you're snoozing to bury your head in the sand and say, I don't have strong enough

assumptions, I'm unwilling to even make any sort of a causal claim, what you're implicitly

806

choosing is to just do causal modeling poorly.

807

um So I think it is better to be honest about what you're trying to achieve.

808

And if you really care about causality, try to model the problem as a causal problem.

809

and to the best of your ability, represent your uncertainty and your assumptions

explicitly and be cautious in how you interpret them, but still go forward somehow.

810

I like to say often, inaction is action.

811

um Time is passing by, right?

812

And if you have a choice of making a policy or not making a policy and you refuse to make

causal claims, you're choosing not to make a policy.

813

Yeah, definitely.

814

Yeah, the fact...

815

The fact of not doing anything is already is already doing something.

816

yeah, you're choosing to stay with the current solution, actually.

817

yeah, yeah.

818

Yeah.

819

And I think this is definitely one of the of the big reasons uh I also see kind of the

same em phenomenon at hand with uh patient models, generally, would say, because they are

820

much better.

821

and being poked at, right?

822

You know when you have divergences, when the sampling's not going well, you can check the

priors, you can check how the posterior is contracting around, how the prior is

823

contracting around the posterior, you can test again the different test values and so on.

824

So it's much easier to poke at a Bayesian model than it is to poke at a classic

Frequentius model.

825

And so that means

826

your assumptions also much more out in the open.

827

And so you have many more things to criticize much transparently.

828

so, yeah, I can definitely see that being weirdly an impediment to putting in production

better models that are more open, but they are easier to criticize.

829

So then it's easier to just delay them.

830

Yeah.

831

Yeah.

832

It's, mean, there are some settings where

833

you can get away with making fewer assumptions.

834

And that's good.

835

But yeah, as you're saying, sometimes you need to.

836

Yeah.

837

And I mean, in when you do causal modeling, you need to like even from a mathematical

perspective, like the the the latter of of causal inference, you know, the three levels

838

that Judy appeals

839

uh demonstrated or not, you know, just a way of thinking about things and just putting

things in buckets.

840

It's actually a mathematical derivation of what you can do with the data model and

assumptions at hand.

841

And if you're not willing to make level three assumptions, so counterfactual assumptions,

then you will never be able to make counterfactual claims.

842

Yeah, that's right.

843

Yeah.

844

It's not like we're doing

845

We're saying, yeah, that's a cool thing.

846

can just divine things into categories.

847

It's actually kind of a, it's a theory, you know, so.

848

Yeah.

849

Yeah.

850

Yeah.

851

To make a choice.

852

So that's, if you don't mind me digressing a little bit, um, there is one caveat about the

kind of Bayesian approach to causal inference that I'm proposing here that I want people

853

to be aware of, is that.

854

Yeah, go ahead.

855

Nerdy digressions is it's the subtitle of this podcast.

856

Great.

857

Okay, good.

858

Good.

859

I'm in comfortable territory then.

860

zooming out a little bit, um this Bayesian approach to causal inference and Cairo's kind

of mathematical underpinnings don't escape this fundamental need for assumptions that

861

you've described.

862

Right?

863

There's no there's no free lunch in Cairo.

864

It doesn't magically mean that you can derive causal conclusions from nothing.

865

um

866

Cairo really should be thought of as a way of writing your assumptions and then seeing

their conclusions.

867

um So the way identifiability shows up in this Bayesian framing is in the posterior

itself.

868

The idea is that um if a query is not identifiable from the data, then the posterior

distribution should never collapse to a single point or the truth, regardless of how much

869

data you get.

870

um

871

that's i think a well-defined kind of mathematical framing of what identifiability is in a

Bayesian setting.

872

the tricky thing is that um if you want to know whether your query is not identifiable or

not, um just running approximate inference turns out to be a pretty bad method.

873

um these kind of non-identified posteriors can get um arbitrarily thin, and you can think

of it as like

874

manifold in a higher dimensional space and expecting any approximate inference algorithm

to like slowly traverse that manifold is asking too much.

875

So I think what will often happen is that if you use an approximate inference algorithm,

it'll find a mode of that kind of infinitely thin posterior and then get stuck there and

876

imply that you have a lot more certainty in your answer than you actually do.

877

So it is still worth doing the kind of explicit identifiability analysis beforehand.

878

just to make sure that those kind of pathologies aren't misleading you in your causal

conclusions.

879

Now, in theory, if the probabilistic inference methods continue to get better and are able

to traverse these very challenging posterior landscapes, this will be a non-issue.

880

um But for now, ah it is an issue.

881

I wrote some work in my PhD about how to address this.

882

think it's kind of an incomplete.

883

The paper I wrote is kind of incomplete.

884

But people can read it if they're interested in it I'll share it in the show notes em for

one way of thinking about identifiability, how to find whether causal questions are

885

identifiable in this kind of Bayesian setting.

886

yeah, definitely.

887

Do share that.

888

It will be very interesting in that too.

889

I know the do-while library has a very good user interface to help people see if their

causal queries are identified.

890

But this is not the innovation framework.

891

So it's going to be, it's going to be very interesting to see.

892

So I haven't looked at do I in a while.

893

um I know a few of those guys quite well.

894

And I know them okay.

895

And I, you know, think highly of their work.

896

um My memory the last time I looked is that it's still very much in the kind of

nonparametric graphical models setting.

897

um So some of the assumptions that you can represent in a system like Cairo,

898

that end up being very practical are very difficult to reason about there.

899

Things like the regression discontinuity design I described earlier.

900

uh OK, I need to play this out here because I've already taken a lot of your time.

901

ah So I had, of course, I had a question about your Gaussian process paper that you

authored a few years ago.

902

So maybe we'll go with that one because I'm very curious.

903

ah

904

I love GPS, I use them all the time.

905

So when I saw a about Gaussian process and causal inference with structure and latent

confounders, I needed to ask you about that.

906

yeah.

907

Sure.

908

Can you tell us what this is about and um how practical this is for people if they want to

use that in their own models?

909

Yeah, sure.

910

that paper is...

911

um

912

is several years old at this point.

913

think it was 2020 when I wrote that.

914

I forget exactly.

915

Yeah, I think the release date is 2021.

916

knowing academia, must have be you must have written in in 2020.

917

Yeah.

918

Yeah, which was, I guess, right.

919

That was just when the COVID was starting.

920

Yeah, which feels like an infinite amount of time ago now.

921

So that that paper was about combining two different ideas.

922

One is using

923

Bayesian nonparametric models, Gaussian processes to do causal inference, and encoding a

particular kind of assumption that we call structured latent confounding in the paper.

924

And the idea behind structured latent confounding is that there are many, settings where

you have a kind of hierarchical structure between ah objects and units in your data.

925

So for example, if I have data for different schools,

926

different students that each belong to that school, there's a many-to-one relationship

between uh schools and students, and there may be many different schools for which I

927

gather data on students.

928

em so that's super super useful in causal inference because you can make assumptions of

the form em any confounding variables, any latent confounding variables, if you can assume

929

that they're at the level of the school and not at the level of the student.

930

So for example, a school is in a particular geographic region.

931

So all the students in that school are subject to the same geographic region, the same

influence of that geographic region.

932

em So if you're willing to make that assumption, em you uh can still estimate causal

effects even though you have this latent confounder because of the structure you've

933

assumed.

934

em

935

One way of thinking about it is like, if I were to bundle students belonging to the same

school and look at the difference in their outcomes under different treatment conditions,

936

because they're all subject to the same school, that wouldn't be biased.

937

So then if I want to aggregate a bunch of different schools together into a kind of

holistic causal estimate, that intuition of being able to like isolate the effect of the

938

confounding variable at the school level still holds as you get to multiple schools.

939

uh

940

So the paper is really somewhat mechanical.

941

It's just showing how to combine these two ideas.

942

So you have a Gaussian process regression for the outcome model and a Gaussian process

latent variable model for modeling this latent confounder.

943

And what we found empirically is that it seemed to do pretty well for effect estimation in

these kind of hierarchical settings.

944

Now, that specific model, I think there are a lot of things that could be improved.

945

would take a long time to talk about all of them.

946

but i think the core idea of taking bayesian non-parametric models and combining them with

these kind of richly structured assumptions is a very powerful one.

947

um and that general idea i've used in, um for example, time series modeling or other kind

of hierarchical or relational models, um maybe not specifically with gaussian processes,

948

maybe with

949

um I don't know, some normalizing flow neural network or something else, and it seems to

work very well.

950

um So I think that the essence of that paper, I think, is generally useful, even if the

specific model is not as compelling.

951

um There's also a little, like if you really want to nerd out in the supplementary

materials, there's some technical detail about how to reason about uh what are called

952

individual treatment effects with Gaussian processes.

953

um

954

The subtlety there is that uh when you're sampling from a GP, you don't have access to the

structural function directly.

955

You kind of only have access to the marginal distribution of data integrating out the

structural functions.

956

um So you can't do the kind of default thing of like passing in an argument and holding

the noise fixed.

957

So there are some tricks in the paper for how to handle that.

958

Hmm.

959

Okay.

960

He's cool.

961

Yeah.

962

How in

963

How did you guys implement that at the time?

964

Were you using Pyro again?

965

No.

966

So um at the time I was a visiting student at um Fakash Mansinkas lab at MIT.

967

uh So uh Fakash's group um produced a probabilistic programming system called GEN, which

is written in Julia.

968

And that was led by Marco Cusumano-Tanner.

969

He's also a really sharp guy, great friend.

970

um

971

So at the time I was doing all my research work in that probabilistic programming

language.

972

has a lot of the same kind of ideas as Pyro.

973

mean, a lot of these probabilistic programming systems look very similar with um some

different emphasis on their designs.

974

um So there, uh it took me a long time to write the models because I didn't have a system

like Kyro at the time.

975

I was manually building out these counterfactual worlds.

976

in just a single program by hand.

977

Yeah, that's hard.

978

Which is hard.

979

Yeah.

980

Yeah.

981

Next time.

982

um OK.

983

Yeah, this is super cool.

984

as usual, the paper is in the show notes, folks, if you're curious.

985

um Sam, before asking you the last two questions, I'm also curious, in general, where do

you see the field you're in?

986

like everything we've talked about right now, basically intersection of probabilistic

programming and causal inference.

987

Where do you see that field going uh in the next few months?

988

And also if you have any advice for people interested in joining this field.

989

Yeah.

990

Yeah.

991

So I mean, it would be a little sad if I said the thing I'm most excited about is not the

thing I'm going to be working on.

992

So with that caveat in mind, uh

993

I'm very excited about this kind of engineering and science focused probabilistic

programming workflow.

994

The kind of models I'm really enthusiastic about are the models that combine kind of

physical laws with statistics or machine learning forward models.

995

And there are a number of different uh ways to combine these two different modeling

paradigms.

996

um I think ah I'm pretty optimistic

997

that these kind of probabilistic programming tools will lead to actual real discoveries,

like actually make science uh faster, more generalizable, make it easier for people to

998

communicate with each other.

999

um I think we should have a bold vision of where we want to kind of bring scientific

computing.

01:29:46,857 --> 01:29:52,961

And I see these tools as uh a really fruitful path to go to a new era of scientific

computing.

01:29:52,961 --> 01:29:54,662

um

01:29:54,734 --> 01:30:10,265

As far as how to get involved, um my recommendation for anyone at a kind high level is to

touch software, get into the implementation, submit pull requests, even just submitting

01:30:10,265 --> 01:30:12,407

issues, writing up examples.

01:30:12,407 --> 01:30:15,689

eh I think it's really, really instructive to write code.

01:30:15,989 --> 01:30:19,631

And it's also a great way to get a built-in community.

01:30:20,052 --> 01:30:23,094

People are much more likely to listen to you and engage with you.

01:30:23,350 --> 01:30:27,333

if you have a conversation attached to a pull request that contributes to their software.

01:30:27,333 --> 01:30:42,275

um I think from an academic perspective, um I am seeing more and more academic communities

being open to this idea, both in science and engineering, causal inference, and machine

01:30:42,275 --> 01:30:42,646

learning.

01:30:42,646 --> 01:30:45,828

um I think people are excited.

01:30:45,828 --> 01:30:50,312

um So it's a good time to write papers about these ideas.

01:30:50,312 --> 01:30:52,846

um In fact,

01:30:52,846 --> 01:30:56,667

One way of thinking about Cairo is it's kind of a paper factory.

01:30:56,667 --> 01:31:04,469

Write a model in Cairo, spend a month doing it, write a paper, add to your h-index if

that's the game you're in.

01:31:04,469 --> 01:31:09,931

um It's a little tongue in cheek, but I'm also sort of serious.

01:31:11,912 --> 01:31:13,332

That makes sense.

01:31:13,332 --> 01:31:14,259

Yeah, and I agree with that.

01:31:14,259 --> 01:31:20,718

That's also a way for you to, if you're starting out, to get really good mentors um who

are...

01:31:20,718 --> 01:31:30,024

are going to have your best interest at mind because, ah well, you are also contributing

to something they really care about.

01:31:30,024 --> 01:31:31,285

It's a win-win.

01:31:31,766 --> 01:31:32,546

Yeah.

01:31:32,546 --> 01:31:32,896

Yeah.

01:31:32,896 --> 01:31:38,630

And specifically, if people are interested in the specific work that I've done, feel free

to email me.

01:31:38,630 --> 01:31:46,075

um I like to make time to just talk to people about their research interests, even if I

get nothing out of it.

01:31:46,235 --> 01:31:49,297

I might say no, but it doesn't hurt to shoot an email.

01:31:49,297 --> 01:31:49,658

Yeah.

01:31:49,658 --> 01:31:50,402

Yeah.

01:31:50,402 --> 01:32:00,910

careful though because you know millions of listeners so I've heard former guests who

can't leave their house now because people are just outside all the time asking for

01:32:01,251 --> 01:32:15,973

selfies and autographs I have a very comfortable couch so that's okay awesome Sam, well

that was really great as you can see from the document I shared with you I still had a lot

01:32:15,973 --> 01:32:19,616

of questions but I need to be respectful of all your time so

01:32:20,058 --> 01:32:21,679

Let's call it a show.

01:32:21,679 --> 01:32:26,960

And of course, let's ask you the last two questions I ask everybody at the end of the

show.

01:32:27,020 --> 01:32:33,462

first one is, if you had unlimited time and resources, which problem would you try to

solve?

01:32:34,182 --> 01:32:36,423

Yeah, I think that's fairly easy for me.

01:32:36,423 --> 01:32:41,244

um I want to solve our environmental problems.

01:32:41,344 --> 01:32:48,626

I'm motivated by the kind of technological and policy questions um behind.

01:32:49,112 --> 01:32:52,185

climate change, but also beyond climate change.

01:32:52,185 --> 01:33:02,343

I think things like just general pollution or waste disposal or energy scarcity are really

important problems.

01:33:02,343 --> 01:33:06,196

And I think it's going to take technology and policy.

01:33:06,196 --> 01:33:16,365

um And I'm hopeful that computational tools like those that I've worked on will help make

that happen.

01:33:16,365 --> 01:33:18,566

um

01:33:18,582 --> 01:33:23,824

In a certain sense, I see one of the core problems as getting people to collaborate.

01:33:23,824 --> 01:33:29,906

um I think that's a really interesting kind of computational problem.

01:33:30,447 --> 01:33:35,269

And I'm hopeful that probabilistic programming technology could help there.

01:33:35,269 --> 01:33:36,789

It's not exactly clear what that looks like.

01:33:36,789 --> 01:33:40,351

But if I was starting a PhD right now, that's what I would work on.

01:33:40,351 --> 01:33:43,972

um Yeah.

01:33:44,493 --> 01:33:44,973

Yeah.

01:33:44,973 --> 01:33:46,373

Love that.

01:33:46,373 --> 01:33:48,360

And second question.

01:33:48,360 --> 01:33:55,332

If you could have dinner with any great scientific mind, dead, alive or fictional, who

would be?

01:33:56,372 --> 01:34:09,406

I'd have to say Isaac Newton, which may be kind of a stereotyped answer, but I think

there's something about his discoveries that seemed very transformational, like a paradigm

01:34:09,406 --> 01:34:09,796

shift.

01:34:09,796 --> 01:34:17,078

um And I'm very curious about what makes, what leads to kind of

01:34:17,354 --> 01:34:21,836

non incremental progress in scientific thinking.

01:34:21,836 --> 01:34:24,798

think sometimes, you know, we need to take big steps.

01:34:24,798 --> 01:34:30,961

And he was one of the most obvious big step scientific thinkers that I know of.

01:34:32,522 --> 01:34:35,444

that's, yeah, to say the least, for sure.

01:34:35,444 --> 01:34:36,004

Yeah.

01:34:36,004 --> 01:34:37,529

Although I hear he was a weird guy.

01:34:37,529 --> 01:34:40,306

So maybe he wouldn't be very pleasant to get dinner with.

01:34:40,647 --> 01:34:42,598

Yeah, I don't know about that.

01:34:42,598 --> 01:34:44,058

But I'll be curious when that happens.

01:34:44,058 --> 01:34:45,449

You let me know, please.

01:34:45,449 --> 01:34:47,310

I'll be happy to join the dinner.

01:34:47,758 --> 01:34:49,718

Yeah, you're invited.

01:34:51,298 --> 01:34:52,358

Awesome, Sam.

01:34:52,838 --> 01:34:57,458

Well, that was really fantastic to have you on the show.

01:34:57,818 --> 01:35:04,298

Please come back anytime you have something new in the world of probabilistic causal

inference.

01:35:04,958 --> 01:35:09,218

The show notes are going to be full for this one again, folks.

01:35:09,458 --> 01:35:14,318

So do give it a look if you want to dig deeper.

01:35:14,578 --> 01:35:15,234

And Sam.

01:35:15,234 --> 01:35:18,637

Thanks again for taking the time and being on this show.

01:35:19,219 --> 01:35:22,762

Yeah, thank you very much for having me and doing what you do.

01:35:26,210 --> 01:35:29,912

This has been another episode of Learning Bayesian Statistics.

01:35:29,912 --> 01:35:40,398

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01:35:40,398 --> 01:35:44,480

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01:36:10,488 --> 01:36:12,800

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01:36:12,800 --> 01:36:22,877

Change your predictions after taking information and if you're picking up less than the

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01:36:22,877 --> 01:36:25,068

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01:36:32,349 --> 01:36:35,890

Let's get them on a solid foundation