Abhinav Kumar

Regardless of whether you plan to use them in applications, everyone should learn about Gaussian processes, and Bayesian methods. They provide a foundation for reasoning about model construction and all sorts of deep learning behaviour that would otherwise appear mysterious.

YouTube video by Causal Foundations E5: What Confounding Really Is

After a bit of a summer pause, I'm back to making episodes. In this episode, I explain the notion of confounding, and clarify why confounders should not be thought of as alternate explanations of an observed effect.

youtu.be/kAgS7cltBhM

Randomized trials (RCTs) help evaluate if deploying AI/ML systems actually improves outcomes (e.g., survival rates in a healthcare context).

But AI/ML systems can change: Do we need a new RCT every time we update the model? Not necessarily, as we show in our UAI paper! arxiv.org/abs/2502.09467

YouTube video by LoG Meetup NYC It's Time to Say Goodbye to Hard (equivariance) Constraints - Andrew Gordon Wilson

I had a great time presenting "It's Time to Say Goodbye to Hard Constraints" at the Flatiron Institute. In this talk, I describe a philosophy for model construction in machine learning. Video now online! www.youtube.com/watch?v=LxuN...

Armin Keki\'c, Jan Schneider, Dieter B\"uchler, Bernhard Sch\"olkopf, Michel Besserve
Learning Nonlinear Causal Reductions to Explain Reinforcement Learning Policies
https://arxiv.org/abs/2507.14901

Hirahara, Illango, and Loff posted on the arXiv a lovely result, showing that determining the communication complexity of a function f is NP-hard. A fundamental question first asked by Yao in '79. The proof is very clean and elegant. A fun read for the weekend!

arxiv.org/pdf/2507.104...

📢ICML alert: In the afternoon poster session, I'll present our paper: "Contextures: Representations from Contexts".

Our central argument: "Representations are learned from the association between input 𝑋 and context variable 𝐴"

📍East: E-1708, July 15, 4.30-7pm

📜 openreview.net/pdf?id=4GZwFPz…

YouTube video by Daily Stoic 7 Simple Daily Habits That Will Change Your Life (Stoic-Inspired)

Here's 7 habits to start this week! youtu.be/cqjf4DJyAaA?...

Learning Actionable Counterfactual Explanations in Large State Spaces

Keziah Naggita, Matthew Walter, Avrim Blum

Action editor: Taylor Killian

https://openreview.net/forum?id=tXnVRpRlR8

#actions #explanations #features

And here are my posters:

Poster 1 - Falsification of Unconfoundedness by Testing Independence of Causal Mechanisms.
Thursday 11:00, E-2212

Poster 2 - Robust estimation of heterogeneous treatment effects in randomized trials leveraging external data.
Friday, Scaling Up Interventions Model workshop.

Zhiyi Dong, Zixuan Liu, Yongyi Mao
On the Hardness of Unsupervised Domain Adaptation: Optimal Learners and Information-Theoretic Perspective
https://arxiv.org/abs/2507.06552

YouTube video by Institut des Hautes Etudes Scientifiques (IHES) Satya N. Majumdar - 1/3 Nonequilibrium Point Processes with Long-range Correlations (...)

I've just finished watching this - youtu.be/M802ElI4u4k?... - trilogy of lectures. All very interesting stuff (and exceptional blackboard work!) - well worth a look (as are a few of the other videos from this same Summer School).

Erik Jahn, Frederick Eberhardt, Leonard J. Schulman
Lower Bounds on the Size of Markov Equivalence Classes
https://arxiv.org/abs/2506.20933

Towards characterizing the value of edge embeddings in Graph Neural Networks Graph neural networks (GNNs) are the dominant approach to solving machine learning problems defined over graphs. Despite much theoretical and empirical work in recent years, our understanding of finer...

In recent work arxiv.org/abs/2410.09867 with D. Rohatgi, @tm157.bsky.social, @zacharylipton.bsky.social , J. Lu and A. Moitra, we revisit fine-grained expressiveness in GNNs---beyond the usual symmetry (Weisfeiler-Lehman) lens. Paper will appear in ICML '25, thread below.

How Bees, Beer Cans and Data Solve the Same Packing Problem (Gift Article) Trying to fit it all in? There’s a trick to it, even in 24 dimensions.

Dear #mathsky, if you repost this, it will let people see the article for free. Thanks!

www.nytimes.com/interactive/...

YouTube video by Lex Fridman Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI | Lex Fridman Podcast #472

A really outstanding interview of Terence Tao, providing an introduction to many topics, including the math of general relativity (youtube.com/watch?v=HUkB...). I love relativity, and in a recent(ish) paper we also consider the wave maps equation (section 5, arxiv.org/abs/2304.14994).

The lesson of causal discovery algorithms for quantum correlations: Causal explanations of Bell-inequality violations require fine-tuning An active area of research in the fields of machine learning and statistics is the development of causal discovery algorithms, the purpose of which is to infer the causal relations that hold among a s...

Here’s the original classic on the topic; arxiv.org/abs/1208.4119 . But what really needs doing, still, is classical E&M. Please reach out if/when you start in on that side of things!

A portrait of mathematician David Hillbert sitting on a chair, with a book in hand.

In 1900, David Hilbert came up with a list of 23 problems to guide the next century of mathematical research. His sixth problem challenged mathematicians to axiomatize physics.
www.quantamagazine.org/epic-effort-...

Testing (Conditional) Mutual Information We investigate the sample complexity of mutual information and conditional mutual information testing. For conditional mutual information testing, given access to independent samples of a triple of ra...

We are happy to share our work in classical distribution testing "Testing (Conditional) Mutual Information" (arxiv.org/abs/2506.03894), which was recently accepted at COLT 2025. (1/6)

I finally wrote a full-fledged blog about this: reading the history of science is an **amazing** yet under-recognized way to develop (emotional) maturity as a researcher.

If you have thoughts/recommendations, please share!
vaishnavh.github.io/2025/04/29/h...

YouTube video by Institute for Pure & Applied Mathematics (IPAM) Samuel Johnston - Horn's problem and free probability - IPAM at UCLA

Very nice talk by an old friend:

youtu.be/dOARVcCClnE?...
"Horn's Problem and Free Probability"
- Samuel Johnston

YouTube video by Yale University In Search of Lost Time Ordering, Naftali Weinberger

While trying to figure out how searchable my channel is on YouTube, I've stumbled across videos of talks I didn't know were there. Here's a talk I gave at Yale, recorded by a professional film crew and well summarized in the description.

www.youtube.com/watch?v=0m2T...

How Paradoxical Questions and Simple Wonder Lead to Great Science | Quanta Magazine Manu Prakash works on the world’s most urgent problems and seemingly frivolous questions at the same time. They add up to a philosophy he calls “recreational biology.”

Manu Prakash invented “frugal science” tools that drastically reduce the cost of diagnosing malaria.Talking to @mollyherring.bsky.social, he discusses the advantages of following curiosity: “Observation is a practice, and if you don’t practice, you lose it.”

I've been revamping and updating my collection of selected references to topics in quantum information on my homepage.

Comments, feedback and suggestions welcome!

felixleditzky.info/selected_ref...

🎉 I'm excited to share that our paper, “Falsification of Unconfoundedness by Testing Independence of Causal Mechanisms” has been accepted to ICML 2025! The camera-ready version is now available on arXiv.

📑 Paper link: arxiv.org/abs/2502.06231

#causalinference #machinelearning #icml2025

YouTube video by Naftali Weinberger Causal Foundations Episode 1: Correlation Does Imply Causation

I decided to make a youtube channel in which I introduce key concepts from causal inference in videos of roughly 10 minutes. The first episode "Correlation Does Imply Causation" is now online. Feedback would be very welcome.

youtu.be/uIUKXY8_G-M

Manu Prakash, a bearded man in plaid and a bioengineer, leans against a wall outside

Manu Prakash, a bearded man, holds a paper-made microscope

"Once, many people feel that they don’t have a voice, and the Foldscope community is a way that you can use creativity to distinguish yourself — not your status, who you know or where you published your paper." www.quantamagazine.org/how-paradoxi...

🚨 New preprint 🚨

We introduce Generative Distribution Embeddings (GDEs) — a framework for learning representations of distributions, not just datapoints.

GDEs enable multiscale modeling and come with elegant statistical theory and some miraculous geometric results!

🧵

For Algorithms, a Little Memory Outweighs a Lot of Time | Quanta Magazine One computer scientist’s “stunning” proof is the first progress in 50 years on one of the most famous questions in computer science.

A new proof upends a major assumption about the relationship between time and memory in computing.

Nice & accessible piece by Stephan Hartmann. I've long liked effective field theories, since their layered picture matches my preferred one for causal models:

- "levels" correspond to zooming in/out
- higher levels aggregate lower ones (under special conditions)
- all models are scale relative