Academic Blog
This is my academic blog. I post about interesting ideas and research topics. I don’t want to constrain myself only around the topics that I do my research on. Thus, I might post about topics that I don’t know a whole lot about, so please let me if you spot any errors.
Posts
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Ye Olde Causal Inference: A Cholera Case Study
In 1855, John Snow (the English physician, not the prince of Dragonstone) presented a compelling study arguing that cholera was caused by a living organism that contaminates water or food and then multiplies within the body, an argument that preceded the foundations of modern microbiology by twenty years. For comparison, other hypotheses at the time were: miasma (bad air), poison on the ground, or an “imbalance in the humors of the body.” What is especially interesting in hindsight is how Snow demonstrated this causation, which was basically through experimental design and bias mitigation rather than by extracting a signal from sampling noise. In particular, sampling error and p-values were not central to his argument.
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Four Ways to Escape to Infinity
Escaping from infinity is different from escaping to infinity. When we say infinity, we are referring to some quantity that becomes unbounded as we go further. But when a thing escapes to infinity, its total mass can stay finite while still somehow managing to evade convergence, often due to degeneracies in the way we measure its mass.
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The Bayesian Learning Rule, or How to Optimize as a Bayesian
Have you ever wondered why the optimization community and the Bayesian community—two fundamental areas of machine learning—have so little in common? When you realize how important they are to machine learning, you start to wonder why they seem so detached from each other. Perhaps it has to do with the origins of the fields, where one comes from applied math and the other comes from statistics. In this post, I’ll talk about The Bayesian Learning Rule (Khan & Rue, 2023), a recent research direction that makes the connection between the two fields principled, clear, and practical under an elegant variational learning framework.
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Log-Sobolev Meets Polyak-Łojasiewicz
The connection between sampling and optimization have been established quite a few times in the literature, with some results going back 40 years ago. Here, I will talk about a connection between two seemingly unrelated inequalities (at least to people working in optimization). It’s very obvious in hindsight, but I found it quite interesting and worth sharing.