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Category: Bayesian Methods

Interpreting Karl Friston (Round Deux)

Interpreting Karl Friston (Round Deux)

He might be getting a Nobel prize some day. But – no one can understand him. You don’t believe me? Have a quick glance at Scott Alexander’s article, “God Help Us, Let’s Try To Understand Friston On Free Energy”. We’re referring, of course, to Karl Friston. I’ve spent the past three-and-a-half years studying Friston’s approach to free energy, which he treats as the guiding principle in the brain. He has extended the classic variational Bayes treatment (frontier-material in machine learning)…

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Seven Essential Machine Learning Equations: A Cribsheet (Really, the Précis)

Seven Essential Machine Learning Equations: A Cribsheet (Really, the Précis)

Making Machine Learning As Simple As Possible Albert Einstein is credited with saying, Everything should be made as simple as possible, but not simpler. Machine learning is not simple. In fact, once you get beyond the simple “building blocks” approach of stacking things higher and deeper (sometimes made all too easy with advanced deep learning packages), you are in the midst of some complex stuff. However, it does not need to be more complex than it has to be.  …

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A Tale of Two Probabilities

A Tale of Two Probabilities

Probabilities: Statistical Mechanics and Bayesian:   Machine learning fuses several different lines of thought, including statistical mechanics, Bayesian probability theory, and neural networks. There are two different ways of thinking about probability in machine learning; one comes from statistical mechanics, and the other from Bayesian logic. Both are important. They are also very different. While these two different ways of thinking about probability are usually very separate, they come together in some of the more advanced machine learning topics, such…

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Approximate Bayesian Inference

Approximate Bayesian Inference

Variational Free Energy I spent some time trying to figure out the derivation for the variational free energy, as expressed in some of Friston’s papers (see citations below). While I made an intuitive justification, I just found this derivation (Kokkinos; see the reference and link below): Other discussions about variational free energy: Whereas maximum a posteriori methods optimize a point estimate of the parameters, in ensemble learning an ensemble is optimized, so that it approximates the entire posterior probability distribution…

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