Sonification of neural data: my experience and outlook
As explained here, in 2022 I had the opportunity to participate in a project bringing together neuroscience and fine arts to engage the public. In this post I want to share my …
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3 min read
Mean field variational inference
In this problem, you will investigate mean field approximate inference algorithms (Koller & Friedman1 11.5). Consider the Markov network in the above figure. Define edge potentials …
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2 min read
Markov chain Monte Carlo sampling
Inverse CDF sampling A simple sampling method adopted by many of the standard math libraries is the inverse probability transform: draw $u \sim \text{Unif}(0, 1)$, then draw $x\sim …
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3 min read
Approximate inference via Gibbs sampling
Consider a setting in which there are $D$ diseases and a patient either has ($d_i=1$) or does not have ($d_i=0$) each disease. The hospital can measure $S$ symptoms, where $s_j=1$ …
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4 min read
Parameter learning in probabilistic graphical models
Parameter learning in Bayesian networks and Markov random fields Cost of learning CRF parameters Consider the process of gradient-ascent training for a conditional random field …
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4 min read
Learning maximum likelihood tree structure with the Chow-Liu algorithm
Write a function ChowLiu(X) -> A where X is a D by N data matrix containing a multivariate data point on each column that returns a Chow-Liu maximum likelihood tree for X. The tree …
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1 min read
Expectation-maximization for a Markov chain mixture model
Assume that a sequence $v_1,\ldots,v_T \in \{1,\dots,V\}$ is generated by a Markov chain. For a single chain of length $T$, we have $$ p(v_1,\dots,v_T) = p(v_1)\prod_{t=1}^{T-1} …
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8 min read
Learning edge direction in a Bayesian network model
Our interest here is to discuss a method to learn the direction of an edge in a belief network. Consider a distribution $$ P(x,y | \theta,M_{y\to x}) = …
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3 min read
Comparing the basic and extended Kalman filters
This notebook doesn't offer much in the way of explanation, but explores implementations of the basic and extended Kalman filters and compares them for different nonlinearities. …
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5 min read
Embedding a Starboard Notebook
Starboard is an exciting open-source project I learned about from a blog post by Patrick Mineault. Basically, it allows the user to run and edit an interactive notebook, including …
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1 min read