<?xml version="1.0" encoding="utf-8" standalone="yes"?><rss version="2.0" xmlns:atom="http://www.w3.org/2005/Atom"><channel><title>Forward-Algorithm on Aayush Bajaj's Augmenting Infrastructure</title><link>https://abaj.ai/tags/forward-algorithm/</link><description>Recent content in Forward-Algorithm on Aayush Bajaj's Augmenting Infrastructure</description><generator>Hugo</generator><language>en</language><copyright>© 2026 Aayush Bajaj</copyright><lastBuildDate>Mon, 31 Aug 2026 00:29:54 +1000</lastBuildDate><atom:link href="https://abaj.ai/tags/forward-algorithm/index.xml" rel="self" type="application/rss+xml"/><item><title>Markov Chains and Hidden Markov Models</title><link>https://abaj.ai/wiki/ml/pgm/markov-models/</link><pubDate>Mon, 31 Aug 2026 00:29:54 +1000</pubDate><guid>https://abaj.ai/wiki/ml/pgm/markov-models/</guid><description>&lt;p>time is just another dimension to factorise over. a &lt;a
 href="https://abaj.ai/wiki/ml/pgm/bayesian-networks/"
 
 
>bayesian network&lt;/a> whose variables are indexed by time steps, with the same local structure copied at every step, is a &lt;em>dynamic bayesian network&lt;/em> — and its two simplest members, the markov chain and the hidden markov model, carry a startling share of applied probability: language models before transformers, speech recognition, robot localisation, pagerank, and the mcmc machinery behind &lt;a
 href="https://abaj.ai/wiki/ml/pgm/approximate-inference/"
 
 
>approximate inference&lt;/a>.&lt;span class="margin-note" data-note="the modern neural take on the same sequence problem is the rnn — same graph, learned transition function">
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