Latent variables, HMMs and Kalman filters
The quantity you care about is hidden, changes over time, and shows itself only through noisy readings. Latent-variable models, hidden Markov models with the forward and Viterbi algorithms derived from scratch, Baum–Welch as EM, and the Kalman filter as Bayes' rule applied over and over to Gaussians.
65 min
After this lesson you can
- Write down a latent-variable model and name the inference and learning problems it poses
- Define an HMM by its initial distribution, transition matrix and emission matrix, and derive the forward algorithm and the likelihood it computes
- Derive the Viterbi algorithm as max-product dynamic programming and trace back the most probable path
- Describe Baum–Welch as EM whose E-step is forward–backward
- Derive the Kalman filter's predict and update steps from Gaussian conditioning, and explain the gain
In this lesson
- Latent variables
- Hidden Markov models
- The Kalman filter: an HMM with Gaussians
- In code
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