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Models that describe data with probability distributions. The course covers Markov chains and hidden Markov models with their forward and Viterbi algorithms, Gaussian mixtures fitted with EM or gradients, Bayesian linear regression, and variational inference for posteriors with no closed form.
01
A Markov chain moves between states with probabilities that depend only on the current state. Its stationary distribution is the long run share of time in each state.
03
Viterbi finds the single most likely state path. It is the forward algorithm with the sum replaced by a max, plus back pointers to recover the path.
Practise it
04
A Gaussian mixture models data as several Gaussians with mixing weights. EM alternates soft assignments of points to components with weighted updates of each component.
05
With a Gaussian prior on the weights and Gaussian noise, the posterior over the weights is Gaussian and has a closed form. Its covariance says how sure the model is about each weight.
06
Variational inference fits a simple distribution to the posterior by maximising the evidence lower bound. The reparameterisation trick makes the sampled bound differentiable.