Discrete HMM Reading List

Dynamax HMMs
1

Hey folks
For the next session we will be focusing on Discrete HMMs. The next session will be live session will be on Sunday the 25th

Our goal is to fully understand this formula

\begin{align} p(y_{1:T}, z_{1:T} \mid \theta) &= \mathrm{Cat}(z_1 \mid \pi) \prod_{t=2}^T \mathrm{Cat}(z_t \mid A_{z_{t-1}}) \prod_{t=1}^T \mathrm{Cat}(y_t \mid B_{z_t}) \end{align}

We’ll do that with the following reading material

Focus on

  • Filtering (forwards algorithm)
  • Smoothing (forwards-backwards algorithm)
  • Most likely state sequence (Viterbi algorithm)

As always this is just my prior. If you have opinions or suggestions please do leave them below!

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2

After about 40 minutes in session 2, @RavinKumar mentions that many times one line of a mathematical equation is transferred into four lines of code.

In this case, it is due to the log-sum-exp trick that is mostly used for numerical stability.
Here’s a link that describes why and how it is used: The Log-Sum-Exp Trick

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This is great. Thank you for sharing!