Probabilistic_Graphical_Models

python implementation of classic probabilistic graphical models

HMM (Hidden Markov Model)

I implement a tensor version (using numpy) of HMM for three classic problems of HMM. For any non-sequential/non-recursive, I bypass the for-loop by using tensor operations. Thus, my numpy implementation could be easily adapted by tensorflow, pytorch.

1. The Evaluation problem: (forward/backward messages) Given 𝜆=(𝜋,𝐴,𝐵) and a sequence of observation 𝑂=(𝑜1,𝑜2,𝑜𝑇) , estimate P(𝑂|𝜆).

2. The Learning problem: (Baum-Welch algorithm, aka EM-algorithm) Given 𝑂=(𝑜1,𝑜2,𝑜𝑇) , estimate best fit parameters 𝜆=(𝜋,𝐴,𝐵).

3. The Decoding problem: (Viterbi's algorithm) Given 𝜆=(𝜋,𝐴,𝐵) and a sequence of observation 𝑂=(𝑜1,𝑜2,𝑜𝑇) , estimate hidden states.

Please see directly the jupyter notebook HMM.ipynb for more details.

Project ongoing: (check list)

• tensor version of basic HMM ...done.
• discrete observation space...done.
• D trajectories version of HMM...done.
• Problem 1, 2...done.
• Problem 3...partially.
• continue version (with gaussian kernel) ... partially.
• D trajectories, continue version
• Monitor likelihood in the Problem 2.