Hands-On Markov Models with Python by Ankur Ankan

Author:Ankur Ankan
Language: eng
Format: epub
Tags: COM042000 - COMPUTERS / Natural Language Processing, COM004000 - COMPUTERS / Intelligence (AI) and Semantics, COM044000 - COMPUTERS / Neural Networks
Publisher: Packt Publishing
Published: 2018-09-26T09:11:35+00:00

>>> mu, sigma = gaussian_mle(data)

>>> mu

1.0437186891666821

>>> sigma

1.967211026428509

In this case, with more data, we can see that the learned values are much closer to our original values.

MLE for HMMs

Having a basic understanding of MLE, we can now move on to applying these concepts to the case of HMMs. In the next few subsections, we will see two possible scenarios of learning in HMMs, namely, supervised learning and unsupervised learning.

Supervised learning

In the case of supervised learning, we use the data generated by sampling the process that we are trying to model. If we are trying to parameterize our HMM model using simple discrete distributions, we can simply apply the MLE to compute the transition and emission distributions by counting the number of transitions from any given state to another state. Similarly, we can compute the emission distribution by counting the output states from different hidden states. Therefore the transition and emission probabilities can be computed as follows:

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