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7.1: Introduction

  • Page ID
    40952
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    In this lecture we will define Markov Chains and HMMs, providing a series of motivating examples. In the second half of this lecture, we wil discuss scoring and decoding. We will learn how to compute the probability of the combination of a particular combination of observations and states. We will introduce the Forward Algorithm, a method for computing the probability of a given sequence of observations, allowing all sequences of states. Finally, we will discuss the problem of determining the most likely path of states corresponding to the given observations, a goal which is achieved by the Viterbi algorithm.

    In the second lecture on HMMs, we will continue our discussion of decoding by exploring posterior decoding, which allows us to compute the most likely state at each point in the sequence. We will then explore how to learn a Hidden Markov Model. We cover both supervised and unsupervised learning, explaining how to use each to learn the model parameters. In supervised learning, we have training data available that labels sequences with particular models. In unsupervised learning, we do not have labels so we must seek to partition the data into discrete categories based on discovered probabilistic similarities. In our discussion of unsupervised learning we will introduce the general and widely applicable Expectation Maximization (EM) algorithm.


    This page titled 7.1: Introduction is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Manolis Kellis et al. (MIT OpenCourseWare) via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.