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Hands-On Markov Models with Python
Hands-On Markov Models with Python

Hands-On Markov Models with Python: Implement probabilistic models for learning complex data sequences using the Python ecosystem

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Hands-On Markov Models with Python

Hidden Markov Models

In the previous chapter, we discussed Markov chains, which are helpful in modelling a sequence of observations across time. In this chapter, we are going to study the Hidden Markov Model (HMM), which is also used to model sequential data but is much more flexible than Markov chains.

In this chapter, we will cover the following topics:

  • Markov models
  • The HMM
  • Evaluation of an HMM
  • Extensions of HMM

Markov models

The Markov model is a stochastic model in which the state of the random variable at the next instance of time depends only on the outcome of the random variable at the current time. The simplest kind of Markov model is a Markov chain, which we discussed in Chapter 1, Introduction to Markov Process.

Suppose we have a set of sequential observations (x1,. . ., xn) obeying the Markov property, then we can state the joint probability distribution for N observations as the following:

Graphical representation of a first-order Markov chain in which the distribution of the current observation is conditioned on the value of the previous observation

The preceding representation of the Markov chain is different from the representations we saw earlier. In this representation, the observations are presented as nodes and the edges represent conditional probability between...

The HMM

An HMM is a specific case of state space model in which the latent variables are discrete and multinomial variables. From the graphical representation, we can also consider an HMM to be a double stochastic process consisting of a hidden stochastic Markov process (of latent variables) that we cannot observe directly, and another stochastic process that produces a sequence of the observation given the first process.

Before moving on to the parameterization, let's consider an example of coin-tossing to get an idea of how it works. Assume that we have two unfair coins, M1 and M2, with M1 having a higher probability (70%) of getting heads and M2 having a higher probability (80%) of getting tails. Someone sequentially flips these two coins, however, we do not know which one. We can only observe the outcome, which can either be heads (H) or tails (T):

We can consider the...

Evaluation of an HMM

In the previous section, we discussed generating an observation sequence of a given HMM. But, in reality, most of the time we are not interested in generating the observation sequence, mostly because we don't know the parameters of the HMM to generate observations in the first place.

For a given HMM representation, in most of the applications, we are always trying to address the following three problems:

  • Evaluation of the model: Given the parameters of the model and the observation sequence, estimating the probability of the sequence
  • Predicting the optimal sequence: Given the parameters of the model and the observation sequence, estimating the most probable sequence of the state sequence that had produced these observations
  • Parameter-learning: Given a sequence of observations, estimating the parameters of the HMM model that generated it

In this section...

Extensions of HMM

In the previous sections, we discussed HMM, sampling from it and evaluating the probability of a given sequence given its parameters. In this section, we are going to discuss some of its variations.

Factorial HMMs

Let's consider the problem of modelling of several objects in a sequence of images. If there are M objects with K different positions and orientations in the image, there are be KM possible states for the system underlying an image. An HMM would require KM distinct states to model the system. This way of representing the system is not only inefficient but also difficult to interpret. We would prefer that our HMM could capture the state space by using M different K-dimensional variables.

A factorial...

Summary

In this chapter, we got a detailed introduction to Markov model and HMM. We talked about parameterizing an HMM, generating samples from it, and their code. We discussed estimating the probability of observation, which would form the basis of inference, which we'll cover in the next chapter. We also talked about various extensions of HMMs.

In the next chapter, we will take an in-depth look at inference in HMMs.

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Key benefits

  • Build a variety of Hidden Markov Models (HMM)
  • Create and apply models to any sequence of data to analyze, predict, and extract valuable insights
  • Use natural language processing (NLP) techniques and 2D-HMM model for image segmentation

Description

Hidden Markov Model (HMM) is a statistical model based on the Markov chain concept. Hands-On Markov Models with Python helps you get to grips with HMMs and different inference algorithms by working on real-world problems. The hands-on examples explored in the book help you simplify the process flow in machine learning by using Markov model concepts, thereby making it accessible to everyone. Once you’ve covered the basic concepts of Markov chains, you’ll get insights into Markov processes, models, and types with the help of practical examples. After grasping these fundamentals, you’ll move on to learning about the different algorithms used in inferences and applying them in state and parameter inference. In addition to this, you’ll explore the Bayesian approach of inference and learn how to apply it in HMMs. In further chapters, you’ll discover how to use HMMs in time series analysis and natural language processing (NLP) using Python. You’ll also learn to apply HMM to image processing using 2D-HMM to segment images. Finally, you’ll understand how to apply HMM for reinforcement learning (RL) with the help of Q-Learning, and use this technique for single-stock and multi-stock algorithmic trading. By the end of this book, you will have grasped how to build your own Markov and hidden Markov models on complex datasets in order to apply them to projects.

Who is this book for?

Hands-On Markov Models with Python is for you if you are a data analyst, data scientist, or machine learning developer and want to enhance your machine learning knowledge and skills. This book will also help you build your own hidden Markov models by applying them to any sequence of data. Basic knowledge of machine learning and the Python programming language is expected to get the most out of the book

What you will learn

  • Explore a balance of both theoretical and practical aspects of HMM
  • Implement HMMs using different datasets in Python using different packages
  • Understand multiple inference algorithms and how to select the right algorithm to resolve your problems
  • Develop a Bayesian approach to inference in HMMs
  • Implement HMMs in finance, natural language processing (NLP), and image processing
  • Determine the most likely sequence of hidden states in an HMM using the Viterbi algorithm
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Publication date : Sep 27, 2018
Length: 178 pages
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Language : English
ISBN-13 : 9781788625449
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Product Details

Publication date : Sep 27, 2018
Length: 178 pages
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ISBN-13 : 9781788625449
Category :
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Concepts :

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Table of Contents

10 Chapters
Introduction to the Markov Process Chevron down icon Chevron up icon
Hidden Markov Models Chevron down icon Chevron up icon
State Inference - Predicting the States Chevron down icon Chevron up icon
Parameter Learning Using Maximum Likelihood Chevron down icon Chevron up icon
Parameter Inference Using the Bayesian Approach Chevron down icon Chevron up icon
Time Series Predicting Chevron down icon Chevron up icon
Natural Language Processing Chevron down icon Chevron up icon
2D HMM for Image Processing Chevron down icon Chevron up icon
Markov Decision Process Chevron down icon Chevron up icon
Other Books You May Enjoy Chevron down icon Chevron up icon

Customer reviews

Rating distribution
Full star icon Full star icon Half star icon Empty star icon Empty star icon 2.3
(4 Ratings)
5 star 0%
4 star 25%
3 star 0%
2 star 50%
1 star 25%
RFEMYGDIO Jan 21, 2019
Full star icon Full star icon Full star icon Full star icon Empty star icon 4
Excelente
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DWH Dec 02, 2018
Full star icon Full star icon Empty star icon Empty star icon Empty star icon 2
Although the algorithms in this book are generally correct it is riddled with crippling errors. There are undefined variables and out of range errors in almost every example. These are still present in the code that you download directly from the publisher. Buyer beware, you'll spend more time troubleshooting than learning.
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Victoria Sherratt Jul 10, 2021
Full star icon Full star icon Empty star icon Empty star icon Empty star icon 2
It's ok, not great. It's printed by Amazon and some of the graphics are a bit low quality. What annoyed me most about this book is the chapter I was most interested in, the authors didn't bother with the code - "it would be too long for this book" - but in later chapters presented pages of back to back code. The book is not long at all so why skirt over it?
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Damian Jan Cordon Jun 26, 2019
Full star icon Empty star icon Empty star icon Empty star icon Empty star icon 1
Las fórmulas y gráficos de este libro son diminutas en el Kindle y no es posible aumentar su tamaño, lo que hace imposible seguir correctamente los razonamientos que aplica ya que no es posible acceder a la justificacion matemática de lo que explica.
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