Book Image

Hands-On Markov Models with Python

By : Ankur Ankan, Abinash Panda
Book Image

Hands-On Markov Models with Python

By: Ankur Ankan, Abinash Panda

Overview of this book

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.

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Table of Contents (11 chapters)
Preface
Preface
Who this book is for
What this book covers
To get the most out of this book
Get in touch
Free Chapter
1
Introduction to the Markov Process
Introduction to the Markov Process
Random variables
Random processes
Markov processes
Installing Python and packages
Markov chains or discrete-time Markov processes
Continuous-time Markov chains
Summary
2
Hidden Markov Models
Hidden Markov Models
Markov models
The HMM
Evaluation of an HMM
Extensions of HMM
Summary
3
State Inference - Predicting the States
State Inference - Predicting the States
State inference in HMM
Dynamic programming
Forward algorithm
Backward algorithm
Forward-backward algorithm (smoothing)
The Viterbi algorithm
Summary
4
Parameter Learning Using Maximum Likelihood
Parameter Learning Using Maximum Likelihood
Maximum likelihood learning
MLE for HMMs
Summary
5
Parameter Inference Using the Bayesian Approach
Parameter Inference Using the Bayesian Approach
Bayesian learning
Bayesian learning in HMM
Code
Summary
6
Time Series Predicting
Time Series Predicting
Stock price prediction using HMM
Summary
7
Natural Language Processing
Natural Language Processing
Part-of-speech tagging
Speech recognition
Summary
8
2D HMM for Image Processing
2D HMM for Image Processing
Recap of 1D HMM
2D HMMs
Summary
9
Markov Decision Process
Markov Decision Process
Reinforcement learning
The Markov reward process
Code example
Summary
10
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Forward algorithm

Let's now formally define our problem for the forward algorithm. In the case of the forward algorithm, we are trying to compute the joint distribution of the position of the robot at any time instance using the output of the sensors till that time instance, as shown in the following diagram:

Forward algorithm: P(Zk, X1:k)

Figure 3.3: HMM showing two time slices, k-1 and k

To compute this probability distribution, we will try to split the joint distribution term into smaller known terms. As we will see, we can write a recursion formula over time for the distribution. We start by introducing a new variable, Zk-1, in the distribution, P(Zk, X1:k), as follows:

The marginalization rule of probability is:

The product rule of probability is:

Here, we are basically using the marginalization rule of probability to introduce Zk-1 and then summing its states....

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