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.
Table of Contents (11 chapters)

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....