Hidden Markov models (HMMs) were first introduced and explored in the early 1970s. They are named after the Russian mathematician Andrey Andreyevich Markov, who pioneered most of the related statistical theory. 

Since the late 1980s, they have been successfully used in analyzing biological sequences originating in speech recognition. Dynamic Bayesian networks are recognized as a subset of the broader Bayesian network family. HMMs are statistical models that uncover previously unsuspected relationships between sets of sequential symbols. In sequence analysis, they are helpful for numerous tasks, including predicting exons and introns, detecting protein domains, and aligning two sequences. 

An HMM aims to infer a model's hidden parameters from its available set of observable ones. The system being modelled is considered a Markov process with unknown parameters. It is essential for a successful HMM to precisely model the source of the observed real data and to be able to simulate that source. Due to their robust statistical foundation, conceptual simplicity, and adaptability, HMMs are fit for diverse classification problems; they have become a fundamental tool in bioinformatics, with applications spanning from speech recognition and optical character recognition to computational biology. An HMM is a popular statistical method for describing biological sequences in Computational Biology.

Follow these steps to implement the HMM algorithm: 

Step 1: Define the state space and the observer space
The set of all possible hidden states is the state space, and the set of all possible views is the observation space.
Step 2: Define the distribution of the starting state
It is how the odds are spread out over the original state.
Step 3: Define the state transition probabilities
 These are the chances of going from one state to the next. It makes up the transition matrix, which shows how likely it is to move from one state to another.
Step 4: Define the likelihood of the observations: 
These are the chances that each report will come from each state. It makes up the emission matrix, which shows how likely each observation will come from each state.
Step 5: Model training
The Baum-Welch algorithm, also called the forward-backwards algorithm, determines the parameters of the probabilities of changing states and the chances of an observation. It is done by changing the settings over and over again until convergence.
Step 6: Figure out the most likely order of secret states.
The Viterbi algorithm determines the most likely order of secret states based on what has been seen. It can guess what will happen next, classify sequences, or find patterns in data that come in a specific order.
Step 7: Model evaluation
Different measurements, like accuracy, precision, recall, or F1 score, can measure how well the HMM works.

Algorithm source: geeksforgeeks

Libraries required 

import numpy as np  
import pandas as pd  
import seaborn as sns  
from tqdm import tqdm  
from matplotlib import pyplot as plt  
from sklearn.model_selection import GroupShuffleSplit  
from hmmlearn import hmm  
from sklearn.metrics import confusion_matrix, classification_report, accuracy_score, precision_score, recall_score, f1_score, roc_auc_score  

Source: Javatpoint

Applications

• HMMs are widely used to model speech sounds and phone structures in speech recognition. Hidden states correspond to sounds or phones, while observations represent acoustic signals. HMMs are ideal for speech recognition because they capture speech structure even in noisy or incomplete data. They are trained on large datasets and use estimated parameters for real-time transcription.
• HMMs are crucial in natural language processing tasks like part-of-speech tagging, named entity recognition, and text classification. They estimate hidden state sequences based on observed words, capturing text structure even in noisy or ambiguous data. HMMs are trained on large datasets and used for NLP tasks like text classification, part-of-speech tagging, and named entity recognition.
• HMMs are widely used in bioinformatics to model DNA, RNA, and protein sequences. Hidden states represent residue types, while observations represent residue sequences. HMMs capture molecule structure even in noisy or incomplete data and are trained on large datasets. Estimated parameters predict molecular sequence structure or function.
• HMMs are utilized in finance to model stock prices, interest rates, and currency exchange rates. Hidden states represent different economic states, while observations represent stock prices, interest rates, or exchange rates. They are trained on large datasets and used for forecasting market trends and investment strategies.

Image source: Unsplash