What does HMM mean in MATHEMATICS

A Hidden Markov Model (HMM) is a probabilistic model used for predicting the likelihood of sequence patterns in data. The model assumes that each state in the sequence can only be observed indirectly, making it an unsupervised learning technique. HMM’s are also used in speech and handwriting recognition, robotics, and automatic image segmentation.

An HMM is based on a Markov chain, which is a system with components that are connected by transitions between states. The components are represented as probability distributions over “hidden” variables. The transition probabilities represent how likely it is for the system to move from one state to another. Based on these transitions, we can calculate the likelihood of observing certain sequences of events given certain prior states.

There are two main types of HMMs – Forward-Backward and Baum-Welch algorithms. In Forward-Backward algorithms, observations at each time step are only dependent on the current and previous states, while Baum-Welch algorithms allow more flexibility by using forward and backward messages to update transition probabilities over time. Both types can be used to identify patterns in data sets or to make predictions about future events based on past observations.

HMMs have been used extensively in speech recognition, handwriting recognition, image segmentation, robotics control systems, and bioinformatics research such as prediction of protein structures and gene regulation networks. They have also been employed for machine translation and topic identification tasks involving natural language processing (NLP).

One advantage of using an HMM is that it allows for flexible modeling of temporal dependence among observations without having to explicitly define all possible combinations of states or parameters for each observation point separately. This makes it easier to build models that capture complex temporal relationships without requiring too much manual intervention or exploratory searching through state space configurations like other machine learning techniques require.

Building an HMM requires two steps – first you must define the model structure which includes specifying the number of states in your model as well as how they interact with each other; then you need to estimate its parameters based on training data using either a maximum likelihood estimation or Bayesian inference approach. Once these two steps have been completed you can use your trained HMM model to make predictions about unseen data points.