Hidden Markov Models
Hidden Markov Models (HMMs) are probabilistic models used to represent systems that transition between hidden states, where observations are dependent on these underlying states. Introduced by Leonard E. Baum in the 1960s, HMMs are widely used in speech recognition, bioinformatics, and natural language processing. The model assumes that the system being modeled is a Markov process with unobserved states, allowing it to estimate sequences of states based on observed data. For example, in speech recognition, HMMs model the sequence of phonemes that generate the acoustic signals, enabling accurate transcription.
https://en.wikipedia.org/wiki/Hidden_Markov_model
A key feature of HMMs is their use of two probabilistic components: the transition probabilities between hidden states and the emission probabilities that relate hidden states to observed outputs. Algorithms like the Forward-Backward Algorithm and the Viterbi Algorithm are integral to HMMs, enabling tasks such as state sequence prediction and parameter estimation. These algorithms are computationally efficient and form the basis for many machine learning applications. For instance, HMMs are used in bioinformatics to predict protein structures and align genetic sequences, where the hidden states represent biological properties.
https://en.wikipedia.org/wiki/Viterbi_algorithm
Modern advancements have extended the application of Hidden Markov Models to integrate with deep learning methods, improving their ability to model complex patterns in data. For example, hybrid HMM-deep learning models are used in speech synthesis and autonomous systems to improve recognition accuracy. Libraries such as hmmlearn for Python and implementations in TensorFlow enable researchers to easily build and customize HMMs for diverse applications. This integration ensures the continued relevance of HMMs in solving problems involving sequential and time-series data.