In this session, we will cover several parametric models:
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Markov models,Hidden Markov Models(HMMs), and theViterbialgorithm are essential concepts in probabilistic modeling and sequential data analysis.-
Markov Model: It describes the probabilistic transitions between states in a system, assuming that the future state depends only on the current state. Markov models are used to understand and predict dynamic processes with sequential dependencies.
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Hidden Markov Model (HMM): An extension of the Markov model that deals with observed and unobserved states. HMMs capture the relationships between hidden states and observed symbols, making them valuable for tasks like speech recognition, bioinformatics, and pattern recognition.
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Viterbi Algorithm: It efficiently finds the most likely sequence of hidden states in an HMM. The algorithm considers state transitions and symbol emissions to compute the optimal path through the model. It is crucial for decoding and inference tasks in HMMs, such as speech recognition and gene finding.
These concepts play a vital role in analyzing sequential data, predicting future states, decoding hidden information, and solving problems in various fields, including speech recognition, natural language processing, and bioinformatics.
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Bayesian network, also known as a probabilistic graphical model, is a graphical representation of probabilistic relationships among variables. It provides a way to model and reason under uncertainty by using probability theory and graph theory. The advantages of using Bayesian networks include their ability to handle uncertainty, model complex dependencies, incorporate prior knowledge, and facilitate transparent and interpretable reasoning. They find applications in various domains, including medical diagnosis, risk assessment, natural language processing, and fault diagnosis.In summary, Bayesian networks provide a graphical and probabilistic framework for modeling and reasoning under uncertainty. They help capture and analyze complex relationships between variables, making them a valuable tool for probabilistic inference and decision-making.