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This project focuses on analyzing trajectories using Hidden Markov Models (HMMs) through three core components: Likelihood Calculation, Decoding, and Learning. The Likelihood component calculates the probability (likelihood) of an observed sequence given the current HMM parameters. This is fundamental for understanding how well the HMM explains the observed data. The Decoding component uses the Viterbi algorithm to determine the most likely sequence of hidden states for a given observed trajectory. This helps to map observed data to inferred underlying states, giving insight into the structure of the trajectory. The Learning component involves training the HMM parameters using the Baum-Welch algorithm, which iteratively adjusts the transition and emission probabilities to maximize the likelihood of the observed data. This is essential for creating a more accurate HMM.

This project explores foundational and modern reinforcement learning techniques through a systematic and practical approach. It implements key algorithms such as Policy Iteration, Value Iteration, SARSA, Q-Learning, and Deep Q-Networks (DQN), showcasing their capabilities in solving decision-making tasks across different environments. The project delves into dynamic programming methods to compute optimal policies, temporal-difference learning for effective policy optimization, and deep reinforcement learning techniques to handle high-dimensional and complex state spaces. Through these implementations, the project demonstrates a comprehensive understanding of both classical and deep learning-based reinforcement learning paradigms. Key features include detailed visualizations, such as learning curves and convergence behaviors, which provide valuable insights into the performance and effectiveness of these algorithms.