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Alpha beta pruning and Probability and Markov chains in Probability -…
Alpha beta pruning and Probability and Markov chains in Probability
Introduction to Alpha-Beta Pruning
Definition and purpose
Alpha: The best (highest-value) choice we have found so far at any point along the path of Maximizer.
Beta: The best (lowest-value) choice we have found so far at any point along the path of Minimizer.
Motivation behind reducing the number of evaluated states in the search tree
Minimax Algorithm
Overview of the minimax algorithm for adversarial search
Evaluation functions and terminal states
Minimax decision-making process
Alpha-Beta Pruning Algorithm
Explanation of the basic Alpha-Beta pruning algorithm
Maintaining alpha and beta values during tree traversal
Pruning branches based on alpha-beta bounds
Problem with minimax
Time Complexity
Computational Resources
Pruning Limitations
Optimal Depth Limit
Trade-off Between Depth and Accuracy
Strategies to optimize search
Iterative Deepening
Transposition Tables
Move Ordering
Quiescence Search
Transposition Cutoffs
Null Move Pruning
Markov chains
Definition and properties of Markov chains
State space, transition probabilities, and transition matrix
Absorbing Markov chain
Garkov
Markov Chain Modeling
Stationary distribution and long-term behavior
Absorbing and non-absorbing states
Calculation of steady-state probabilities.
Examples
Modeling weather patterns
Random walks
PageRank algorithm
Hidden Markov Models (HMMs)
Introduction to Hidden Markov Models
Forward-Backward Algorithm
Examples
Speech recognition
Part-of-speech tagging
Bioinformatics
Monte Carlo Methods
Introduction to Monte Carlo Methods
Overview of simulation-based techniques
Monte Carlo integration
Markov Chain Monte Carlo (MCMC)
Metropolis-Hastings algorithm
Gibbs sampling
Applications of Monte Carlo Methods
Bayesian inference.
Risk analysis and decision-making
Game playing and optimization.
Stochastic games
Sequential Interactions
Uncertainty and Randomness
Multiple Agents
State Transitions
Markovian Property
Stochastic process
collection of random variables
indeterminate outcome
represents evolution of system over time
Chaos Theory
Definition
Fractals
Based on deterministic processes
PHYLO
Aligning genetic sequences through a puzzle game