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Uncertainty & Probability - Coggle Diagram
Uncertainty & Probability
Key Concepts
Belief State
Representation of all possible states of the world, acting as the agent's short-term memory.
Contingency Plans:
Plans that account for uncertainty in the environment, especially when future percepts are unknown (e.g., the flight example).
Deterministic vs. Probabilistic Processes
Probabilistic
Predictions are based on probabilities due to uncertainty (e.g., the quantum universe).
Deterministic
All data required for prediction is available.
Decision Theory
Rational Decision-Making
Balances likelihood of achieving goals with benefits.
Utility Theory
Assigns values to outcomes to prioritize decisions.
Decision-Making Process
Involves analyzing alternatives and selecting the course of action that maximizes benefits. Decision Theory = Probability Theory + Utility Theory.
Probability Theory
Conditional Probability
The probability of event A occurring, given that event B has occurred (P(A|B)).
Sample Space
All possible outcomes (e.g., sum of two dice rolls).
Random Variable
Maps sample points to numerical values.
Probability Notation
P(A): Probability that event A will occur.
P(A ∩ B): Probability of both events A and B occurring. P(A ∪ B): Probability of either event A or B occurring.
Markov Chains
systems that undergo transitions based only on the current state, not previous states (memoryless).
Applications
Weather prediction, random walks, stock market fluctuations, genetic
Transition Matrix
Represents the probability of transitioning between states
Real-World Applications
Weather Prediction
MCMC (Markov Chain Monte Carlo)
Hidden Markov Models (HMM)
Page Ranking
DNA Sequencing
Speech Processing
References
https://www.statslab.cam.ac.uk/~rrw1/markov/index.html
https://coggle.it/diagram/aBhK0E46SWnH-w5y/t/uncertainty-probability