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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.
Challenges
World Knowledge
Problems where uncertainty is inherent (e.g., medical diagnosis, car repairs, etc.).
Diagnosis Involving Uncertainty
Understanding how to handle uncertainty in real-world applications where data is incomplete or noisy.
Decision Theory
Rational Decision-Making
Selecting the best action based on the likelihood of achieving goals.
Utility Theory
Every state has a degree of usefulness, and decisions are made to maximize expected utility.
Decision-Making Process
Involves analyzing alternatives and selecting the course of action that maximizes benefits.
Probability Theory
Conditional Probability
The probability of event A occurring, given that event B has occurred (P(A|B)).
Sample Space
All possible outcomes of an event (e.g., rolling a die).
Expected Value
The average or expected outcome from a probability distribution (E(X)).
Probability Functions
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
A mathematical system where the next state depends 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
Absorbing Markov Chains
Chains that have at least one absorbing state
Real-World Applications
Weather Prediction
MCMC (Markov Chain Monte Carlo)
Hidden Markov Models (HMM)
Page Ranking
DNA Sequencing
Speech Processing
Population Genetics
web links
https://www.geeksforgeeks.org/markov-chain/
https://www.sciencedirect.com/topics/mathematics/probability-theory
https://www.sciencedirect.com/science/article/pii/S1364815220309622