第十九章 人工智能

a brief review of the second semester of the course 12/05/16 6:46 AM

probability

probability gives us a formal mechanism to reason about uncertainty; important concepts include:

* random variables * joint distribution between 2 or more random variables * conditional distributions Pr(X | Y) = Pr(X, Y) / Pr(Y) * sum rule and product rule * Bayes' rule * independence and conditional independence * chain rule allows us to factorize a joint distribution into conditional distributions

(Hidden) Markov models

MMs and HMMs are specials of Bayes nets, allow us to reason about time series of RVs

• structure of MM/HMMs * the stationary distribution
• filtering: are always trying to infer Pr(X_t | E_1 ... E_t)
• exact inference for filtering (elapse time/update/forward algorithm)

Particle filtering

Particle filtering is a sampling approach to HMMs that is useful when the state space is very large

Bayes's nets

Bayes nets give us a mechanism to easily model situations and encode conditional independence

• nodes are RVs, edges indicate (often causal) relationships in a DAG
• the graph structure encodes conditional independences
• constructing a reasonable BN is possible with knowledge about the problem
• D-separation gives us an algorithm for determining whether two RVs are conditionally independent given a set of evidence

Decision diagrams / VPI

decision diagrams / value of perfect information give us a framework for decision making that is compatible with probability

• maximize the expected utility!!
• value of perfect information allows us to determine if gathering information is worth the cost