14. Probability Theory 2 Flashcards
What is probabilistic inference?
The process of computing the probability of a query given known probabilities and evidence.
How can probabilities be updated?
By incorporating new evidence using conditional probabilities and Bayes’ Rule.
What is a joint probability query?
A query that asks for the probability of multiple variables occurring together (e.g., P(A,B)).
What are the three types of variables in probabilistic inference?
Query variables, evidence variables, and hidden variables.
What is inference by enumeration?
A method for computing probabilities by summing over all possible values of hidden variables. P(Q,E)=∑_{H} P(Q,H,E).
What is the worst-case complexity of inference by enumeration?
Time complexity: O(d^n) , Space complexity: O(d^n), where d is the domain size and n is the number of variables.
What is the chain rule of probability?
A formula that expresses a joint probability as a product of conditional probabilities: P(X_1, X_2, …, X_n) = P(X_1) P(X_2 | X_1) P(X_3 | X_1, X_2) … P(X_n | X_1, X_2, …, X_{n-1}) ]
What is a conditional probability query?
A query that asks for the probability of an event given some evidence (e.g., P(A | B))
How is a conditional probability computed?
By normalizing the joint probability: P(Q | E) = \frac{P(Q, E)}{P(E)}
What is marginalization?
The process of summing over hidden variables to obtain the probability of a subset of variables. P(X) = \sum_Y P(X, Y)
What are sensitivity and specificity in probabilistic inference?
Sensitivity measures the percentage of actual positives correctly identified, and specificity measures the percentage of actual negatives correctly identified. P(effect) = sensitivity p(cause) + (1- specificity)(1 - p(cause))
How does Bayes’ Rule help in medical diagnosis?
It allows calculation of the probability of a disease given a positive test result by considering both false positives and false negatives.
Why is causal knowledge more reliable than diagnostic knowledge?
Causal probabilities (e.g., P(Symptom | Disease)) remain stable, while diagnostic probabilities (e.g., ( P(Disease | Symptom)) may change due to external factors.
