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29 Terms
1
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Q: Why do we need probability in AI?
To handle partial observability, noisy sensors, uncertain action outcomes, and the complexity of real worlds (e.g., airport-on-time example).
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Q: Two reasons probabilistic assertions are useful?
Laziness (don’t enumerate every exception) and ignorance (don’t know all facts/initial conditions).
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Q: What is subjective probability?
Probabilities reflect the agent’s state of knowledge and update with evidence (e.g., time of day, accident reports).
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Q: What combines with probability to choose actions?
Utility theory; together with probability it forms decision theory.
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Q: Example trade-off in airport story?
Risk of missing the flight vs. time wasted waiting earlier.
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Q: What’s a random variable?
A symbol with a domain of mutually exclusive, exhaustive values (e.g., Weather ∈ {sunny, rainy, cloudy, snow}).
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Q: What’s an elementary proposition?
Assigning a value to a variable (e.g., Weather=sunny).
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Q: What’s an atomic event?
A complete assignment to all variables; atomic events are mutually exclusive and exhaustive.
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Q: Core probability axioms?
0 ≤ P(A) ≤ 1; P(true)=1; P(false)=0; P(A∨B)=P(A)+P(B)−P(A∧B).
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Q: What is a prior probability?
Belief before new evidence (e.g., P(Cavity=true)=0.1).
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Q: What is a probability distribution?
Values for all outcomes of a variable; sums to 1.
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Q: What is a joint distribution?
Probabilities for every atomic event over multiple variables; in principle answers any query.
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Q: Definition of conditional probability?
P(a|b) = P(a∧b)/P(b), if P(b)>0.
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Q: Product rule?
P(a∧b)=P(a|b)P(b)=P(b|a)P(a).
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Q: Chain rule (informal)?
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Q: How to compute P(φ) from the joint?
Sum probabilities of all atomic events where φ is true.
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Q: How to compute conditionals by enumeration?
Compute joint for query+evidence, then normalize over query values (denominator acts as normalization constant α).
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Q: Independence definition (any of three equivalent forms)?
P(A|B)=P(A), or P(B|A)=P(B), or P(A,B)=P(A)P(B).
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Q: Why is independence powerful?
Reduces parameters—from exponential to linear in favorable cases.
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Q: Conditional independence (Toothache, Catch, Cavity) example?
Catch ⟂ Toothache | Cavity, i.e., P(Catch|Toothache,Cavity)=P(Catch|Cavity).
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Q: Factorization using conditional independence?
P(Toothache,Catch,Cavity)=P(Toothache|Cavity)·P(Catch|Cavity)·P(Cavity).
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Q: Bayes’ rule (scalar form)?
P(a|b)=P(b|a)P(a)/P(b).
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Q: Why is Bayes’ rule useful?
Turns causal probabilities into diagnostic ones (e.g., P(Cause|Effect) from P(Effect|Cause)).
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Q: Medical toy example insight (meningitis & stiff neck)?
Even with high sensitivity, a rare disease keeps a small posterior (base rates matter).
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Q: Naïve Bayes assumption?
Effects are conditionally independent given the single cause.
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Q: Naïve Bayes joint form?
P(Cause,Effect₁,…,Effectₙ) = P(Cause)·∏ᵢ P(Effectᵢ|Cause).
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Q: Why is Naïve Bayes attractive?
Linear number of parameters; surprisingly effective despite strong independence assumptions.
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Q: Core pipeline for answering queries with enumeration?
Fix evidence → sum out hidden variables → normalize over query variable(s).
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Q: Big picture of independence tools?
Independence and conditional independence shrink representation and inference complexity—crucial beyond toy domains.
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