CS188 Notes II
BN
Inference
Inference by enumeration
- Select the entries consisitent with the evidence.
- Sum out H (Hidden variables) to get joint of Query and evidence
- Normalize
Variable Elimination
- Op 1: Join Factors
- Op 2: Eliminiate (Marginalizing Early)
- Op 3: Normalize
Sampling
Prior sampling
- 根据贝叶斯网络的拓扑排序，从根节点开始，按照条件概率分布逐步生成样本。
- 适用于贝叶斯网络的联合分布抽样，但可能导致低效样本（例如，许多样本不符合证据）。
Rejection sampling
- 先按照直接采样生成样本，然后拒绝不符合证据变量的样本。
- 适用于查询条件概率 P(X∣E)P(X | E)P(X∣E)，
Likelilhood weighting
- 固定证据变量 E，只对非证据变量进行采样。
- E 的概率贡献度为
- 每个样本权重是所有概率贡献度乘积
Gibbs sampling
Procedure：Keep track of a full instantiation x 1, x 2, …, xn. Start with an arbitrary instantiation consistent with the evidence. Sample one variable at a time, conditioned on all the rest, but keep evidence fixed. Keep repeating this for a long time.
example:
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