信念伝播
Belief Propagation（BP）は、 algorithm used in the 人工知能の分野 and 機械学習 for performing inference on グラフモデル, particularly Bayesian networks and Markov random fields. These models represent complex relationships among variables using graphs, where nodes represent variables, and edges represent dependencies between them.
信念伝播の主な目的は、観測された証拠に基づいてネットワーク内の各変数の周辺確率を計算することです。これは、これらの確率を直接計算することが計算コストが高い、またはモデルの複雑さのために実行不可能な場合に特に有用です。
Belief Propagation operates by passing “messages” between nodes in the graph, where each message encodes information about the beliefs (probabilities) of the sending node regarding the state of the receiving node. This process continues iteratively until the messages converge, meaning that they no longer change significantly, at which point the algorithm can derive the marginal probabilities.
信念伝播には主に二つの形式があります：
- 和-積アルゴリズム： Used for computing marginal distributions by summing over possible values of 隠れ変数.
- 最大-積アルゴリズム： Used for computing the most probable configuration of the variables by taking the maximum instead of the sum.
Belief Propagation is particularly powerful in applications such as error-correcting codes, computer vision, and 自然言語処理. However, it is important to note that while BP can provide approximate solutions in many cases, it may not always converge or yield accurate results in graphs with cycles.