Maximum Likelihood Distribution Graphs

Why

How to select distribution graphs.¹

Definition

Let $(G, A)$ be a typed graph on $\set{1, \dots , n}$. Let $S \subset \set{1, \dots , n}$. Let $x^1, \dots , x^n$ be a dataset in $A_S = \prod_{j \in S} A_j$ (see Function Graphs). The observation likelihood for this dataset is the observation distribution likelihood of the dataset $\prod_{i =1}^{n} p_S(x^i)$.

A maximum likelihood distribution graph is one that maximizes the observation likelihood. The maximum likelihood distribution graph with respect to a parametric distribution family is the member of the family that maximizes the observation likelihood.

1. Future editions will modify. ↩︎