Content deleted Content added
Fgnievinski (talk | contribs) |
|||
| (6 intermediate revisions by 4 users not shown) | |||
Line 3:
{{Machine learning|Structured prediction}}
{{More footnotes|date=May 2017}}
A '''graphical model''' or '''probabilistic graphical model''' ('''PGM''') or '''structured probabilistic model''' is a [[probabilistic model]] for which a [[Graph (discrete mathematics)|graph]] expresses the [[conditional dependence]] structure between [[random variable]]s.
==Types
Generally, probabilistic graphical models use a graph-based representation as the foundation for encoding a distribution over a multi-dimensional space and a graph that is a compact or [[Factor graph|factorized]] representation of a set of independences that hold in the specific distribution. Two branches of graphical representations of distributions are commonly used, namely, [[Bayesian network]]s and [[Markov random field]]s. Both families encompass the properties of factorization and independences, but they differ in the set of independences they can encode and the factorization of the distribution that they induce.<ref name=koller09>{{cite book
|author=Koller, D.
Line 25:
===Undirected Graphical Model===
[[File:Examples of an Undirected Graph.svg|thumb|alt=An undirected graph with four vertices.|An undirected graph with four vertices
The undirected graph shown may have one of several interpretations; the common feature is that the presence of an edge implies some sort of dependence between the corresponding random variables. From this graph, we might deduce that B, C, and D are all [[Conditional independence|conditionally independent]] given A. This means that if the value of A is known, then the values of B, C, and D provide no further information about each other. Equivalently (in this case), the joint probability distribution can be factorized as:
:<math>P[A,B,C,D] = f_{AB}[A,B] \cdot f_{AC}[A,C] \cdot f_{AD}[A,D]</math>
Line 36:
{{main|Bayesian network}}
[[File:Example of a Directed Graph.svg|thumb|alt=Example of a directed acyclic graph on four vertices.|Example of a directed acyclic graph on four vertices
Line 65:
|title=Proceedings of the Twelfth Conference on Uncertainty in Artificial Intelligence
|year=1996
|publisher=Morgan Kaufmann Pub.
|isbn=978-1-55860-412-4
}}
Line 72 ⟶ 73:
*[[Dependency network (graphical model)|Dependency network]] where cycles are allowed
*Tree-augmented classifier or '''TAN model'''
[[File:Tan corral.png|thumb| TAN model for "corral dataset"
*Targeted Bayesian network learning (TBNL) [[File:Tbnl corral.jpg|thumb|TBNL model for "corral dataset"]]
*A [[factor graph]] is an undirected [[bipartite graph]] connecting variables and factors. Each factor represents a function over the variables it is connected to. This is a helpful representation for understanding and implementing [[belief propagation]].
| |||