CS 6782: Fall 2010 Probabilistic Graphical Models
نویسنده
چکیده
In a probabilistic graphical model, each node represents a random variable, and the links express probabilistic relationships between these variables. The structure that graphical models exploit is the independence properties that exist in many real-world phenomena. The graph then captures the way in which the joint distribution over all of the random variables can be decomposed into a product of factors each depending only on a subset of the variables. Directed graphs are useful for expressing causal relationships between random variables, whereas undirected graphs are better suited to expressing soft constraints between random variables. When we apply a graphical model to a problem in machine learning problem, we will typically set some of the random variables to specific values, as observed variables. Other unobserved variables would be latent variables. The primary role of the latent variables is to allow a complicated distribution over the observed variables to be represented in terms of a model constructed from simpler (typically exponential family) conditional distributions. Generally speaking, with no independence captured in the graph (i.e., the graph is complete), the parameter size would be exponential to the number of latent variables. There are several ways to reduce the independent parameter dimensionality: 1) add independence assumptions, i.e., remove links in the graph, 2) share parameters, also known as tying of parameters, 3) use parameterized models for the conditional distributions instead of complete tables of conditional probability values.
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تاریخ انتشار 2010