Probabilistic Graphical Model 1.3節 - Part 1

以下內容是我閱讀Probabilistic Graphical Model, Koller 2009一書的讀書筆記，未來將不定期新增內容，此技術屬AI人工智慧範疇。

1.3 Overview and Roadmap

We begin in part I, by describing the most basic type of graphical models, which are the focus of most of the book. These models encode distributions over a fixed set of random variables. We describe how graphs can be used to encode distributions over such spaces, and what the properties of such distributions are.

• In chapter 3, we describe the Bayesian network representation, based on directed graphs. We describe how a Bayesian network can encode a probability distribution. We also analyze the independence properties induced by the graph structure.

• In chapter 4, we move to Markov networks, the other main category of probabilistic graphical models. Here also we describe the independencies defined by the graph and the induced factorization of the distribution. We also discuss the relationship between Markov networks and Bayesian networks, and briefly describe a framework that unifies both.

• In chapter 5, we delve a little deeper into the representation of the parameters in probabilistic models, focusing mostly on Bayesian networks, whose parameterization is more constrained. We describe representations that capture some of the finer-grained structure of the distribution, and show that, here also, capturing structure can provide significant gains.

• In chapter 6, we turn to formalisms that extend the basic framework of probabilistic graphical models to settings where the set of variables is no longer rigidly circumscribed in advance. One such setting is a temporal one, where we wish to model a system whose state evolves over time, requiring us to consider distributions over entire trajectories, We describe a compact representation — a dynamic Bayesian network — that allows us to represent structured systems that evolve over time. We then describe a family of extensions that introduce various forms of higher level structure into the framework of probabilistic graphical models. Specifically, we focus on domains containing objects (whether concrete or abstract), characterized by attributes, and related to each other in various ways. Such domains can include repeated structure, since different objects of the same type share the same probabilistic model. These languages provide a significant extension to the expressive power of the standard graphical models.

• In chapter 7, we take a deeper look at models that include continuous variables. Specifically, we explore the properties of the multivariate Gaussian distribution and the representation of such distributions as both directed and undirected graphical models. Although the class of Gaussian distributions is a limited one and not suitable for all applications, it turns out to play a critical role even when dealing with distributions that are not Gaussian.

• In chapter 8, we take a deeper, more technical look at probabilistic models, defining a general framework called the exponential family, that encompasses a broad range of distributions. This chapter provides some basic concepts and tools that will turn out to play an important role in later development.