Introduction to Statistical Relational Learning (Adaptive Computation and Machine Learning series)
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Handling inherent uncertainty and exploiting compositional structure are fundamental to understanding and designing large-scale systems. Statistical relational learning builds on ideas from probability theory and statistics to address uncertainty while incorporating tools from logic, databases and programming languages to represent structure. In Introduction to Statistical Relational Learning, leading researchers in this emerging area of machine learning describe current formalisms, models, and algorithms that enable effective and robust reasoning about richly structured systems and data. The early chapters provide tutorials for material used in later chapters, offering introductions to representation, inference and learning in graphical models, and logic. The book then describes object-oriented approaches, including probabilistic relational models, relational Markov networks, and probabilistic entity-relationship models as well as logic-based formalisms including Bayesian logic programs, Markov logic, and stochastic logic programs. Later chapters discuss such topics as probabilistic models with unknown objects, relational dependency networks, reinforcement learning in relational domains, and information extraction. By presenting a variety of approaches, the book highlights commonalities and clarifies important differences among proposed approaches and, along the way, identifies important representational and algorithmic issues. Numerous applications are provided throughout.Lise Getoor is Assistant Professor in the Department of Computer Science at the University of Maryland. Ben Taskar is Assistant Professor in the Computer and Information Science Department at the University of Pennsylvania.
assignments, and iteratively apply equations to the current values of the left-hand side to deﬁne a new value for the right-hand side. We initialize all of the δi→j ’s to 1, and then iteratively apply (2.8), computing the left-hand side δi→j of each equality in terms of the right-hand side (essentially converting each equality sign to an assignment). Clearly, a single iteration of this process does not usually suﬃce to make the equalities hold; however, under certain conditions (which hold in
distribution. 188.8.131.52 Generating Samples The burn-in time for a large Markov chain is often quite large. Thus, the naive algorithm described above has to execute a large number of sampling steps for 2.3 Inference 41 every usable sample. However, a key observation is that, if x(t) is sampled from π, then x(t+1) is also sampled from π. Thus, once we have run the chain long enough that we are sampling from the stationary distribution (or a distribution close to it), we can continue generating
us to make ﬁner distinctions when constructing a probabilistic model. In particular, they allow us to specialize CPDs for diﬀerent subclasses in the hierarchy. Deﬁnition 5.23 A probabilistic relational model with subclass hierarchy is deﬁned as follows. For each class X ∈ X , we have a class hierarchy H[X] = (C[X], ≺); a subclass indicator attribute X.Class such that V(X.Class) = C[(]H[X]); a CPD for X.Class; for each subclass c ∈ C[X] and attribute A ∈ A(X) we have either a set of parents Pac
school example, we can compute the suﬃcient statistics with the following SQL query: SELECT grade, intelligence, diﬃculty, count(*) FROM from registration, student, course GROUP BY grade, intelligence, diﬃculty In some cases, it is useful to materialize a view that can be used to compute the suﬃcient statistics. This is beneﬁcial when the relationship between the child attribute and the parent attribute is many-one rather than one-one or one-many. For example, consider the dependence of
natural language processing. Chapter 19 by Bunescu and Mooney shows how RMNs can be used for information extraction. An advantage of their approach is that inference and learning support “collective information extraction” in which dependencies between extractions are exploited. They present results on extracting protein names from biomedical abstracts. Chapter 20, by Roth and Yih, also investigates SRL approaches for information extraction, speciﬁcally for combining named entity and relation