We consider the problem of structured classification, where the task is to predict a label y from an input x, and y has meaningful internal structure. Ourframework includes supervised training of Markov random fields and weighted context-free grammars as special cases. We describe an algorithm that solves the large-margin optimization problem defined in [12], using an exponential-family (Gibbs distribution) representation of structured objects. The algorithm is efficient--even in cases where the number of labels y is exponential in size--provided that certain expectations underGibbs distributions can be calculated efficiently. The method for structured labels relies on a more general result, specifically the application ofexponentiated gradient updates [7, 8] to quadratic programs.

Many real-world domains are relational in nature, consisting of a set of objects related to each other in complex ways. This paper focuses on predicting the existence and the type of links between entities in such domains. We apply the relational Markov network framework of Taskar et al. to define a joint probabilistic model over the entire link graph -- entity attributes and links. The application of the RMN algorithm to this task requires the definition of probabilistic patterns over subgraph structures. We apply this method to two new relational datasets, one involving university webpages, and the other a social network. We show that the collective classification approach of RMNs, and the introduction of subgraph patterns over link labels, provide significant improvements in accuracy over flat classification, which attempts to predict each link in isolation.

In typical classification tasks, we seek a function which assigns a label to a single object.Kernel-based approaches, such as support vector machines (SVMs), which maximize the margin of confidence of the classifier, are the method of choice for many such tasks. Their popularity stems both from the ability to use high-dimensional feature spaces, and from their strong theoretical guarantees. However,many real-world tasks involve sequential, spatial, or structured data, where multiple labels must be assigned. Existing kernel-based methods ignore structurein the problem, assigning labels independently to each object, losing much useful information. Conversely, probabilistic graphical models, such as Markov networks, can represent correlations between labels, by exploiting problem structure, but cannot handle high-dimensional feature spaces, and lack strong theoretical generalization guarantees.

Many real-world domains are relational in nature, consisting of a set of objects related to each other in complex ways. This paper focuses on predicting the existence and the type of links between entities in such domains. We apply the relational Markov network framework of Taskar et al. to define a joint probabilistic modelover the entire link graph -- entity attributes and links. The application of the RMN algorithm to this task requires the definition of probabilistic patterns over subgraph structures. We apply this method to two new relational datasets, one involving university webpages, and the other a social network. We show that the collective classification approach of RMNs, and the introduction of subgraph patterns over link labels, provide significant improvements in accuracy over flat classification, which attempts to predict each link in isolation.