Efficient training methods for conditional random fields
Many applications require predicting not a just a single variable, but multiple variables that depend on each other. Recent attention has therefore focused on structured prediction methods, which combine the modeling flexibility of graphical models with the ability to employ complex, dependent features typical of traditional classification methods. Especially popular have been conditional random fields (CRFs), which are graphical models of the conditional distribution over outputs given a set of observed features. Unfortunately, parameter estimation in CRFs requires repeated inference, which can be computationally expensive. Complex graphical structures are increasingly desired in practical applications, but then training time often becomes prohibitive.
In this thesis, I investigate efficient training methods for conditional random fields with complex graphical structure, focusing on local methods which avoid propagating information globally along the graph. First, I investigate piecewise training, which trains each of a model's factors separately. I present three views of piecewise training: as maximizing the likelihood in a so-called "node-split graph", as maximizing the Bethe likelihood with uniform messages, and as generalizing the pseudo-moment matching estimator of Wainwright et al. . Second, I propose piecewise pseudolikelihood, a hybrid procedure which "pseudolikelihood-izes" the piecewise likelihood, and is therefore more efficient if the variables have large cardinality. Piecewise pseudolikelihood performs well even on applications in which standard pseudolikelihood performs poorly. Finally, motivated by the connection between piecewise training and BP, I explore training methods using beliefs arising from stopping BP before convergence. I propose a new schedule for message propagation that improves upon the dynamic schedule proposed recently by Elidan et al. , and present suggestive results applying dynamic schedules to the system of equations that combine inference and learning.
I also present two novel families of loopy CRFs, which appear as test cases throughout. First is the dynamic CRF, which combines the factorized state representation of dynamic Bayesian networks with the modeling flexibility of conditional models. The second of these is the skip-chain CRF, which models the fact that identical words are likely to have the same label, even if they occur far apart.