Bethe Projections for Non-Local Inference

Many inference problems in structured prediction are naturally solved by augmenting a tractable dependency structure with complex, non-local auxiliary objectives. This includes the mean field family of variational inference algorithms, soft- or hard-constrained inference using Lagrangian relaxation or linear programming, collective graphical models, and forms of semi-supervised learning such as posterior regularization. We present a method to discriminatively learn broad families of inference objectives, capturing powerful non-local statistics of the latent variables, while maintaining tractable and provably fast inference using non-Euclidean projected gradient descent with a distance-generating function given by the Bethe entropy. We demonstrate the performance and flexibility of our method by (1) extracting structured citations from research papers by learning soft global constraints, (2) achieving state-of-the-art results on a widely-used handwriting recognition task using a novel learned non-convex inference procedure, and (3) providing a fast and highly scalable algorithm for the challenging problem of inference in a collective graphical model applied to bird migration.Comment: minor bug fix to appendix. appeared in UAI 201

Pairwise Learning via Stagewise Training in Proximal Setting

The pairwise objective paradigms are an important and essential aspect of machine learning. Examples of machine learning approaches that use pairwise objective functions include differential network in face recognition, metric learning, bipartite learning, multiple kernel learning, and maximizing of area under the curve (AUC). Compared to pointwise learning, pairwise learning's sample size grows quadratically with the number of samples and thus its complexity. Researchers mostly address this challenge by utilizing an online learning system. Recent research has, however, offered adaptive sample size training for smooth loss functions as a better strategy in terms of convergence and complexity, but without a comprehensive theoretical study. In a distinct line of research, importance sampling has sparked a considerable amount of interest in finite pointwise-sum minimization. This is because of the stochastic gradient variance, which causes the convergence to be slowed considerably. In this paper, we combine adaptive sample size and importance sampling techniques for pairwise learning, with convergence guarantees for nonsmooth convex pairwise loss functions. In particular, the model is trained stochastically using an expanded training set for a predefined number of iterations derived from the stability bounds. In addition, we demonstrate that sampling opposite instances at each iteration reduces the variance of the gradient, hence accelerating convergence. Experiments on a broad variety of datasets in AUC maximization confirm the theoretical results.Comment: 10 Page

A survey of cost-sensitive decision tree induction algorithms

The past decade has seen a significant interest on the problem of inducing decision trees that take account of costs of misclassification and costs of acquiring the features used for decision making. This survey identifies over 50 algorithms including approaches that are direct adaptations of accuracy based methods, use genetic algorithms, use anytime methods and utilize boosting and bagging. The survey brings together these different studies and novel approaches to cost-sensitive decision tree learning, provides a useful taxonomy, a historical timeline of how the field has developed and should provide a useful reference point for future research in this field