The partition function plays a key role in probabilistic modeling including conditional random fields, graphical models, and maximum likelihood estimation. To optimize partition functions, this article introduces a quadratic variational upper bound. This inequality facilitates majorization methods: optimization of complicated functions through the iterative solution of simpler sub-problems. Such bounds remain efficient to compute even when the partition function involves a graphical model (with small tree-width) or in latent likelihood settings. For large-scale problems, low-rank versions of the bound are provided and outperform LBFGS as well as first-order methods. Several learning applications are shown and reduce to fast and convergent update rules. Experimental results show advantages over state-of-the-art optimization methods.

This paper proposes a novel boosting algorithm called VadaBoost which is motivated by recent empirical Bernstein bounds. VadaBoost iteratively minimizes a cost function that balances the sample mean and the sample variance of the exponential loss. Each step of the proposed algorithm minimizes the cost efficiently by providing weighted data to a weak learner rather than requiring a brute force evaluation of all possible weak learners. Thus, the proposed algorithm solves a key limitation of previous empirical Bernstein boosting methods which required brute force enumeration of all possible weak learners. Experimental results confirm that the new algorithm achieves the performance improvements of EBBoost yet goes beyond decision stumps to handle any weak learner. Significant performance gains are obtained over AdaBoost for arbitrary weak learners including decision trees (CART).

Many real-world networks are described by both connectivity information and features for every node. To better model and understand these networks, we present structure preserving metric learning (SPML), an algorithm for learning a Mahalanobis distance metric from a network such that the learned distances are tied to the inherent connectivity structure of the network. Like the graph embedding algorithm structure preserving embedding, SPML learns a metric which is structure preserving, meaning a connectivity algorithm such as k-nearest neighbors will yield the correct connectivity when applied using the distances from the learned metric. We show a variety of synthetic and real-world experiments where SPML predicts link patterns from node features more accurately than standard techniques. We further demonstrate a method for optimizing SPML based on stochastic gradient descent which removes the running-time dependency on the size of the network and allows the method to easily scale to networks of thousands of nodes and millions of edges.

In classification problems, Support Vector Machines maximize the margin of separation between two classes. While the paradigm has been successful, the solution obtained by SVMs is dominated by the directions with large data spread and biased to separate the classes by cutting along large spread directions. This article proposes a novel formulation to overcome such sensitivity and maximizes the margin relative to the spread of the data. The proposed formulation can be efficiently solved and experiments on digit datasets show drastic performance improvements over SVMs.

A method is proposed for semiparametric estimation where parametric and nonparametric criteria are exploited in density estimation and unsupervised learning.

Two algorithmic implementations of the method are formalized.

We propose a new method for constructing hyperkenels and define two promising special cases that can be computed in closed form. These we call the Gaussian and Wishart hyperkernels. The former is especially attractive in that it has an interpretable regularization scheme reminiscent of that of the Gaussian RBF kernel. We discuss how kernel learning can be used not just for improving the performance of classification and regression methods, but also as a stand-alone algorithm for dimensionality reduction and relational or metric learning.

We present a method for localizing and separating sound sources in stereo recordings thatis robust to reverberation and does not make any assumptions about the source statistics. The method consists of a probabilistic model of binaural multisource recordingsand an expectation maximization algorithm for finding the maximum likelihood parameters of that model. These parameters include distributions over delays and assignments of time-frequency regions to sources. We evaluate this method against two comparable algorithms on simulations of simultaneous speech from two or three sources. Our method outperforms the others in anechoic conditionsand performs as well as the better of the two in the presence of reverberation.

Recent years have seen the development of several approaches to kernel learning [5] [1]

Jensen's inequality is a powerful mathematical tool and one of the workhorses in statistical learning. Its applications therein include the EM algorithm, Bayesian estimation and Bayesian inference. Jensen computes simple lower bounds on otherwise intractable quantities such as products of sums and latent log-likelihoods. This simplification then permits operations like integration and maximization. Quite often (i.e. in discriminative learning) upper bounds are needed as well. We derive and prove an efficient analytic inequality that provides such variational upper bounds. This inequality holds for latent variable mixtures of exponential family distributions and thus spans a wide range of contemporary statistical models. We also discuss applications of the upper bounds including maximum conditional likelihood, large margin discriminative models and conditional Bayesian inference. Convergence, efficiency and prediction results are shown.