We present a fast online solver for large scale maximum-flow problems as they occur in portfolio optimization, inventory management, computer vision, and logistics. Our algorithm solves an integer linear program in an online fashion. It exploits total unimodularity of the constraint matrix and a Lagrangian relaxation to solve the problem as a convex online game. The algorithm generates approximate solutions of max-flow problems by performing stochastic gradient descent on a set of flows. We apply the algorithm to optimize tier arrangement of over 80 Million web pages on a layered set of caches to serve an incoming query stream optimally. We provide an empirical demonstration of the effectiveness of our method on real query-pages data.

To understand the relationship between genomic variations among population and complex diseases, it is essential to detect eQTLs which are associated with phenotypic effects. However, detecting eQTLs remains a challenge due to complex underlying mechanisms and the very large number of genetic loci involved compared to the number of samples. Thus, to address the problem, it is desirable to take advantage of the structure of the data and prior information about genomic locations such as conservation scores and transcription factor binding sites. In this paper, we propose a novel regularized regression approach for detecting eQTLs which takes into account related traits simultaneously while incorporating many regulatory features. We first present a Bayesian network for a multi-task learning problem that includes priors on SNPs, making it possible to estimate the significance of each covariate adaptively.

We analyse matching pursuit for kernel principal components analysis by proving that the sparse subspace it produces is a sample compression scheme. We show that this bound is tighter than the KPCA bound of Shawe-Taylor et al swck-05 and highly predictive of the size of the subspace needed to capture most of the variance in the data. We analyse a second matching pursuit algorithm called kernel matching pursuit (KMP) which does not correspond to a sample compression scheme. However, we give a novel bound that views the choice of subspace of the KMP algorithm as a compression scheme and hence provide a VC bound to upper bound its future loss. Finally we describe how the same bound can be applied to other matching pursuit related algorithms.

Regularized risk minimization often involves non-smooth optimization, either because of the loss function (e.g., hinge loss) or the regularizer (e.g., $\ell_1$-regularizer). Gradient descent methods, though highly scalable and easy to implement, are known to converge slowly on these problems. In this paper, we develop novel accelerated gradient methods for stochastic optimization while still preserving their computational simplicity and scalability. The proposed algorithm, called SAGE (Stochastic Accelerated GradiEnt), exhibits fast convergence rates on stochastic optimization with both convex and strongly convex objectives. Experimental results show that SAGE is faster than recent (sub)gradient methods including FOLOS, SMIDAS and SCD.

It has been established that the second-order stochastic gradient descent (2SGD) method can potentially achieve generalization performance as well as empirical optimum in a single pass (i.e., epoch) through the training examples. However, 2SGD requires computing the inverse of the Hessian matrix of the loss function, which is prohibitively expensive. This paper presents Periodic Step-size Adaptation (PSA), which approximates the Jacobian matrix of the mapping function and explores a linear relation between the Jacobian and Hessian to approximate the Hessian periodically and achieve near-optimal results in experiments on a wide variety of models and tasks. Papers published at the Neural Information Processing Systems Conference.

Locality information is crucial in datasets where each variable corresponds to a measurement in a manifold (silhouettes, motion trajectories, 2D and 3D images). Although these datasets are typically under-sampled and high-dimensional, they often need to be represented with low-complexity statistical models, which are comprised of only the important probabilistic dependencies in the datasets. Most methods attempt to reduce model complexity by enforcing structure sparseness. However, sparseness cannot describe inherent regularities in the structure. Hence, in this paper we first propose a new class of Gaussian graphical models which, together with sparseness, imposes local constancy through ${\ell}_1$-norm penalization.

Recently, supervised dimensionality reduction has been gaining attention, owing to the realization that data labels are often available and strongly suggest important underlying structures in the data. In this paper, we present a novel convex supervised dimensionality reduction approach based on exponential family PCA and provide a simple but novel form to project new testing data into the embedded space. This convex approach successfully avoids the local optima of the EM learning. Moreover, by introducing a sample-based multinomial approximation to exponential family models, it avoids the limitation of the prevailing Gaussian assumptions of standard PCA, and produces a kernelized formulation for nonlinear supervised dimensionality reduction. A training algorithm is then devised based on a subgradient bundle method, whose scalability can be gained through a coordinate descent procedure.

We consider the problem of binary classification where the classifier may abstain instead of classifying each observation. The Bayes decision rule for this setup, known as Chow's rule, is defined by two thresholds on posterior probabilities. From simple desiderata, namely the consistency and the sparsity of the classifier, we derive the double hinge loss function that focuses on estimating conditional probabilities only in the vicinity of the threshold points of the optimal decision rule. We show that, for suitable kernel machines, our approach is universally consistent. We cast the problem of minimizing the double hinge loss as a quadratic program akin to the standard SVM optimization problem and propose an active set method to solve it efficiently.

Second-order maximum-entropy models have recently gained much interest for describing the statistics of binary spike trains. Here, we extend this approach to take continuous stimuli into account as well. By constraining the joint second-order statistics, we obtain a joint Gaussian-Boltzmann distribution of continuous stimuli and binary neural firing patterns, for which we also compute marginal and conditional distributions. This model has the same computational complexity as pure binary models and fitting it to data is a convex problem. We show that the model can be seen as an extension to the classical spike-triggered average/covariance analysis and can be used as a non-linear method for extracting features which a neural population is sensitive to.

While many perceptual and cognitive phenomena are well described in terms of Bayesian inference, the necessary computations are intractable at the scale of real-world tasks, and it remains unclear how the human mind approximates Bayesian inference algorithmically. We explore the proposal that for some tasks, humans use a form of Markov Chain Monte Carlo to approximate the posterior distribution over hidden variables. As a case study, we show how several phenomena of perceptual multistability can be explained as MCMC inference in simple graphical models for low-level vision. Papers published at the Neural Information Processing Systems Conference.