We also find hyperparameters of the covariance function in the same joint optimization.

Sparse PCA seeks approximate sparse "eigenvectors" whose projections capture the maximal variance of data. As a cardinality-constrained and non-convex optimization problem, it is NPhard and is encountered in a wide range of applied fields, from bio-informatics to finance. Recent progress has focused mainly on continuous approximation and convex relaxation of the hard cardinality constraint. In contrast, we consider an alternative discrete spectral formulation based on variational eigenvalue bounds and provide an effective greedy strategy as well as provably optimal solutions using branch-and-bound search. Moreover, the exact methodology used reveals a simple renormalization step that improves approximate solutions obtained by any continuous method. The resulting performance gain of discrete algorithms is demonstrated on real-world benchmark data and in extensive Monte Carlo evaluation trials.

This paper presents a rigorous statistical analysis characterizing regimes in which active learning significantly outperforms classical passive learning. Activelearning algorithms are able to make queries or select sample locations in an online fashion, depending on the results of the previous queries. In some regimes, this extra flexibility leads to significantly faster rates of error decay than those possible in classical passive learning settings. Thenature of these regimes is explored by studying fundamental performance limits of active and passive learning in two illustrative nonparametric function classes. In addition to examining the theoretical potentialof active learning, this paper describes a practical algorithm capable of exploiting the extra flexibility of the active setting and provably improvingupon the classical passive techniques. Our active learning theory and methods show promise in a number of applications, including field estimation using wireless sensor networks and fault line detection.

Diffusion Tensor Magnetic Resonance Imaging (DT-MRI) is a non invasive methodfor brain neuronal fibers delineation. Here we show a modification forDT-MRI that allows delineation of neuronal fibers which are infiltrated by edema. We use the Muliple Tensor Variational (MTV) framework which replaces the diffusion model of DT-MRI with a multiple componentmodel and fits it to the signal attenuation with a variational regularizationmechanism. In order to reduce free water contamination weestimate the free water compartment volume fraction in each voxel, remove it, and then calculate the anisotropy of the remaining compartment.

We present a computational model of human eye movements in an object classdetection task. The model combines state-of-the-art computer vision object class detection methods (SIFT features trained using AdaBoost) witha biologically plausible model of human eye movement to produce a sequence of simulated fixations, culminating with the acquisition ofa target. We validated the model by comparing its behavior to the behavior of human observers performing the identical object class detection task (looking for a teddy bear among visually complex nontarget objects).We found considerable agreement between the model and human data in multiple eye movement measures, including number of fixations, cumulative probability of fixating the target, and scanpath distance.

Recurrent networks that perform a winner-take-all computation have been studied extensively. Although some of these studies include spiking networks,they consider only analog input rates. We present results of this winner-take-all computation on a network of integrate-and-fire neurons which receives spike trains as inputs. We show how we can configure theconnectivity in the network so that the winner is selected after a predetermined number of input spikes. We discuss spiking inputs with both regular frequencies and Poisson-distributed rates. The robustness of the computation was tested by implementing the winner-take-all network on an analog VLSI array of 64 integrate-and-fire neurons which have an innate variance in their operating parameters.

We analyze classification error on unseen cases, i.e. cases that are different fromthose in the training set. Unlike standard generalization error, this off-training-set error may differ significantly from the empirical error withhigh probability even with large sample sizes. We derive a datadependent boundon the difference between off-training-set and standard generalization error. Our result is based on a new bound on the missing mass, which for small samples is stronger than existing bounds based on Good-Turing estimators. As we demonstrate on UCI data-sets, our bound gives nontrivial generalization guarantees in many practical cases. In light of these results, we show that certain claims made in the No Free Lunch literature are overly pessimistic.

Sets", we consider the problem of retrieving items from a concept or cluster, given a query consisting of a few items from that cluster. We formulate this as a Bayesian inference problem and describe avery simple algorithm for solving it. Our algorithm uses a modelbased concept of a cluster and ranks items using a score which evaluates the marginal probability that each item belongs to a cluster containing the query items. For exponential family models with conjugate priors this marginal probability is a simple function of sufficient statistics. We focus on sparse binary data and show that our score can be evaluated exactly usinga single sparse matrix multiplication, making it possible to apply our algorithm to very large datasets. We evaluate our algorithm on three datasets: retrieving movies from EachMovie, finding completions of author sets from the NIPS dataset, and finding completions of sets of words appearing in the Grolier encyclopedia.

This paper proposes an algorithm to convert a T -stage stochastic decision problem with a continuous state space to a sequence of supervised learning problems.The optimization problem associated with the trajectory tree and random trajectory methods of Kearns, Mansour, and Ng, 2000, is solved using the Gauss-Seidel method. The algorithm breaks a multistage reinforcementlearning problem into a sequence of single-stage reinforcement learningsubproblems, each of which is solved via an exact reduction to a weighted-classification problem that can be solved using off-the-self methods. Thus the algorithm converts a reinforcement learning probleminto simpler supervised learning subproblems. It is shown that the method converges in a finite number of steps to a solution that cannot be further improved by componentwise optimization. The implication ofthe proposed algorithm is that a plethora of classification methods can be applied to find policies in the reinforcement learning problem.

We propose consensus propagation, an asynchronous distributed protocol for averaging numbers across a network.