Theproblem of support union recovery is to recover the subset of covariates that are active in at least one of the regression problems.

Motivated by applications like elections, webpage ranking, revenue maximization etc.,we consider the question of inferring popular rankings using constrained data. More specifically, we consider the problem of inferring a probability distribution overthe group of permutations using its first order marginals. We first prove that it is not possible to recover more than O(n) permutations over n elements withthe given information. We then provide a simple and novel algorithm that can recover up to O(n) permutations under a natural stochastic model; in this sense, the algorithm is optimal. In certain applications, the interest is in recovering onlythe most popular (or mode) ranking. As a second result, we provide an algorithm based on the Fourier Transform over the symmetric group to recover the mode under a natural majority condition; the algorithm turns out to be a maximum weightmatching on an appropriately defined weighted bipartite graph. The questions considered are also thematically related to Fourier Transforms over the symmetric group and the currently popular topic of compressed sensing.

Recent research suggests that neural systems employ sparse coding. However, there is limited theoretical understanding of fundamental resolution limits in such sparse coding. This paper considers a general sparse estimation problem of detecting the sparsity pattern of a $k$-sparse vector in $\R^n$ from $m$ random noisy measurements. Our main results provide necessary and sufficient conditions on the problem dimensions, $m$, $n$ and $k$, and the signal-to-noise ratio (SNR) for asymptotically-reliable detection. We show a necessary condition for perfect recovery at any given SNR for all algorithms, regardless of complexity, is $m = \Omega(k\log(n-k))$ measurements. This is considerably stronger than all previous necessary conditions. We also show that the scaling of $\Omega(k\log(n-k))$ measurements is sufficient for a trivial ``maximum correlation'' estimator to succeed. Hence this scaling is optimal and does not require lasso, matching pursuit, or more sophisticated methods, and the optimal scaling can thus be biologically plausible.

We report a compact realization of short-term depression (STD) in a VLSI stochastic synapse. The behavior of the circuit is based on a subtractive single release model of STD. Experimental results agree well with simulation and exhibit expected STD behavior: the transmitted spike train has negative autocorrelation and lower power spectral density at low frequencies which can remove redundancy in the input spike train, and the mean transmission probability is inversely proportional to the input spike rate which has been suggested as an automatic gain control mechanism in neural systems. The dynamic stochastic synapse could potentially be a powerful addition to existing deterministic VLSI spiking neural systems.

We study the convergence and the rate of convergence of a local manifold learning algorithm: LTSA [13]. The main technical tool is the perturbation analysis on the linear invariant subspace that corresponds to the solution of LTSA. We derive a worst-case upper bound of errors for LTSA which naturally leads to a convergence result. We then derive the rate of convergence for LTSA in a special case.

We propose Dirichlet-Bernoulli Alignment (DBA), a generative model for corpora in which each pattern (e.g., a document) contains a set of instances (e.g., paragraphs in the document) and belongs to multiple classes. By casting predefined classes as latent Dirichlet variables (i.e., instance level labels), and modeling the multi-label of each pattern as Bernoulli variables conditioned on the weighted empirical average of topic assignments, DBA automatically aligns the latent topics discovered from data to human-defined classes. DBA is useful for both pattern classification and instance disambiguation, which are tested on text classification and named entity disambiguation for web search queries respectively.

Classical Game Theoretic approaches that make strong rationality assumptions have difficulty modeling observed behaviour in Economic games of human subjects. We investigate the role of finite levels of iterated reasoning and non-selfish utility functions in a Partially Observable Markov Decision Process model that incorporates Game Theoretic notions of interactivity. Our generative model captures a broad class of characteristic behaviours in a multi-round Investment game. We invert the generative process for a recognition model that is used to classify 200 subjects playing an Investor-Trustee game against randomly matched opponents.

We present a sparse approximation approach for dependent output Gaussian processes (GP). Employing a latent function framework, we apply the convolution process formalism to establish dependencies between output variables, where each latent function is represented as a GP. Based on these latent functions, we establish an approximation scheme using a conditional independence assumption between the output processes, leading to an approximation of the full covariance which is determined by the locations at which the latent functions are evaluated. We show results of the proposed methodology for synthetic data and real world applications on pollution prediction and a sensor network.

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. Moreover, SAGE can also be extended for online learning, resulting in a simple but powerful algorithm.

We show how to model documents as bags of words using family of two-layer, undirected graphical models. Each member of the family has the same number of binary hidden units but a different number of ``softmax visible units. All of the softmax units in all of the models in the family share the same weights to the binary hidden units. We describe efficient inference and learning procedures for such a family. Each member of the family models the probability distribution of documents of a specific length as a product of topic-specific distributions rather than as a mixture and this gives much better generalization than Latent Dirichlet Allocation for modeling the log probabilities of held-out documents. The low-dimensional topic vectors learned by the undirected family are also much better than LDA topic vectors for retrieving documents that are similar to a query document. The learned topics are more general than those found by LDA because precision is achieved by intersecting many general topics rather than by selecting a single precise topic to generate each word.