The Indian buffet process (IBP) is an exchangeable distribution over binary matrices used in Bayesian nonparametric featural models. In this paper we propose a three-parameter generalization of the IBP exhibiting power-law behavior. We achieve this by generalizing the beta process (the de Finetti measure of the IBP) to the \emph{stable-beta process} and deriving the IBP corresponding to it. We find interesting relationships between the stable-beta process and the Pitman-Yor process (another stochastic process used in Bayesian nonparametric models with interesting power-law properties). We show that our power-law IBP is a good model for word occurrences in documents with improved performance over the normal IBP.

Query expansion is a long-studied approach for improving retrieval effectiveness by enhancing the user's original query with additional related words. Current algorithms for automatic query expansion can often improve retrieval accuracy on average, but are not robust: that is, they are highly unstable and have poor worst-case performance for individual queries. To address this problem, we introduce anovel formulation of query expansion as a convex optimization problem over a word graph. The model combines initial weights from a baseline feedback algorithmwith edge weights based on word similarity, and integrates simple constraints to enforce set-based criteria such as aspect balance, aspect coverage, and term centrality. Results across multiple standard test collections show consistent andsignificant reductions in the number and magnitude of expansion failures, while retaining the strong positive gains of the baseline algorithm. Our approach does not assume a particular retrieval model, making it applicable to a broad class of existing expansion algorithms.

Kernel learning is a powerful framework for nonlinear data modeling. Using the kernel trick, a number of problems have been formulated as semidefinite programs (SDPs). These include Maximum Variance Unfolding (MVU) (Weinberger et al., 2004) in nonlinear dimensionality reduction, and Pairwise Constraint Propagation (PCP) (Li et al., 2008) in constrained clustering. Although in theory SDPs can be efficiently solved, the high computational complexity incurred in numerically processing the huge linear matrix inequality constraints has rendered the SDP approach unscalable. In this paper, we show that a large class of kernel learning problems can be reformulated as semidefinite-quadratic-linear programs (SQLPs), which only contain a simple positive semidefinite constraint, a second-order cone constraint and a number of linear constraints. These constraints are much easier to process numerically, and the gain in speedup over previous approaches is at least of the order $m^{2.5}$, where m is the matrix dimension. Experimental results are also presented to show the superb computational efficiency of our approach.

Representing distributions over permutations can be a daunting task due to the fact that the number of permutations of n objects scales factorially in n. One recent way that has been used to reduce storage complexity has been to exploit probabilistic independence, but as we argue, full independence assumptions impose strong sparsity constraints on distributions and are unsuitable for modeling rankings. We identify a novel class of independence structures, called riffled independence, which encompasses a more expressive family of distributions while retaining many of the properties necessary for performing efficient inference and reducing sample complexity. In riffled independence, one draws two permutations independently, then performs the riffle shuffle, common in card games, to combine the two permutations to form a single permutation. In ranking, riffled independence corresponds to ranking disjoint sets of objects independently, then interleaving those rankings. We provide a formal introduction and present algorithms for using riffled independence within Fourier-theoretic frameworks which have been explored by a number of recent papers.

Object matching is a fundamental operation in data analysis. It typically requires the definition of a similarity measure between the classes of objects to be matched. Instead, we develop an approach which is able to perform matching by requiring a similarity measure only within each of the classes. This is achieved by maximizing the dependency between matched pairs of observations by means of the Hilbert Schmidt Independence Criterion. This problem can be cast as one of maximizing a quadratic assignment problem with special structure and we present a simple algorithm for finding a locally optimal solution.

We propose in this paper RecLasso, analgorithm to solve the Lasso with online (sequential) observations. We introduce an optimization problem that allows us to compute an homotopy from the current solution to the solution after observing a new data point. We compare ourmethod to Lars and Coordinate Descent, and present an application to compressive sensing with sequential observations. Our approach can easily be extended to compute an homotopy from the current solution to the solution that corresponds to removing a data point, which leads to an efficient algorithm for leave-one-out cross-validation. We also propose an algorithm to automatically update the regularization parameter after observing a new data point.

Before the age of 4 months, infants make inductive inferences about the motions of physical objects. Developmental psychologists have provided verbal accounts of the knowledge that supports these inferences, but often these accounts focus on categorical rather than probabilistic principles. We propose that infant object perception is guided in part by probabilistic principles like persistence: things tend to remain the same, and when they change they do so gradually. To illustrate this idea, we develop an ideal observer model that includes probabilistic formulations of rigidity and inertia. Like previous researchers, we suggest that rigid motions are expected from an early age, but we challenge the previous claim that expectations consistent with inertia are relatively slow to develop (Spelke et al., 1992). We support these arguments by modeling four experiments from the developmental literature.

In the quest to make Brain Computer Interfacing (BCI) more usable, dry electrodes have emerged that get rid of the initial 30 minutes required for placing an electrode cap. Another time consuming step is the required individualized adaptation to the BCI user, which involves another 30 minutes calibration for assessing a subjects brain signature. In this paper we aim to also remove this calibration proceedure from BCI setup time by means of machine learning. In particular, we harvest a large database of EEG BCI motor imagination recordings (83 subjects) for constructing a library of subject-specific spatio-temporal filters and derive a subject independent BCI classifier. Our offline results indicate that BCI-na\{i}ve users could start real-time BCI use with no prior calibration at only a very moderate performance loss."

From an information-theoretic perspective, a noisy transmission system such as a visual Brain-Computer Interface (BCI) speller could benefit from the use of error-correcting codes. However, optimizing the code solely according to the maximal minimum-Hamming-distance criterion tends to lead to an overall increase in target frequency of target stimuli, and hence a significantly reduced average target-to-target interval (TTI), leading to difficulties in classifying the individual event-related potentials (ERPs) due to overlap and refractory effects. Clearly any change to the stimulus setup must also respect the possible psychophysiological consequences. Here we report new EEG data from experiments in which we explore stimulus types and codebooks in a within-subject design, finding an interaction between the two factors. Our data demonstrate that the traditional, row-column code has particular spatial properties that lead to better performance than one would expect from its TTIs and Hamming-distances alone, but nonetheless error-correcting codes can improve performance provided the right stimulus type is used.

We present a new family of linear time algorithms based on sufficient statistics for string comparison with mismatches under the string kernels framework. Our algorithms improve theoretical complexity bounds of existing approaches while scaling well with respect to the sequence alphabet size, the number of allowed mismatches and the size of the dataset. In particular, on large alphabets with loose mismatch constraints our algorithms are several orders of magnitude faster than the existing algorithms for string comparison under the mismatch similarity measure. We evaluate our algorithms on synthetic data and real applications in music genre classification, protein remote homology detection and protein fold prediction. The scalability of the algorithms allows us to consider complex sequence transformations, modeled using longer string features and larger numbers of mismatches, leading to a state-of-the-art performance with significantly reduced running times.