Conditional Random Sampling (CRS) was originally proposed for efficiently computing pairwise ($l_2$, $l_1$) distances, in static, large-scale, and sparse data sets such as text and Web data. It was previously presented using a heuristic argument. This study extends CRS to handle dynamic or streaming data, which much better reflect the real-world situation than assuming static data. Compared with other known sketching algorithms for dimension reductions such as stable random projections, CRS exhibits a significant advantage in that it is ``one-sketch-for-all.'' In particular, we demonstrate that CRS can be applied to efficiently compute the $l_p$ distance and the Hilbertian metrics, both are popular in machine learning. Although a fully rigorous analysis of CRS is difficult, we prove that, with a simple modification, CRS is rigorous at least for an important application of computing Hamming norms. A generic estimator and an approximate variance formula are provided and tested on various applications, for computing Hamming norms, Hamming distances, and $\chi^2$ distances.

Sequential optimal design methods hold great promise for improving the efficiency ofneurophysiology experiments. However, previous methods for optimal experimental design have incorporated only weak prior information about the underlying neuralsystem (e.g., the sparseness or smoothness of the receptive field). Here we describe how to use stronger prior information, in the form of parametric modelsof the receptive field, in order to construct optimal stimuli and further improve the efficiency of our experiments. For example, if we believe that the receptive field is well-approximated by a Gabor function, then our method constructs stimulithat optimally constrain the Gabor parameters (orientation, spatial frequency, etc.) using as few experimental trials as possible. More generally, we may believe a priori that the receptive field lies near a known sub-manifold of the full parameter space; in this case, our method chooses stimuli in order to reduce the uncertainty along the tangent space of this sub-manifold as rapidly as possible. Applications to simulated and real data indicate that these methods may in many cases improve the experimental efficiency.

We propose a new fast Gaussian summation algorithm for high-dimensional datasets with high accuracy. First, we extend the original fast multipole-type methods to use approximation schemes with both hard and probabilistic error. Second, we utilize a new data structure called subspace tree which maps each data point in the node to its lower dimensional mapping as determined by any linear dimension reduction method such as PCA. This new data structure is suitable for reducing the cost of each pairwise distance computation, the most dominant cost in many kernel methods. Our algorithm guarantees probabilistic relative error on each kernel sum, and can be applied to high-dimensional Gaussian summations which are ubiquitous inside many kernel methods as the key computational bottleneck. We provide empirical speedup results on low to high-dimensional datasets up to 89 dimensions.

How does one extract unknown but stereotypical events that are linearly superimposed within a signal with variable latencies and variable amplitudes? One could think of using template matching or matching pursuit to find the arbitrarily shifted linear components. However, traditional matching approaches require that the templates be known a priori. To overcome this restriction we use instead semi Non-Negative Matrix Factorization (semi-NMF) that we extend to allow for time shifts when matching the templates to the signal. The algorithm estimates templates directly from the data along with their non-negative amplitudes. The resulting method can be thought of as an adaptive template matching procedure. We demonstrate the procedure on the task of extracting spikes from single channel extracellular recordings. On these data the algorithm essentially performs spike detection and unsupervised spike clustering. Results on simulated data and extracellular recordings indicate that the method performs well for signal-to-noise ratios of 6dB or higher and that spike templates are recovered accurately provided they are sufficiently different.

We introduce a new interpretation of multiscale random fields (MSRFs) that admits efficient optimization in the framework of regular (single level) random fields (RFs). It is based on a new operator, called append, that combines sets of random variables (RVs) to single RVs. We assume that a MSRF can be decomposed into disjoint trees that link RVs at different pyramid levels. The append operator is then applied to map RVs in each tree structure to a single RV. We demonstrate the usefulness of the proposed approach on a challenging task involving grouping contours of target shapes in images. MSRFs provide a natural representation of multiscale contour models, which are needed in order to cope with unstable contour decompositions. The append operator allows us to find optimal image labels using the classical framework of relaxation labeling, Alternative methods like Markov Chain Monte Carlo (MCMC) could also be used.

We consider the problem of obtaining the approximate maximum a posteriori estimate of a discrete random field characterized by pairwise potentials that form a truncated convex model. For this problem, we propose an improved st-mincut based move making algorithm. Unlike previous move making approaches, which either provide a loose bound or no bound on the quality of the solution (in terms of the corresponding Gibbs energy), our algorithm achieves the same guarantees as the standard linear programming (LP) relaxation. Compared to previous approaches based on the LP relaxation, e.g. interior-point algorithms or tree-reweighted message passing (TRW), our method is faster as it uses only the efficient st-mincut algorithm in its design. Furthermore, it directly provides us with a primal solution (unlike TRW and other related methods which attempt to solve the dual of the LP). We demonstrate the effectiveness of the proposed approach on both synthetic and standard real data problems. Our analysis also opens up an interesting question regarding the relationship between move making algorithms (such as $\alpha$-expansion and the algorithms presented in this paper) and the randomized rounding schemes used with convex relaxations. We believe that further explorations in this direction would help design efficient algorithms for more complex relaxations.

In this theoretical contribution we provide mathematical proof that two of the most important classes of network learning - correlation-based differential Hebbian learningand reward-based temporal difference learning - are asymptotically equivalent when timing the learning with a local modulatory signal. This opens the opportunity to consistently reformulate most of the abstract reinforcement learning frameworkfrom a correlation based perspective that is more closely related to the biophysics of neurons.

We present a new co-clustering problem of images and visual features. The problem involvesa set of non-object images in addition to a set of object images and features to be co-clustered. Co-clustering is performed in a way that maximises discrimination of object images from non-object images, thus emphasizing discriminative features.This provides a way of obtaining perceptual joint-clusters of object images and features. We tackle the problem by simultaneously boosting multiplestrong classifiers which compete for images by their expertise. Each boosting classifier is an aggregation of weak-learners, i.e. simple visual features. The obtained classifiers are useful for object detection tasks which exhibit multimodalities, e.g.multi-category and multi-view object detection tasks. Experiments on a set of pedestrian images and a face data set demonstrate that the method yields intuitive image clusters with associated features and is much superior toconventional boosting classifiers in object detection tasks.

We provide statistical performance guarantees for a recently introduced kernel classifier that optimizes the $L_2$ or integrated squared error (ISE) of a difference of densities. The classifier is similar to a support vector machine (SVM) in that it is the solution of a quadratic program and yields a sparse classifier. Unlike SVMs, however, the $L_2$ kernel classifier does not involve a regularization parameter. We prove a distribution free concentration inequality for a cross-validation based estimate of the ISE, and apply this result to deduce an oracle inequality and consistency of the classifier on the sense of both ISE and probability of error. Our results can also be specialized to give performance guarantees for an existing method of $L_2$ kernel density estimation.

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.