Correlations between spike counts are often used to analyze neural coding. The noise is typically assumed to be Gaussian. Yet, this assumption is often inappropriate, especially for low spike counts. In this study, we present copulas as an alternative approach. With copulas it is possible to use arbitrary marginal distributions such as Poisson or negative binomial that are better suited for modeling noise distributions of spike counts. Furthermore, copulas place a wide range of dependence structures at the disposal and can be used to analyze higher order interactions. We develop a framework to analyze spike count data by means of copulas. Methods for parameter inference based on maximum likelihood estimates and for computation of Shannon entropy are provided. We apply the method to our data recorded from macaque prefrontal cortex. The data analysis leads to three significant findings: (1) copula-based distributions provide better fits than discretized multivariate normal distributions; (2) negative binomial margins fit the data better than Poisson margins; and (3) a dependence model that includes only pairwise interactions overestimates the information entropy by at least 19% compared to the model with higher order interactions.

This learning problem arises frequently in many application areas ranging from signal processing, computer vision, over robotics to computer graphics. We present a new algorithmic scheme for the solution of this general learning problem based on regularized empirical risk minimization. The regularization functional takes into account the geometry of input and output manifold, and we show that it implements a prior which is particularly natural. Moreover, we demonstrate that our algorithm performs well in a difficult surface registration problem.

Suppose we train an animal in a conditioning experiment. Can one predict how a given animal, under given experimental conditions, would perform the task? Since various factors such as stress, motivation, genetic background, and previous errors in task performance can influence animal behaviour, this appears to be a very challenging aim. Reinforcement learning (RL) models have been successful inmodeling animal (and human) behaviour, but their success has been limited because of uncertainty as to how to set meta-parameters (such as learning rate, exploitation-exploration balance and future reward discount factor) that strongly influence model performance. We show that a simple RL model whose metaparameters arecontrolled by an artificial neural network, fed with inputs such as stress, affective phenotype, previous task performance, and even neuromodulatory manipulations,can successfully predict mouse behaviour in the "hole-box" - a simple conditioning task. Our results also provide important insights on how stress and anxiety affect animal learning, performance accuracy, and discounting of future rewards, and on how noradrenergic systems can interact with these processes.

We tackle the computational problem of query-conditioned search. Given a machine-learned scoring rule and a query distribution, we build a predictive index by precomputing lists of potential results sorted based on an expected score of the result over future queries. The predictive index datastructure supports an anytime algorithm for approximate retrieval of the top elements. The general approach is applicable to webpage ranking, internet advertisement, and approximate nearest neighbor search. It is particularly effective in settings where standard techniques (e.g., inverted indices) are intractable. We experimentally find substantial improvement over existing methods for internet advertisement and approximate nearest neighbors.

The low-rank matrix completion problem is a fundamental problem with many important applications. Recently, [4],[13] and [5] obtained the first nontrivial theoretical results for the problem assuming that the observed entries are sampled uniformly at random. Unfortunately, most real-world datasets do not satisfy this assumption, but instead exhibit power-law distributed samples. In this paper, we propose a graph theoretic approach to matrix completion that solves the problem for more realistic sampling models. Our method is simpler to analyze than previous methodswith the analysis reducing to computing the threshold for complete cascades in random graphs, a problem of independent interest. By analyzing the graph theoretic problem, we show that our method achieves exact recovery when the observed entries are sampled from the Chung-Lu-Vu model, which can generate power-lawdistributed graphs. We also hypothesize that our algorithm solves the matrix completion problem from an optimal number of entries for the popular preferentialattachment model and provide strong empirical evidence for the claim. Furthermore, our method is easy to implement and is substantially faster than existing methods. We demonstrate the effectiveness of our method on random instanceswhere the low-rank matrix is sampled according to the prevalent random graph models for complex networks and present promising preliminary results on the Netflix challenge dataset.

Dynamic Bayesian networks have been applied widely to reconstruct the structure of regulatory processes from time series data. The standard approach is based on the assumption of a homogeneous Markov chain, which is not valid in many real-world scenarios. Recent research efforts addressing this shortcoming have considered undirected graphs, directed graphs for discretized data, or over-flexible models that lack any information sharing between time series segments. In the present article, we propose a non-stationary dynamic Bayesian network for continuous data, in which parameters are allowed to vary between segments, and in which a common network structure provides essential information sharing across segments. Our model is based on a Bayesian change-point process, and we apply a variant of the allocation sampler of Nobile and Fearnside to infer the number and location of the change-points.

Subspace-based learning problems involve data whose elements are linear subspaces of a vector space. To handle such data structures, Grassmann kernels have been proposed and used previously. In this paper, we analyze the relationship between Grassmann kernels and probabilistic similarity measures. Firstly, we show that the KL distance in the limit yields the Projection kernel on the Grassmann manifold, whereas the Bhattacharyya kernel becomes trivial in the limit and is suboptimal for subspace-based problems. Secondly, based on our analysis of the KL distance, we propose extensions of the Projection kernel which can be extended to the set of affine as well as scaled subspaces. We demonstrate the advantages of these extended kernels for classification and recognition tasks with Support Vector Machines and Kernel Discriminant Analysis using synthetic and real image databases.

Adaptation of visually guided reaching movements in novel visuomotor environments (e.g.wearing prism goggles) comprises not only motor adaptation but also substantial sensory adaptation, corresponding to shifts in the perceived spatial location of visual and proprioceptive cues. Previous computational modelsof the sensory component of visuomotor adaptation have assumed that it is driven purely by the discrepancy introduced between visual andproprioceptive estimates of hand position and is independent of any motor component of adaptation. We instead propose a unified model in which sensory and motor adaptation are jointly driven by optimal Bayesian estimation of the sensory and motor contributions to perceived errors. Our model is able to account for patterns of performance errors during visuomotor adaptationas well as the subsequent perceptual aftereffects. This unified model also makes the surprising prediction that force field adaptation willelicit similar perceptual shifts, even though there is never any discrepancy between visual and proprioceptive observations. We confirm this prediction with an experiment.

We show how smoother priors can preserve the benefits of these sparse priors while adding stability to the Maximum A-Posteriori (MAP) estimate that makes it more useful for prediction problems. Additionally, we show how to calculate the derivative of the MAP estimate efficiently withimplicit differentiation. One prior that can be differentiated this way is KL-regularization. We demonstrate its effectiveness on a wide variety of applications, andfind that online optimization of the parameters of the KL-regularized model can significantly improve prediction performance.

We consider robust least-squares regression with feature-wise disturbance. We show that this formulation leads to tractable convex optimization problems, and we exhibit a particular uncertainty set for which the robust problem is equivalent to $\ell_1$ regularized regression (Lasso). This provides an interpretation of Lasso from a robust optimization perspective. We generalize this robust formulation to consider more general uncertainty sets, which all lead to tractable convex optimization problems. Therefore, we provide a new methodology for designing regression algorithms, which generalize known formulations. The advantage is that robustness to disturbance is a physical property that can be exploited: in addition to obtaining new formulations, we use it directly to show sparsity properties of Lasso, as well as to prove a general consistency result for robust regression problems, including Lasso, from a unified robustness perspective.