Continuous attractor neural networks (CANNs) are emerging as promising models for describing the encoding of continuous stimuli in neural systems. Due to the translational invariance of their neuronal interactions, CANNs can hold a continuous family of neutrally stable states. In this study, we systematically explore how neutral stability of a CANN facilitates its tracking performance, a capacity believed to have wide applications in brain functions. We develop a perturbative approach that utilizes the dominant movement of the network stationary states in the state space. We quantify the distortions of the bump shape during tracking, and study their effects on the tracking performance. Results are obtained on the maximum speed for a moving stimulus to be trackable, and the reaction time to catch up an abrupt change in stimulus.

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.

In this paper we introduce the MeanNN approach for estimation of main information theoretic measures such as differential entropy, mutual information and divergence. As opposed to other nonparametric approaches the MeanNN results in smooth differentiable functions of the data samples with clear geometrical interpretation. Then we apply the proposed estimators to the ICA problem and obtain a smooth expression for the mutual information that can be analytically optimized by gradient descent methods. The improved performance on the proposed ICA algorithm is demonstrated on standard tests in comparison with state-of-the-art techniques.

With the increased availability of data for complex domains, it is desirable to learn Bayesian network structures that are sufficiently expressive for generalization while also allowing for tractable inference. While the method of thin junction trees can, in principle, be used for this purpose, its fully greedy nature makes it prone to overfitting, particularly when data is scarce. In this work we present a novel method for learning Bayesian networks of bounded treewidth that employs global structure modifications and that is polynomial in the size of the graph and the treewidth bound. At the heart of our method is a triangulated graph that we dynamically update in a way that facilitates the addition of chain structures that increase the bound on the model's treewidth by at most one. We demonstrate the effectiveness of our ``treewidth-friendly'' method on several real-life datasets. Importantly, we also show that by using global operators, we are able to achieve better generalization even when learning Bayesian networks of unbounded treewidth.

Is accurate classification possible in the absence of hand-labeled data?

This paper addresses the important tradeoff between privacy and learnability, when designing algorithms for learning from private databases. First we apply an idea of Dwork et al. to design a specific privacy-preserving machine learning algorithm, logistic regression. This involves bounding the sensitivity of logistic regression, and perturbing the learned classifier with noise proportional to the sensitivity. Noting that the approach of Dwork et al. has limitations when applied to other machine learning algorithms, we then present another privacy-preserving logistic regression algorithm. The algorithm is based on solving a perturbed objective, and does not depend on the sensitivity. We prove that our algorithm preserves privacy in the model due to Dwork et al., and we provide a learning performance guarantee. Our work also reveals an interesting connection between regularization and privacy.

We investigate a topic at the interface of machine learning and cognitive science. Human active learning, where learners can actively query the world for information, is contrasted with passive learning from random examples. Furthermore, we compare human active learning performance with predictions from statistical learning theory. We conduct a series of human category learning experiments inspired by a machine learning task for which active and passive learning error bounds are well understood, and dramatically distinct. Our results indicate that humans are capable of actively selecting informative queries, and in doing so learn better and faster than if they are given random training data, as predicted by learning theory. However, the improvement over passive learning is not as dramatic as that achieved by machine active learning algorithms. To the best of our knowledge, this is the first quantitative study comparing human category learning in active versus passive settings.

Identification and comparison of nonlinear dynamical systems using noisy and sparse experimental data is a vital task in many fields, however current methods are computationally expensive and prone to error due in part to the nonlinear nature of the likelihood surfaces induced. We present an accelerated sampling procedure which enables Bayesian inference of parameters in nonlinear ordinary and delay differential equations via the novel use of Gaussian processes (GP). Our method involves GP regression over time-series data, and the resulting derivative and time delay estimates make parameter inference possible without solving the dynamical system explicitly, resulting in dramatic savings of computational time. We demonstrate the speed and statistical accuracy of our approach using examples of both ordinary and delay differential equations, and provide a comprehensive comparison with current state of the art methods.

We consider a generalization of stochastic bandit problems where the set of arms, X, is allowed to be a generic topological space. We constraint the mean-payoff function with a dissimilarity function over X in a way that is more general than Lipschitz. We construct an arm selection policy whose regret improves upon previous result for a large class of problems. In particular, our results imply that if X is the unit hypercube in a Euclidean space and the mean-payoff function has a finite number of global maxima around which the behavior of the function is locally Hölder with a known exponent, then the expected regret is bounded up to a logarithmic factor by $n$, i.e., the rate of the growth of the regret is independent of the dimension of the space. Moreover, we prove the minimax optimality of our algorithm for the class of mean-payoff functions we consider.

Statistical evolutionary models provide an important mechanism for describing and understanding the escape response of a viral population under a particular therapy. We present a new hierarchical model that incorporates spatially varying mutation and recombination rates at the nucleotide level. It also maintains sep- arate parameters for treatment and control groups, which allows us to estimate treatment effects explicitly. We use the model to investigate the sequence evolu- tion of HIV populations exposed to a recently developed antisense gene therapy, as well as a more conventional drug therapy. The detection of biologically rele- vant and plausible signals in both therapy studies demonstrates the effectiveness of the method.