Intelligent agents are often faced with the need to choose actions with uncertain consequences, and to modify those actions according to ongoing sensory processing and changing task demands. The requisite ability to dynamically modify or cancel planned actions is known as inhibitory control in psychology. We formalize inhibitory control as a rational decision-making problem, and apply to it to the classical stop-signal task. Using Bayesian inference and stochastic control tools, we show that the optimal policy systematically depends on various parameters of the problem, such as the relative costs of different action choices, the noise level of sensory inputs, and the dynamics of changing environmental demands. Our normative model accounts for a range of behavioral data in humans and animals in the stop-signal task, suggesting that the brain implements statistically optimal, dynamically adaptive, and reward-sensitive decision-making in the context of inhibitory control problems.

We consider the problem of identifying an activation pattern in a complex, large-scale network that is embedded in very noisy measurements. This problem is relevant to several applications, such as identifying traces of a biochemical spread by a sensor network, expression levels of genes, and anomalous activity or congestion in the Internet. Extracting such patterns is a challenging task specially if the network is large (pattern is very high-dimensional) and the noise is so excessive that it masks the activity at any single node. However, typically there are statistical dependencies in the network activation process that can be leveraged to fuse the measurements of multiple nodes and enable reliable extraction of high-dimensional noisy patterns. In this paper, we analyze an estimator based on the graph Laplacian eigenbasis, and establish the limits of mean square error recovery of noisy patterns arising from a probabilistic (Gaussian or Ising) model based on an arbitrary graph structure. We consider both deterministic and probabilistic network evolution models, and our results indicate that by leveraging the network interaction structure, it is possible to consistently recover high-dimensional patterns even when the noise variance increases with network size.

When learning models that are represented in matrix forms, enforcing a low-rank constraint can dramatically improve the memory and run time complexity, while providing a natural regularization of the model. However, naive approaches for minimizing functions over the set of low-rank matrices are either prohibitively time consuming (repeated singular value decomposition of the matrix) or numerically unstable (optimizing a factored representation of the low rank matrix). We build on recent advances in optimization over manifolds, and describe an iterative online learning procedure, consisting of a gradient step, followed by a second-order retraction back to the manifold. While the ideal retraction is hard to compute, and so is the projection operator that approximates it, we describe another second-order retraction that can be computed efficiently, with run time and memory complexity of O((n+m)k) for a rank-k matrix of dimension m x n, given rank one gradients. We use this algorithm, LORETA, to learn a matrix-form similarity measure over pairs of documents represented as high dimensional vectors. LORETA improves the mean average precision over a passive- aggressive approach in a factorized model, and also improves over a full model trained over pre-selected features using the same memory requirements. LORETA also showed consistent improvement over standard methods in a large (1600 classes) multi-label image classification task.

Hypothesis testing on point processes has several applications such as model fitting, plasticity detection, and non-stationarity detection. Standard tools for hypothesis testing include tests on mean firing rate and time varying rate function. However, these statistics do not fully describe a point process and thus the tests can be misleading. In this paper, we introduce a family of non-parametric divergence measures for hypothesis testing. We extend the traditional Kolmogorov--Smirnov and Cramer--von-Mises tests for point process via stratification. The proposed divergence measures compare the underlying probability structure and, thus, is zero if and only if the point processes are the same. This leads to a more robust test of hypothesis. We prove consistency and show that these measures can be efficiently estimated from data. We demonstrate an application of using the proposed divergence as a cost function to find optimally matched spike trains.

When stimulated with complex action potential sequences synapses exhibit spike timing-dependent plasticity (STDP) with attenuated and enhanced pre- and postsynaptic contributions to long-term synaptic modifications. In order to investigate the functional consequences of these contribution dynamics (CD) we propose a minimal model formulated in terms of differential equations. We find that our model reproduces a wide range of experimental results with a small number of biophysically interpretable parameters. The model allows to investigate the susceptibility of STDP to arbitrary time courses of pre- and postsynaptic activities, i.e. its nonlinear filter properties. We demonstrate this for the simple example of small periodic modulations of pre- and postsynaptic firing rates for which our model can be solved. It predicts synaptic strengthening for synchronous rate modulations. For low baseline rates modifications are dominant in the theta frequency range, a result which underlines the well known relevance of theta activities in hippocampus and cortex for learning. We also find emphasis of low baseline spike rates and suppression for high baseline rates. The latter suggests a mechanism of network activity regulation inherent in STDP. Furthermore, our novel formulation provides a general framework for investigating the joint dynamics of neuronal activity and the CD of STDP in both spike-based as well as rate-based neuronal network models.

Gaussian graphical models are of great interest in statistical learning. Because the conditional independencies between different nodes correspond to zero entries in the inverse covariance matrix of the Gaussian distribution, one can learn the structure of the graph by estimating a sparse inverse covariance matrix from sample data, by solving a convex maximum likelihood problem with an $\ell_1$-regularization term. In this paper, we propose a first-order method based on an alternating linearization technique that exploits the problem's special structure; in particular, the subproblems solved in each iteration have closed-form solutions. Moreover, our algorithm obtains an $\epsilon$-optimal solution in $O(1/\epsilon)$ iterations. Numerical experiments on both synthetic and real data from gene association networks show that a practical version of this algorithm outperforms other competitive algorithms.

We discuss an online learning framework in which the agent is allowed to say ``I don't know'' as well as making incorrect predictions on given examples. We analyze the trade off between saying ``I don't know'' and making mistakes. If the number of don't know predictions is forced to be zero, the model reduces to the well-known mistake-bound model introduced by Littlestone [Lit88]. On the other hand, if no mistakes are allowed, the model reduces to KWIK framework introduced by Li et. al. [LLW08]. We propose a general, though inefficient, algorithm for general finite concept classes that minimizes the number of don't-know predictions if a certain number of mistakes are allowed. We then present specific polynomial-time algorithms for the concept classes of monotone disjunctions and linear separators.

We address the problem of estimating the F-measure of a given model as accurately as possible on a fixed labeling budget. This problem occurs whenever an estimate cannot be obtained from held-out training data; for instance, when data that have been used to train the model are held back for reasons of privacy or do not reflect the test distribution. In this case, new test instances have to be drawn and labeled at a cost. An active estimation procedure selects instances according to an instrumental sampling distribution. An analysis of the sources of estimation error leads to an optimal sampling distribution that minimizes estimator variance. We explore conditions under which active estimates of F-measures are more accurate than estimates based on instances sampled from the test distribution.

Estimating 3D pose from monocular images is a highly ambiguous problem. Physical constraints can be exploited to restrict the space of feasible configurations. In this paper we propose an approach to constraining the prediction of a discriminative predictor. We first show that the mean prediction of a Gaussian process implicitly satisfies linear constraints if those constraints are satisfied by the training examples. We then show how, by performing a change of variables, a GP can be forced to satisfy quadratic constraints. As evidenced by the experiments, our method outperforms state-of-the-art approaches on the tasks of rigid and non-rigid pose estimation.

We develop a deterministic single-pass algorithm for latent Dirichlet allocation (LDA) in order to process received documents one at a time and then discard them in an excess text stream. Our algorithm does not need to store old statistics for all data. The proposed algorithm is much faster than a batch algorithm and is comparable to the batch algorithm in terms of perplexity in experiments.