We study a setting in which Poisson processes generate sequences of decision-making events. The optimization goal is allowed to depend on the rate of decision outcomes; the rate may depend on a potentially long backlog of events and decisions. We model the problem as a Poisson process with a throttling policy that enforces a data-dependent rate limit and reduce the learning problem to a convex optimization problem that can be solved efficiently. This problem setting matches applications in which damage caused by an attacker grows as a function of the rate of unsuppressed hostile events. We report on experiments on abuse detection for an email service.

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 propose a novel Bayesian nonparametric approach to learning with probabilistic deterministic finite automata (PDFA). We define and develop and sampler for a PDFA with an infinite number of states which we call the probabilistic deterministic infinite automata (PDIA). Posterior predictive inference in this model, given a finite training sequence, can be interpreted as averaging over multiple PDFAs of varying structure, where each PDFA is biased towards having few states. We suggest that our method for averaging over PDFAs is a novel approach to predictive distribution smoothing. We test PDIA inference both on PDFA structure learning and on both natural language and DNA data prediction tasks. The results suggest that the PDIA presents an attractive compromise between the computational cost of hidden Markov models and the storage requirements of hierarchically smoothed Markov models.

Feature selection is an important component of many machine learning applications. Especially in many bioinformatics tasks, efficient and robust feature selection methods are desired to extract meaningful features and eliminate noisy ones. In this paper, we propose a new robust feature selection method with emphasizing joint ℓ2,1-norm minimization on both loss function and regularization. The ℓ2,1-norm based loss function is robust to outliers in data points and the ℓ2,1-norm regularization selects features across all data points with joint sparsity. An efficient algorithm is introduced with proved convergence. Our regression based objective makes the feature selection process more efficient. Our method has been applied into both genomic and proteomic biomarkers discovery. Extensive empirical studies were performed on six data sets to demonstrate the effectiveness of our feature selection method.

We present a simple and effective approach to learning tractable conditional random fieldswith structure that depends on the evidence. Our approach retains the advantages of tractable discriminative models, namely efficient exact inference and arbitrarily accurate parameter learning in polynomial time. At the same time, our algorithm does not suffer a large expressive power penalty inherent to fixed tractable structures. On real-life relational datasets, our approach matches or exceeds stateof the art accuracy of the dense models, and at the same time provides an order of magnitude speedup.

We apply the framework of kernel dimension reduction, originally designed for supervised problems, to unsupervised dimensionality reduction. In this framework, kernel-based measures of independence are used to derive low-dimensional representations that maximally capture information in covariates in order to predict responses. We extend this idea and develop similarly motivated measures for unsupervised problems where covariates and responses are the same. Our empirical studies show that the resulting compact representation yields meaningful and appealing visualization and clustering of data. Furthermore, when used in conjunction with supervised learners for classification, our methods lead to lower classification errors than state-of-the-art methods, especially when embedding data in spaces of very few dimensions.

The max-norm was proposed as a convex matrix regularizer by Srebro et al (2004) and was shown to be empirically superior to the trace-norm for collaborative filtering problems. Although the max-norm can be computed in polynomial time, there are currently no practical algorithms for solving large-scale optimization problems that incorporate the max-norm. The present work uses a factorization technique of Burer and Monteiro (2003) to devise scalable first-order algorithms for convex programs involving the max-norm. These algorithms are applied to solve huge collaborative filtering, graph cut, and clustering problems. Empirically, the new methods outperform mature techniques from all three areas.

Many studies have explored the impact of response variability on the quality of sensory codes. The source of this variability is almost always assumed to be intrinsic to the brain. However, when inferring a particular stimulus property, variability associated with other stimulus attributes also effectively act as noise. Here we study the impact of such stimulus-induced response variability for the case of binocular disparity inference. We characterize the response distribution for the binocular energy model in response to random dot stereograms and find it to be very different from the Poisson-like noise usually assumed. We then compute the Fisher information with respect to binocular disparity, present in the monocular inputs to the standard model of early binocular processing, and thereby obtain an upper bound on how much information a model could theoretically extract from them. Then we analyze the information loss incurred by the different ways of combining those inputs to produce a scalar single-neuron response. We find that in the case of depth inference, monocular stimulus variability places a greater limit on the extractable information than intrinsic neuronal noise for typical spike counts. Furthermore, the largest loss of information is incurred by the standard model for position disparity neurons (tuned-excitatory), that are the most ubiquitous in monkey primary visual cortex, while more information from the inputs is preserved in phase-disparity neurons (tuned-near or tuned-far) primarily found in higher cortical regions.

In the neural-network parameter space, an attractive field is likely to be induced by singularities. In such a singularity region, first-order gradient learning typically causes a long plateau with very little change in the objective function value E (hence, a flat region). Therefore, it may be confused with ``attractive'' local minima. Our analysis shows that the Hessian matrix of E tends to be indefinite in the vicinity of (perturbed) singular points, suggesting a promising strategy that exploits negative curvature so as to escape from the singularity plateaus. For numerical evidence, we limit the scope to small examples (some of which are found in journal papers) that allow us to confirm singularities and the eigenvalues of the Hessian matrix, and for which computation using a descent direction of negative curvature encounters no plateau. Even for those small problems, no efficient methods have been previously developed that avoided plateaus.

In this paper, we propose a matrix-variate normal penalty with sparse inverse covariances to couple multiple tasks. Learning multiple (parametric) models can be viewed as estimating a matrix of parameters, where rows and columns of the matrix correspond to tasks and features, respectively. Following the matrix-variate normal density, we design a penalty that decomposes the full covariance of matrix elements into the Kronecker product of row covariance and column covariance, which characterizes both task relatedness and feature representation. Several recently proposed methods are variants of the special cases of this formulation. To address the overfitting issue and select meaningful task and feature structures, we include sparse covariance selection into our matrix-normal regularization via L-1 penalties on task and feature inverse covariances. We empirically study the proposed method and compare with related models in two real-world problems: detecting landmines in multiple fields and recognizing faces between different subjects. Experimental results show that the proposed framework provides an effective and flexible way to model various different structures of multiple tasks.