Correlation filters (CFs) are a class of classifiers that are attractive for object localization and tracking applications. Traditionally, CFs have been designed in the frequency domain using the discrete Fourier transform (DFT), where correlation is efficiently implemented. However, existing CF designs do not account for the fact that the multiplication of two DFTs in the frequency domain corresponds to a circular correlation in the time/spatial domain. Because this was previously unaccounted for, prior CF designs are not truly optimal, as their optimization criteria do not accurately quantify their optimization intention. In this paper, we introduce new zero-aliasing constraints that completely eliminate this aliasing problem by ensuring that the optimization criterion for a given CF corresponds to a linear correlation rather than a circular correlation. This means that previous CF designs can be significantly improved by this reformulation. We demonstrate the benefits of this new CF design approach with several important CFs. We present experimental results on diverse data sets and present solutions to the computational challenges associated with computing these CFs. Code for the CFs described in this paper and their respective zero-aliasing versions is available at http://vishnu.boddeti.net/projects/correlation-filters.html

Data association, the problem of reasoning over correspondence between targets and measurements, is a fundamental problem in tracking. This paper presents a graphical model formulation of data association and applies an approximate inference method, belief propagation (BP), to obtain estimates of marginal association probabilities. We prove that BP is guaranteed to converge, and bound the number of iterations necessary. Experiments reveal a favourable comparison to prior methods in terms of accuracy and computational complexity.

In this paper, we consider an $\ell_{0}$-norm penalized formulation of the generalized eigenvalue problem (GEP), aimed at extracting the leading sparse generalized eigenvector of a matrix pair. The formulation involves maximization of a discontinuous nonconcave objective function over a nonconvex constraint set, and is therefore computationally intractable. To tackle the problem, we first approximate the $\ell_{0}$-norm by a continuous surrogate function. Then an algorithm is developed via iteratively majorizing the surrogate function by a quadratic separable function, which at each iteration reduces to a regular generalized eigenvalue problem. A preconditioned steepest ascent algorithm for finding the leading generalized eigenvector is provided. A systematic way based on smoothing is proposed to deal with the "singularity issue" that arises when a quadratic function is used to majorize the nondifferentiable surrogate function. For sparse GEPs with special structure, algorithms that admit a closed-form solution at every iteration are derived. Numerical experiments show that the proposed algorithms match or outperform existing algorithms in terms of computational complexity and support recovery.

In this article, we derive a new stepsize adaptation for the normalized least mean square algorithm (NLMS) by describing the task of linear acoustic echo cancellation from a Bayesian network perspective. Similar to the well-known Kalman filter equations, we model the acoustic wave propagation from the loudspeaker to the microphone by a latent state vector and define a linear observation equation (to model the relation between the state vector and the observation) as well as a linear process equation (to model the temporal progress of the state vector). Based on additional assumptions on the statistics of the random variables in observation and process equation, we apply the expectation-maximization (EM) algorithm to derive an NLMS-like filter adaptation. By exploiting the conditional independence rules for Bayesian networks, we reveal that the resulting EM-NLMS algorithm has a stepsize update equivalent to the optimal-stepsize calculation proposed by Yamamoto and Kitayama in 1982, which has been adopted in many textbooks. As main difference, the instantaneous stepsize value is estimated in the M step of the EM algorithm (instead of being approximated by artificially extending the acoustic echo path). The EM-NLMS algorithm is experimentally verified for synthesized scenarios with both, white noise and male speech as input signal.

We derive a convex optimization problem for the task of segmenting sequential data, which explicitly treats presence of outliers. We describe two algorithms for solving this problem, one exact and one a top-down novel approach, and we derive a consistency results for the case of two segments and no outliers. Robustness to outliers is evaluated on two real-world tasks related to speech segmentation. Our algorithms outperform baseline segmentation algorithms.

This paper examines the problem of locating outlier columns in a large, otherwise low-rank, matrix. We propose a simple two-step adaptive sensing and inference approach and establish theoretical guarantees for its performance; our results show that accurate outlier identification is achievable using very few linear summaries of the original data matrix -- as few as the squared rank of the low-rank component plus the number of outliers, times constant and logarithmic factors. We demonstrate the performance of our approach experimentally in two stylized applications, one motivated by robust collaborative filtering tasks, and the other by saliency map estimation tasks arising in computer vision and automated surveillance, and also investigate extensions to settings where the data are noisy, or possibly incomplete.

In this work, we propose a simple yet effective solution to the problem of connectome inference in calcium imaging data. The proposed algorithm consists of two steps. First, processing the raw signals to detect neural peak activities. Second, inferring the degree of association between neurons from partial correlation statistics. This paper summarises the methodology that led us to win the Connectomics Challenge, proposes a simplified version of our method, and finally compares our results with respect to other inference methods.

The expressive power of a Gaussian process (GP) model comes at a cost of poor scalability in the data size. To improve its scalability, this paper presents a low-rank-cum-Markov approximation (LMA) of the GP model that is novel in leveraging the dual computational advantages stemming from complementing a low-rank approximate representation of the full-rank GP based on a support set of inputs with a Markov approximation of the resulting residual process; the latter approximation is guaranteed to be closest in the Kullback-Leibler distance criterion subject to some constraint and is considerably more refined than that of existing sparse GP models utilizing low-rank representations due to its more relaxed conditional independence assumption (especially with larger data). As a result, our LMA method can trade off between the size of the support set and the order of the Markov property to (a) incur lower computational cost than such sparse GP models while achieving predictive performance comparable to them and (b) accurately represent features/patterns of any scale. Interestingly, varying the Markov order produces a spectrum of LMAs with PIC approximation and full-rank GP at the two extremes. An advantage of our LMA method is that it is amenable to parallelization on multiple machines/cores, thereby gaining greater scalability. Empirical evaluation on three real-world datasets in clusters of up to 32 computing nodes shows that our centralized and parallel LMA methods are significantly more time-efficient and scalable than state-of-the-art sparse and full-rank GP regression methods while achieving comparable predictive performances.

Bell's Theorem shows that quantum mechanical correlations can violate the constraints that the causal structure of certain experiments impose on any classical explanation. It is thus natural to ask to which degree the causal assumptions -- e.g. locality or measurement independence -- have to be relaxed in order to allow for a classical description of such experiments. Here, we develop a conceptual and computational framework for treating this problem. We employ the language of Bayesian networks to systematically construct alternative causal structures and bound the degree of relaxation using quantitative measures that originate from the mathematical theory of causality. The main technical insight is that the resulting problems can often be expressed as computationally tractable linear programs. We demonstrate the versatility of the framework by applying it to a variety of scenarios, ranging from relaxations of the measurement independence, locality and bilocality assumptions, to a novel causal interpretation of CHSH inequality violations.

Online advertising is an important and huge industry. Having knowledge of the website attributes can contribute greatly to business strategies for ad-targeting, content display, inventory purchase or revenue prediction. Classical inferences on users and sites impose challenge, because the data is voluminous, sparse, high-dimensional and noisy. In this paper, we introduce a stochastic blockmodeling for the website relations induced by the event of online user visitation. We propose two clustering algorithms to discover the instrinsic structures of websites, and compare the performance with a goodness-of-fit method and a deterministic graph partitioning method. We demonstrate the effectiveness of our algorithms on both simulation and AOL website dataset.