Venkatesh Saligrama

Boolean Compressed Sensing and Noisy Group Testing

The fundamental task of group testing is to recover a small distinguished subset of items from a large population while efficiently reducing the total number of tests (measurements). The key contribution of this paper is in adopting a new information-theoretic perspective on group testing problems. We formulate the group testing problem as a channel coding/decoding problem and derive a single-letter characterization for the total number of tests used to identify the defective set. Although the focus of this paper is primarily on group testing, our main result is generally applicable to other compressive sensing models.

Video anomaly detection based on local statistical aggregates

Anomalies in many video surveillance applications have local spatio-temporal signatures, namely, they occur over a small time window or a small spatial region. The distinguishing feature of these scenarios is that outside this spatio-temporal anomalous region, activities appear normal. We develop a probabilistic framework to account for such local spatio-temporal anomalies. We show that our framework admits elegant characterization of optimal decision rules. A key insight of the paper is that if anomalies are local optimal decision rules are local even when the nominal behavior exhibits global spatial and temporal statistical dependencies. This insight helps collapse the large ambient data dimension for detecting local anomalies. Consequently, consistent data-driven local empirical rules with provable performance can be derived with limited training data. Our empirical rules are based on scores functions derived from local nearest neighbor distances. These rules aggregate statistics across spatio-temporal locations & scales, and produce a single composite score for video segments. We demonstrate the efficacy of our scheme on several video surveillance datasets and compare with existing work.

Distributed Detection in Sensor Networks With Packet Losses and Finite Capacity Links

We consider the problem of classifying among a set of M hypotheses via distributed noisy sensors. The sensors can collaborate over a communication network and the task is to arrive at a consensus about the event after exchanging messages. We apply a variant of belief propagation as a strategy for collaboration to arrive at a solution to the distributed classification problem. We show that the message evolution can be reformulated as the evolution of a linear dynamical system, which is primarily characterized by network connectivity. We show that a consensus to the centralized maximum a posteriori (MAP) estimate can almost always reached by the sensors for any arbitrary network. We then extend these results in several directions. First, we demonstrate that these results continue to hold with quantization of the messages, which is appealing from the point of view of finite bit rates supportable between links. We then demonstrate robustness against packet losses, which implies that optimal decisions can be achieved with asynchronous transmissions as well. Next, we present an account of energy requirements for distributed detection and demonstrate significant improvement over conventional decentralized detection. Finally, extensions to distributed estimation are described

Information Theoretic Bounds for Compressed Sensing

In this paper, we derive information theoretic performance bounds to sensing and reconstruction of sparse phenomena from noisy projections. We consider two settings: output noise models where the noise enters after the projection and input noise models where the noise enters before the projection. We consider two types of distortion for reconstruction: support errors and mean-squared errors. Our goal is to relate the number of measurements, m , and SNR, to signal sparsity, k, distortion level, d, and signal dimension, n . We consider support errors in a worst-case setting. We employ different variations of Fanos inequality to derive necessary conditions on the number of measurements and SNR required for exact reconstruction. To derive sufficient conditions, we develop new insights on max-likelihood analysis based on a novel superposition property. In particular, this property implies that small support errors are the dominant error events. Consequently, our ML analysis does not suffer the conservatism of the union bound and leads to a tighter analysis of max-likelihood. These results provide order-wise tight bounds. For output noise models, we show that asymptotically an SNR of ((n)) together with (k (n/k)) measurements is necessary and sufficient for exact support recovery. Furthermore, if a small fraction of support errors can be tolerated, a constant SNR turns out to be sufficient in the linear sparsity regime. In contrast for input noise models, we show that support recovery fails if the number of measurements scales as o(n(n)/SNR), implying poor compression performance for such cases. Motivated by the fact that the worst-case setup requires significantly high SNR and substantial number of measurements for input and output noise models, we consider a Bayesian setup. To derive necessary conditions, we develop novel extensions to Fanos inequality to handle continuous domains and arbitrary distortions. We then develop a new max-likelihood analysis over the set of rate distortion quantization points to characterize tradeoffs between mean-squared distortion and the number of measurements using rate-distortion theory. We show that with constant SNR the number of measurements scales linearly with the rate-distortion function of the sparse phenomena.

Foreground-Adaptive Background Subtraction

Background subtraction is a powerful mechanism for detecting change in a sequence of images that finds many applications. The most successful background subtraction methods apply probabilistic models to background intensities evolving in time; nonparametric and mixture-of-Gaussians models are but two examples. The main difficulty in designing a robust background subtraction algorithm is the selection of a detection threshold. In this paper, we adapt this threshold to varying video statistics by means of two statistical models. In addition to a nonparametric background model, we introduce a foreground model based on small spatial neighborhood to improve discrimination sensitivity. We also apply a Markov model to change labels to improve spatial coherence of the detections. The proposed methodology is applicable to other background models as well.

Abnormal events detection based on spatio-temporal co-occurences

We explore a location based approach for behavior modeling and abnormality detection. In contrast to the conventional object based approach where an object may first be tagged, identified, classified, and tracked, we proceed directly with event characterization and behavior modeling at the pixel(s) level based on motion labels obtained from background subtraction. Since events are temporally and spatially dependent, this calls for techniques that account for statistics of spatiotemporal events. Based on motion labels, we learn co-occurrence statistics for normal events across space-time. For one (or many) key pixel(s), we estimate a co-occurrence matrix that accounts for any two active labels which co-occur simultaneously within the same spatiotemporal volume. This co-occurrence matrix is then used as a potential function in a Markov random field (MRF) model to describe the probability of observations within the same spatiotemporal volume. The MRF distribution implicitly accounts for speed, direction, as well as the average size of the objects passing in front of each key pixel. Furthermore, when the spatiotemporal volume is large enough, the co-occurrence distribution contains the average normal path followed by moving objects. The learned normal co-occurrence distribution can be used for abnormal detection. Our method has been tested on various outdoor videos representing various challenges.

Zero-Shot Learning via Semantic Similarity Embedding

In this paper we consider a version of the zero-shot learning problem where seen class source and target domain data are provided. The goal during test-time is to accurately predict the class label of an unseen target domain instance based on revealed source domain side information (e.g. attributes) for unseen classes. Our method is based on viewing each source or target data as a mixture of seen class proportions and we postulate that the mixture patterns have to be similar if the two instances belong to the same unseen class. This perspective leads us to learning source/target embedding functions that map an arbitrary source/target domain data into a same semantic space where similarity can be readily measured. We develop a max-margin framework to learn these similarity functions and jointly optimize parameters by means of cross validation. Our test results are compelling, leading to significant improvement in terms of accuracy on most benchmark datasets for zero-shot recognition.

Wireless Ad Hoc Networks: Strategies and Scaling Laws for the Fixed SNR Regime

This paper deals with throughput scaling laws for random ad hoc wireless networks in a rich scattering environment. We develop schemes to optimize the ratio lambda(n) of achievable network sum capacity to the sum of the point-to-point capacities of source-destinations (S-D) pairs operating in isolation. Our focus in this paper is on fixed signal-to-noise ratio (SNR) networks, i.e., networks where the worst case SNR over the S-D pairs is fixed independent of n. For such fixed SNR networks, which include fixed area networks as a special case, we show that collaborative strategies yield a scaling law of lambda(n)=Omega(1/n1/3) in contrast to multihop strategies which yield a scaling law of lambda(n)=Theta(1/radicn). While networks where worst case SNR goes to zero do not preclude the possibility of collaboration, multihop strategies achieve optimal throughput. The plausible reason is that the gains due to collaboration cannot offset the effect of vanishing receive SNR. This suggests that for fixed SNR networks, a network designer should look for network protocols that exploit collaboration

Zero-Shot Learning via Joint Latent Similarity Embedding

Zero-shot recognition (ZSR) deals with the problem of predicting class labels for target domain instances based on source domain side information (e.g. attributes) of unseen classes. We formulate ZSR as a binary prediction problem. Our resulting classifier is class-independent. It takes an arbitrary pair of source and target domain instances as input and predicts whether or not they come from the same class, i.e. whether there is a match. We model the posterior probability of a match since it is a sufficient statistic and propose a latent probabilistic model in this context. We develop a joint discriminative learning framework based on dictionary learning to jointly learn the parameters of our model for both domains, which ultimately leads to our class-independent classifier. Many of the existing embedding methods can be viewed as special cases of our probabilistic model. On ZSR our method shows 4.90% improvement over the state-of-the-art in accuracy averaged across four benchmark datasets. We also adapt ZSR method for zero-shot retrieval and show 22.45% improvement accordingly in mean average precision (mAP).

Video Anomaly Identification

This article describes a family of unsupervised approaches to video anomaly detection based on statistical activity analysis. Approaches based on activity analysis provide intriguing possibilities for region-of-interest (ROI) processing since relevant activities and their locations are detected prior to higher-level processing such as object tracking, tagging, and classification. This strategy is essential for scalability of video analysis to cluttered environments with a multitude of objects and activities. Activity analysis approaches typically do not involve object tracking, and yet they inherently account for spatiotemporal dependencies. They are robust to clutter arising from multiple activities and contamination arising from poor background subtraction or occlusions. They can sometimes also be employed for fusing activities from multiple cameras. We illustrate successful application of activity analysis to anomaly detection in various scenarios, including the detection of abandoned objects, crowds of people, and illegal U-turns.