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Understanding the generalization properties of deep learning models is critical for their successful usage in many applications, especially in the regimes where the number of training samples is limited. We study the generalization properties of deep neural networks (DNNs) via the Jacobian matrix of the network. Our analysis is general to arbitrary network structures, types of non-linearities and...
We consider problems where one wishes to represent a parameter associated with a signal source - subject to a certain rate and distortion - based on the observation of a number of realizations of the source signal. By reducing these indirect vector quantization problems to a standard vector quantization one, we provide a bound to the fundamental interplay between the rate and distortion in the large-rate...
Real-world data processing problems often involve multiple data modalities, e.g., panchromatic and multispectral images, positron emission tomography (PET) and magnetic resonance imaging (MRI) images. As these modalities capture information associated with the same phenomenon, they must necessarily be correlated, although the precise relation is rarely known. In this paper, we propose a coupled dictionary...
In support of art investigation, we propose a new source separation method that unmixes a single X-ray scan acquired from double-sided paintings. Unlike prior source separation methods, which are based on statistical or structural incoherence of the sources, we use visual images taken from the front- and back-side of the panel to drive the separation process. The coupling of the two imaging modalities...
In this paper, we study the problem of projection kernel design for the reconstruction of high-dimensional signals from low-dimensional measurements in the presence of side information, assuming that the signal of interest and the side information signal are described by a joint Gaussian mixture model (GMM). In particular, we consider the case where the projection kernel for the signal of interest...
The Internet-of-Things (IoT) is the key enabling technology for transforming current urban environments into so-called Smart Cities. One of the goals behind making cities smarter is to provide a healthy environment that improves the citizens' quality of life and wellbeing. In this work, we introduce a novel data aggregation mechanism tailored to the application of large-scale air pollution monitoring...
The classical compressed sensing (CS) paradigm can be modified so as to leverage a signal correlated to the signal of interest, called side information, which is assumed to be provided a priori at the decoder in order to aid reconstruction. In this work, we propose a novel CS reconstruction method based on belief propagation principles, which manages to exploit side information generated from a diverse...
We address the problem of reference-based compressed sensing: reconstruct a sparse signal from few linear measurements using as prior information a reference signal, a signal similar to the signal we want to reconstruct. Access to reference signals arises in applications such as medical imaging, e.g., through prior images of the same patient, and compressive video, where previously reconstructed frames...
This paper investigates the impact of projection design on the reconstruction of high-dimensional signals from low-dimensional measurements in the presence of side information. In particular, we assume that both the signal of interest and the side information are described by a joint Gaussian mixture model (GMM) distribution. Sharp necessary and sufficient conditions on the number of measurements...
We propose a feature design framework that considers simultaneously performance and computational complexity. In particular, we incorporate these two metrics, which are very important to many low-energy on-chip applications such as implantable neural interfaces, onto an optimization problem. This allows us to strike a balance between the performance of the signal processing task and the computational...
This paper offers a characterization of performance limits for classification and reconstruction of high-dimensional signals from noisy compressive measurements, in the presence of side information. We assume the signal of interest and the side information signal are drawn from a correlated mixture of distributions/components, where each component associated with a specific class label follows a Gaussian...
This paper studies the performance associated with the classification of linear subspaces corrupted by noise with a mismatched classifier. In particular, we consider a problem where the classifier observes a noisy signal, the signal distribution conditioned on the signal class is zero-mean Gaussian with low-rank covariance matrix, and the classifier knows only the mismatched parameters in lieu of...
We address the problem of Compressed Sensing (CS) with side information. Namely, when reconstructing a target CS signal, we assume access to a similar signal. This additional knowledge, the side information, is integrated into CS via ℓ1-ℓ1 and ℓ1-ℓ2 minimization. We then provide lower bounds on the number of measurements that these problems require for successful reconstruction of the target signal...
This paper advocates the use of the emerging distributed compressive sensing (DCS) paradigm in order to deploy energy harvesting (EH) wireless sensor networks (WSN) with practical network lifetime and data gathering rates that are substantially higher than the state-of-the-art. In particular, we argue that there are two fundamental mechanisms in an EH WSN: i) the energy diversity associated with the...
We characterize the minimum number of measurements needed to drive to zero the minimum mean squared error (MMSE) of Gaussian mixture model (GMM) input signals in the low-noise regime. The result also hints at almost phase-transition optimal recovery procedures based on a classification and reconstruction approach.
This paper puts forth projections designs for compressive classification of Gaussian mixture models. In particular, we capitalize on the asymptotic characterization of the behavior of an (upper bound to the) misclassification probability associated with the optimal Maximum-A-Posteriori (MAP) classifier, which depends on quantities that are dual to the concepts of the diversity gain and coding gain...
Motivated by applications in high-dimensional signal processing, we derive fundamental limits on the performance of compressive linear classifiers. By analogy with Shannon theory, we define the classification capacity, which quantifies the maximum number of classes that can be discriminated with low probability of error, and the diversity-discrimination tradeoff, which quantifies the tradeoff between...
We unveil asymptotic characterizations of the average minimum mean-squared error (MMSE) and the average mutual information in scalar fading coherent channels, where the receiver knows the exact fading channel state but the transmitter knows only the fading channel distribution, driven by a range of inputs both in the regimes of low-SNR — and at the heart of the novelty of the contribution — high-SNR...
This paper presents fundamental limits associated with compressive classification of Gaussian mixture source models. In particular, we offer an asymptotic characterization of the behavior of the (upper bound to the) misclassification probability associated with the optimal Maximum-A-Posteriori (MAP) classifier that depends on quantities that are dual to the concepts of diversity gain and coding gain...
This paper investigates power allocation strategies over a bank of independent parallel Gaussian wiretap channels where a legitimate transmitter and a legitimate receiver communicate in the presence of an eavesdropper and a friendly jammer. We give algorithms to compute the optimal power allocation strategy of the jammer in the degraded scenario. We also give an algorithm to compute power allocations...
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