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We consider the estimation problem for jointly stable random variables. Under two specific dependency models: a linear transformation of two independent stable variables and a sub-Gaussian symmetric $\alpha$-stable (S$\alpha$S) vector, we…
Suppose a linear model y = Hx + n, where inputs x, n are independent Gaussian mixtures. The problem is to design the transfer matrix H so as to minimize the mean square error (MSE) when estimating x from y. This problem has important…
We consider a problem of finding a target located in a finite $d$-dimensional domain, using $N$ independent random walkers, when partial information on the target location is given as a probability distribution. When $N$ is large, the…
In this paper, based on the theory of defining sets, two classes of at most six-weight linear codes over $\mathbb{F}_p$ are constructed. The weight distributions of the linear codes are determined by means of Gaussian period and Weil sums.…
In this paper we consider the computation of channel capacity for ergodic multiple-input multiple-output channels with additive white Gaussian noise. Two scenarios are considered. Firstly, a time-varying channel is considered in which both…
We derive closed-form expressions for the Bayes optimal decision boundaries in binary classification of high dimensional overlapping Gaussian mixture model (GMM) data, and show how they depend on the eigenstructure of the class covariances,…
We study secure source-coding with causal disclosure, under the Gaussian distribution. The optimality of Gaussian auxiliary random variables is shown in various scenarios. We explicitly characterize the tradeoff between the rates of…
This paper studies an integrated learning and optimization problem in which a prediction model estimates the right-hand-side parameters of a linear program (LP) using a contextual vector. Considering that such a prediction alters the…
We consider the transmission of a memoryless bivariate Gaussian source over an average-power-constrained one-to-two Gaussian broadcast channel. The transmitter observes the source and describes it to the two receivers by means of an…
We study communication over a Gaussian multiple-access channel (MAC) with two types of transmitters: Digital transmitters hold a message from a discrete set that needs to be communicated to the receiver with vanishing error probability.…
This paper studies the problem of estimating the covariance of a collection of vectors using only highly compressed measurements of each vector. An estimator based on back-projections of these compressive samples is proposed and analyzed. A…
We consider the problem of recovering linear image $Bx$ of a signal $x$ known to belong to a given convex compact set $X$ from indirect observation $\omega=Ax+\sigma\xi$ of $x$ corrupted by Gaussian noise $\xi$. It is shown that under some…
Sorting networks are oblivious sorting algorithms with many practical applications and rich theoretical properties. Propositional encodings of sorting networks are a key tool for proving concrete bounds on the minimum number of comparators…
This paper proposes a highly accurate algorithm to estimate the signal-to-noise ratio (SNR) for a linear system from a single realization of the received signal. We assume that the linear system has a Gaussian matrix with one sided left…
Linear precoding techniques can achieve near- optimal capacity due to the special channel property in down- link massive MIMO systems, but involve high complexity since complicated matrix inversion of large size is required. In this paper,…
In this article, we are proposing a closed-form solution for the capacity of the single quantum channel. The Gaussian distributed input has been considered for the analytical calculation of the capacity. In our previous couple of papers, we…
We consider the problem of breaking a multivariate (vector) time series into segments over which the data is well explained as independent samples from a Gaussian distribution. We formulate this as a covariance-regularized maximum…
Recent works on Bayesian neural networks (BNNs) have highlighted the need to better understand the implications of using Gaussian priors in combination with the compositional structure of the network architecture. Similar in spirit to the…
We study the spherical cap packing problem with a probabilistic approach. Such probabilistic considerations result in an asymptotic sharp universal uniform bound on the maximal inner product between any set of unit vectors and a…
We consider fully connected and feedforward deep neural networks with dependent and possibly heavy-tailed weights, as introduced in [26], to address limitations of the standard Gaussian prior. It has been proved in [26] that, as the number…