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In the recent years, Deep Neural Networks (DNNs) have managed to succeed at tasks that previously appeared impossible, such as human-level object recognition, text synthesis, translation, playing games and many more. In spite of these major achievements, o ...
We study the computational complexity of the optimal transport problem that evaluates the Wasser- stein distance between the distributions of two K-dimensional discrete random vectors. The best known algorithms for this problem run in polynomial time in th ...
Randomized trace estimation is a popular and well-studied technique that approximates the trace of a large-scale matrix B by computing the average of x(T) Bx for many samples of a random vector X. Often, B is symmetric positive definite (SPD) but a number ...
Secrecy by design is examined as an approach to information-theoretic secrecy. The main idea behind this approach is to design an information processing system from the ground up to be perfectly secure with respect to an explicit secrecy constraint. The pr ...
In this work, the probability of an event under some joint distribution is bounded by measuring it with the product of the marginals instead (which is typically easier to analyze) together with a measure of the dependence between the two random variables. ...
Network information theory studies the communication of information in a network and considers its fundamental limits. Motivating from the extensive presence of the networks in the daily life, the thesis studies the fundamental limits of particular network ...
Wyner's common information is a measure that quantifies and assesses the commonality between two random variables. Based on this, we introduce a novel two-step procedure to construct features from data, referred to as Common Information Components Analysis ...
We study generalization properties of random features (RF) regression in high dimensions optimized by stochastic gradient descent (SGD) in under-/overparameterized regime. In this work, we derive precise non-asymptotic error bounds of RF regression under b ...
Testing mutual independence among several random vectors of arbitrary dimensions is a challenging problem in Statistics, and it has gained considerable interest in recent years. In this article, we propose some nonparametric tests based on different notion ...
Consider a linear elliptic PDE defined over a stochastic stochastic geometry a function of N random variables. In many application, quantify the uncertainty propagated to a quantity of interest (QoI) is an important problem. The random domain is split into ...