Related papers: Gaussian Approximation of Quantization Error for E…
We consider the rate-distortion function for lossy source compression, as well as the channel capacity for error correction, through the lens of distributional robustness. We assume that the distribution of the source or of the additive…
Compared with word embedding based on point representation, distribution-based word embedding shows more flexibility in expressing uncertainty and therefore embeds richer semantic information when representing words. The Wasserstein…
Given any deep fully connected neural network, initialized with random Gaussian parameters, we bound from above the quadratic Wasserstein distance between its output distribution and a suitable Gaussian process. Our explicit inequalities…
We study the problem of quantifying how far an empirical distribution deviates from Gaussianity under the framework of optimal transport. By exploiting the cone geometry of the relative translation invariant quadratic Wasserstein space, we…
We consider a continuous-time bandlimited additive white Gaussian noise channel with 1-bit output quantization. On such a channel the information is carried by the temporal distances of the zero-crossings of the transmit signal. The set of…
Noise is a vital factor in determining the accuracy of processing the information of the quantum channel. One must consider classical noise effects associated with quantum noise sources for more realistic modelling of quantum channels. A…
We investigate the limits of communication over the discrete-time Additive White Gaussian Noise (AWGN) channel, when the channel output is quantized using a small number of bits. We first provide a proof of our recent conjecture on the…
This paper considers the problem of regression over distributions, which is becoming increasingly important in machine learning. Existing approaches often ignore the geometry of the probability space or are computationally expensive. To…
We provide statistical theory for conditional and unconditional Wasserstein generative adversarial networks (WGANs) in the framework of dependent observations. We prove upper bounds for the excess Bayes risk of the WGAN estimators with…
In this paper, we consider single- and multi-user Gaussian channels with feedback under expected power constraints and with non-vanishing error probabilities. In the first of two contributions, we study asymptotic expansions for the…
Generative Adversarial Networks (GANs) have been used to model the underlying probability distribution of sample based datasets. GANs are notoriuos for training difficulties and their dependence on arbitrary hyperparameters. One recent…
We study the Wasserstein distance $W_2$ for Gaussian samples. We establish the exact rate of convergence $\sqrt{\log\log n/n}$ of the expected value of the $W_2$ distance between the empirical and true $c.d.f.$'s for the normal…
Generative adversarial nets (GANs) and variational auto-encoders have significantly improved our distribution modeling capabilities, showing promise for dataset augmentation, image-to-image translation and feature learning. However, to…
Compressed sensing is by now well-established as an effective tool for extracting sparsely distributed information, where sparsity is a discrete concept, referring to the number of dominant nonzero signal components in some basis for the…
We propose a distributionally robust approach to risk-sensitive estimation of an unknown signal x from an observed signal y. The unknown signal and observation are modeled as random vectors whose joint probability distribution is unknown,…
The problem of distributed estimation of a parametric physical field is stated as a maximum likelihood estimation problem. Sensor observations are distorted by additive white Gaussian noise. Prior to data transmission, each sensor quantizes…
The adapted Wasserstein distance is a metric for quantifying distributional uncertainty and assessing the sensitivity of stochastic optimization problems on time series data. A computationally efficient alternative to it, is provided by the…
We propose a covert communication protocol for the spread-spectrum multiple random access with additive white Gaussian noise (AWGN) channel. No existing paper has studied covert communication for the random access channel. Our protocol…
Covert communication over an additive white Gaussian noise (AWGN) channel with finite block length is investigated in this paper. The attention is on the covert criterion, which has not been considered in finite block length circumstance.…
Gaussian Process regression is a kernel method successfully adopted in many real-life applications. Recently, there is a growing interest on extending this method to non-Euclidean input spaces, like the one considered in this paper,…