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Convolutional sparse coding (CSC) can learn representative shift-invariant patterns from multiple kinds of data. However, existing CSC methods can only model noises from Gaussian distribution, which is restrictive and unrealistic. In this…
For a system consisting of several Dirac fields and a particle, we study the Cauchy problem with random initial data. We assume that the initial measure has zero mean value, a finite mean charge density, a translation-invariant covariance…
The most common way of estimating the anomalous diffusion exponent from single-particle trajectories consists in a linear fitting of the dependence of the time averaged mean square displacement on the lag time at the log-log scale. However,…
In this letter, we consider two sets of observations defined as subspace signals embedded in noise and we wish to analyze the distance between these two subspaces. The latter entails evaluating the angles between the subspaces, an issue…
We present an efficient algorithm to compute tight upper bounds of collision probability between two objects with positional uncertainties, whose error distributions are represented with non-Gaussian forms. Our approach can handle noisy…
Sampling from the output distribution of chaotic quantum evolutions, and of pseudo-random universal quantum circuits in particular, has been proposed as a prominent milestone for near-term quantum supremacy. The same paper notes that…
Stochastic differential equations have proved to be a valuable governing framework for many real-world systems which exhibit ``noise'' or randomness in their evolution. One quality of interest in such systems is the shape of their…
With an ever-expanding ecosystem of noisy and intermediate-scale quantum devices, exploring their possible applications is a rapidly growing field of quantum information science. In this work, we demonstrate that variational quantum…
We study a fixed step-size noisy distributed gradient descent algorithm for solving optimization problems in which the objective is a finite sum of smooth but possibly non-convex functions. Random perturbations are introduced to the…
Single-channel deep speech enhancement approaches often estimate a single multiplicative mask to extract clean speech without a measure of its accuracy. Instead, in this work, we propose to quantify the uncertainty associated with clean…
Multiplicative noise arises in inverse problems when, for example, uncertainty on measurements is proportional to the size of the measurement itself. The likelihood that arises is hence more complicated than that from additive noise. We…
For a general class of diffusion processes with multiplicative noise, describing a variety of physical as well as financial phenomena, mostly typical of complex systems, we obtain the analytical solution for the moments at all times. We…
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…
Giving a convincing experimental evidence of the quantum supremacy over classical simulations is a challenging goal. Noise is considered to be the main problem in such a demonstration, hence it is urgent to understand the effect of noise.…
Mixtures of Gaussian factors are powerful tools for modeling an unobserved heterogeneous population, offering - at the same time - dimension reduction and model-based clustering. Unfortunately, the high prevalence of spurious solutions and…
Noise Contrastive Estimation (NCE) is a popular approach for learning probability density functions parameterized up to a constant of proportionality. The main idea is to design a classification problem for distinguishing training data from…
This paper addresses the following question: given a sample of i.i.d. random variables with finite variance, can one construct an estimator of the unknown mean that performs nearly as well as if the data were normally distributed? One of…
We derive an efficient stochastic algorithm for inverse problems that present an unknown linear forcing term and a set of nonlinear parameters to be recovered. It is assumed that the data is noisy and that the linear part of the problem is…
We present a quantum algorithm for efficiently sampling transformed Gaussian random fields on $d$-dimensional domains, based on an enhanced version of the classical moving average method. Pointwise transformations enforcing boundedness are…
We introduce and initiate the study of new parameters associated with any norm and any log-concave measure on $\mathbb R^n$, which provide sharp distributional inequalities. In the Gaussian context this investigation sheds light to the…