Related papers: Some results on the Weiss-Weinstein bound for cond…
We present a learned unsupervised denoising method for arbitrary types of data, which we explore on images and one-dimensional signals. The training is solely based on samples of noisy data and examples of noise, which -- critically -- do…
Let $W_i=\{W_i(t), t\in \mathbb{R}_+\}, i=1,2$ be two Wiener processes and $W_3=\{W_3(\mathbf{t}), \mathbf{t}\in \mathbb{R}_+^2\}$ be a two-parameter Brownian sheet, all three processes being mutually independent. We derive upper and lower…
This paper investigates the effectiveness of factorial speech processing models in noise-robust automatic speech recognition tasks. For this purpose, the paper proposes an idealistic approach for modeling state-conditional observation…
We consider the problem of learning causal models from observational data generated by linear non-Gaussian acyclic causal models with latent variables. Without considering the effect of latent variables, one usually infers wrong causal…
Unnormalized (or energy-based) models provide a flexible framework for capturing the characteristics of data with complex dependency structures. However, the application of standard Bayesian inference methods has been severely limited…
With their ability to handle an increased amount of information, multivariate and multichannel signals can be used to solve problems normally not solvable with signals obtained from a single source. One such problem is the decomposition…
We use analytical examples and asymptotic forms to examine the mathematical structure and physical meaning of the seismic cross correlation measurement. We show that in general, cross correlations are not Green's functions of medium, and…
One major drawback of state-of-the-art artificial intelligence is its lack of explainability. One approach to solve the problem is taking causality into account. Causal mechanisms can be described by structural causal models. In this work,…
Sampling from an unknown distribution, accessible only through discrete samples, is a fundamental problem at the core of generative AI. The current state-of-the-art methods follow a two-step process: first, estimating the score function…
The problem of source localization with ad hoc microphone networks in noisy and reverberant enclosures, given a training set of prerecorded measurements, is addressed in this paper. The training set is assumed to consist of a limited number…
Variational source conditions proved useful for deriving convergence rates for Tikhonov's regularization method and also for other methods. Up to now such conditions have been verified only for few examples or for situations which can be…
Source separation is one of the signal processing's main emerging domain. Many techniques such as maximum likelihood (ML), Infomax, cumulant matching, estimating function, etc. have been used to address this difficult problem.…
Given near or far field wave measurements generated by some unknown time- and space-dependent acoustic source, we seek to rapidly determine a domain in space-time, as small as possible, that contains the support of a source radiating these…
The problem of estimating multiple loss parameters of an optical system using the most general ancilla-assisted parallel strategy is solved under energy constraints. An upper bound on the quantum Fisher information matrix is derived…
Discovering causal relations among observed variables in a given data set is a major objective in studies of statistics and artificial intelligence. Recently, some techniques to discover a unique causal model have been explored based on…
Inspired by classical sensitivity results for nonlinear optimization, we derive and discuss new quantitative bounds to characterize the solution map and dual variables of a parametrized nonlinear program. In particular, we derive explicit…
Accurately estimating the parameters of the nanohertz gravitational-wave background is essential for understanding its origin. The background is typically modeled with a power-law spectrum, parametrized with an amplitude $A$, which…
We consider linear and nonlinear hyperbolic SPDEs with mixed derivatives with additive space-time Gaussian white noise of the form $Y_{xt}=F(Y) + \sigma W_{xt}.$ Such equations, which transform to linear and nonlinear wave equations,…
Suppose $X = (X_x, x$ in $Z^d)$ is a family of i.i.d. variables in some measurable space, $B_0$ is a bounded set in $R^d$, and for $t > 1$, $H_t$ is a measure on $tB_0$ determined by the restriction of $X$ to lattice sites in or adjacent to…
Flow maps enable high-quality image generation in a single forward pass. However, unlike iterative diffusion models, their lack of an explicit sampling trajectory impedes incorporating external constraints for conditional generation and…