Related papers: Testing distribution in deconvolution problems
We consider the convolution model where i.i.d. random variables $X_i$ having unknown density $f$ are observed with additive i.i.d. noise, independent of the $X$'s. We assume that the density $f$ belongs to either a Sobolev class or a class…
We study evolution equations of drift-diffusion type when various parameters are random. Motivated by applications in pedestrian dynamics, we focus on the case when the total mass is, due to boundary or reaction terms, not conserved. After…
We introduce a new predictive mechanism that operates in the presence of hidden confounding across distributionally diverse data sources while ensuring consistent estimation of causal parameters-despite their recognized suboptimality for…
We study the problem of denoising observations \(Y_i=X_i+Z_i\), where the latent variables \(X_i\) are sampled from a low-dimensional manifold in \(\mathbb{R}^n\) and the noise variables \(Z_i\) are isotropic Gaussian. We propose a…
For a set of dependent random variables, without stationary or the strong mixing assumptions, we derive the asymptotic independence between their sums and maxima. Then we apply this result to high-dimensional testing problems, where we…
In this paper, we consider the problem of testing independence in high-dimensional settings with missing data. Building upon a recently proposed Kendall-based statistic, we introduce two new modifications specifically designed to…
We study a well-known problem concerning a random variable $Z$ uniformly distributed between two independent random variables. A new extension has been introduced for this problem and fairly large classes of randomly weighted average…
We study the problem of domain adaptation under distribution shift, where the shift is due to a change in the distribution of an unobserved, latent variable that confounds both the covariates and the labels. In this setting, neither the…
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…
Given data sampled from a number of variables, one is often interested in the underlying causal relationships in the form of a directed acyclic graph. In the general case, without interventions on some of the variables it is only possible…
We investigate the problem of jointly testing two hypotheses and estimating a random parameter based on data that is observed sequentially by sensors in a distributed network. In particular, we assume the data to be drawn from a Gaussian…
We consider the limiting distribution of the quantity $X^s/(X+Y)^r$, where $X$ and $Y$ are two independent Binomial random variables with a common success probability and a number of trials $n$ and $m$, respectively, and $r,s$ are positive…
A common assumption in causal inference from observational data is that there is no hidden confounding. Yet it is, in general, impossible to verify this assumption from a single dataset. Under the assumption of independent causal mechanisms…
The paper discusses the estimation of a continuous density function of the target random field $X_{\bf{i}}$, $\bf{i}\in \mathbb {Z}^N$ which is contaminated by measurement errors. In particular, the observed random field $Y_{\bf{i}}$,…
We consider the estimation of average treatment effects in observational studies and propose a new framework of robust causal inference with unobserved confounders. Our approach is based on distributionally robust optimization and proceeds…
Accurate noise modelling is important for training of deep learning reconstruction algorithms. While noise models are well known for traditional imaging techniques, the noise distribution of a novel sensor may be difficult to determine a…
We research adaptive maximum likelihood-type estimation for an ergodic diffusion process where the observation is contaminated by noise. This methodology leads to the asymptotic independence of the estimators for the variance of observation…
We study a discrete denoising diffusion framework that integrates a sample-efficient estimator of single-site conditionals with round-robin noising and denoising dynamics for generative modeling over discrete state spaces. Rather than…
Causal discovery estimates the underlying physical process that generates the observed data: does X cause Y or does Y cause X? Current methodologies use structural conditions to turn the causal query into a statistical query, when only…
Suppose that at any stage of a statistical experiment a control variable $X$ that affects the distribution of the observed data $Y$ at this stage can be used. The distribution of $Y$ depends on some unknown parameter $\theta$, and we…