Related papers: Support and distribution inference from noisy data
We consider so-called univariate unlinked (sometimes ``decoupled,'' or ``shuffled'') regression when the unknown regression curve is monotone. In standard monotone regression, one observes a pair $(X,Y)$ where a response $Y$ is linked to a…
A common challenge in the natural sciences is to disentangle distinct, unknown sources from observations. Examples of this source separation task include deblending galaxies in a crowded field, distinguishing the activity of individual…
This paper studies estimation of and inference on a distribution function $F$ that is concave on the nonnegative half line and admits a density function $f$ with potentially unbounded support. When $F$ is strictly concave, we show that the…
This paper builds Wasserstein ambiguity sets for the unknown probability distribution of dynamic random variables leveraging noisy partial-state observations. The constructed ambiguity sets contain the true distribution of the data with…
This paper primarily considers the robust estimation problem under Wasserstein distance constraints on the parameter and noise distributions in the linear measurement model with additive noise, which can be formulated as an…
In this paper, we consider the problem of propagating an uncertain distribution by a possibly non-linear function and quantifying the resulting uncertainty. We measure the uncertainty using the Wasserstein distance, and for a given input…
We study density estimation for classes of shift-invariant distributions over $\mathbb{R}^d$. A multidimensional distribution is "shift-invariant" if, roughly speaking, it is close in total variation distance to a small shift of it in any…
Despite the importance of denoising in modern machine learning and ample empirical work on supervised denoising, its theoretical understanding is still relatively scarce. One concern about studying supervised denoising is that one might not…
Assume that we observe i.i.d.~points lying close to some unknown $d$-dimensional $\mathcal{C}^k$ submanifold $M$ in a possibly high-dimensional space. We study the problem of reconstructing the probability distribution generating the…
For a class of partially observed diffusions, conditions are given for the map from the initial condition of the signal to filtering distribution to be contractive with respect to Wasserstein distances, with rate which does not necessarily…
The blind deconvolution problem amounts to reconstructing both a signal and a filter from the convolution of these two. It constitutes a prominent topic in mathematical and engineering literature. In this work, we analyze a sparse version…
We consider several detection situations where, under the alternative hypothesis, the signal admits a low complexity model and, under both the null and the alternative hypotheses, the distribution of the background noise is {unknown}. We…
Isotonic regression is a standard problem in shape-constrained estimation where the goal is to estimate an unknown nondecreasing regression function $f$ from independent pairs $(x_i, y_i)$ where $\mathbb{E}[y_i]=f(x_i), i=1, \ldots n$.…
We propose a class of estimators for deconvolution in mixture models based on a simple two-step "bin-and-smooth" procedure applied to histogram counts. The method is both statistically and computationally efficient: by exploiting recent…
We propose an image deconvolution algorithm when the data is contaminated by Poisson noise. The image to restore is assumed to be sparsely represented in a dictionary of waveforms such as the wavelet or curvelet transform. Our key…
Discrete diffusion models are increasingly competitive for language modeling, yet it remains unclear how their denoising objectives organize learning. Although these objectives target the full data distribution, we show that the exact…
Recent work has shown that Transformers can perform in-context learning for linear regression under restrictive assumptions, including i.i.d. data, Gaussian noise, and Gaussian regression coefficients. However, real-world data often violate…
We study the {\em robust proper learning} of univariate log-concave distributions (over continuous and discrete domains). Given a set of samples drawn from an unknown target distribution, we want to compute a log-concave hypothesis…
In this work we analyze a convex-programming method for estimating superpositions of point sources or spikes from nonuniform samples of their convolution with a known kernel. We consider a one-dimensional model where the kernel is either a…
The problem of modeling the relationship between univariate distributions and one or more explanatory variables has found increasing interest. Traditional functional data methods cannot be applied directly to distributional data because of…