Related papers: Uncoupled isotonic regression via minimum Wasserst…
The problem of inferring pair-wise and higher-order interactions in complex systems involving large numbers of interacting variables, from observational data, is fundamental to many fields. Known to the statistical physics community as the…
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…
We consider the nonparametric regression estimation problem of recovering an unknown response function f on the basis of spatially inhomogeneous data when the design points follow a known compactly supported density g with a finite number…
We study the non-parametric isotonic regression problem for bivariate elicitable functionals that are given as an elicitable univariate functional and its Bayes risk. Prominent examples for functionals of this type are (mean, variance) and…
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…
Composite quantile regression has been used to obtain robust estimators of regression coefficients in linear models with good statistical efficiency. By revealing an intrinsic link between the composite quantile regression loss function and…
Covariate shift arises when covariate distributions differ between source and target populations while the conditional distribution of the response remains invariant, and it underlies problems in missing data and causal inference. We…
In this paper we study minimax and adaptation rates in general isotonic regression. For uniform deterministic and random designs in $[0,1]^d$ with $d\ge 2$ and $N(0,1)$ noise, the minimax rate for the $\ell_2$ risk is known to be bounded…
We review the theory of, and develop algorithms for transforming a finite point set in ${\bf R}^d$ into a set in \emph{radial isotropic position} by a nonsingular linear transformation followed by rescaling each image point to the unit…
We consider noisy observations of a distribution with unknown support. In the deconvolution model, it has been proved recently [19] that, under very mild assumptions, it is possible to solve the deconvolution problem without knowing the…
We consider a data-driven robust hypothesis test where the optimal test will minimize the worst-case performance regarding distributions that are close to the empirical distributions with respect to the Wasserstein distance. This leads to a…
We want to reconstruct a signal based on inhomogeneous data (the amount of data can vary strongly), using the model of regression with a random design. Our aim is to understand the consequences of inhomogeneity on the accuracy of estimation…
We consider the problem of estimating an unknown $\theta\in {\mathbb{R}}^n$ from noisy observations under the constraint that $\theta$ belongs to certain convex polyhedral cones in ${\mathbb{R}}^n$. Under this setting, we prove bounds for…
We introduce a general formulation for an implicit equation-free method in the setting of slow-fast systems. First, we give a rigorous convergence result for equation-free analysis showing that the implicitly defined coarse-level time…
Regression analysis for responses taking values in general metric spaces has received increasing attention, particularly for settings with Euclidean predictors $X \in \mathbb{R}^p$ and non-Euclidean responses $Y$ in metric spaces. While…
We consider the problem of solving the optimal transport problem between two empirical distributions with missing values. Our main assumption is that the data is missing completely at random (MCAR), but we allow for heterogeneous…
The problem of finding suitable point embedding or geometric configurations given only Euclidean distance information of point pairs arises both as a core task and as a sub-problem in a variety of machine learning applications. In this…
Optimal transport has found widespread applications in signal processing and machine learning. Among its many equivalent formulations, optimal transport seeks to reconstruct a random variable/vector with a prescribed distribution at the…
A general model-independent discussion of mesonic correlation functions is given. We derive new inequalities, including one stronger than Weingarten's inequality. Mesonic correlation functions are calculated in the random instanton vacuum…
In compact settings, the convergence rate of the empirical optimal transport cost to its population value is well understood for a wide class of spaces and cost functions. In unbounded settings, however, hitherto available results require…