Related papers: Minimax Rate for Optimal Transport Regression Betw…
We present a framework for performing regression when both covariate and response are probability distributions on a compact interval $\Omega\subset\mathbb{R}$. Our regression model is based on the theory of optimal transportation and links…
Distribution regression seeks to estimate the conditional distribution of a multivariate response given a continuous covariate. This approach offers a more complete characterization of dependence than traditional regression methods.…
We present an optimal transport framework for performing regression when both the covariate and the response are probability distributions on a compact Euclidean subset $\Omega\subset\mathbb{R}^d$, where $d>1$. Extending beyond compactly…
Brenier's theorem is a cornerstone of optimal transport that guarantees the existence of an optimal transport map $T$ between two probability distributions $P$ and $Q$ over $\mathbb{R}^d$ under certain regularity conditions. The main goal…
We study distributed estimation of a Gaussian mean under communication constraints in a decision theoretical framework. Minimax rates of convergence, which characterize the tradeoff between the communication costs and statistical accuracy,…
We consider the problem of defining and fitting models of autoregressive time series of probability distributions on a compact interval of $\mathbb{R}$. An order-$1$ autoregressive model in this context is to be understood as a Markov…
The theoretical advances on the properties of scoring rules over the past decades have broadened the use of scoring rules in probabilistic forecasting. In meteorological forecasting, statistical postprocessing techniques are essential to…
We consider nonparametric regression under covariate shift, where we observe samples from both the target distribution and a related but distinct source distribution. We introduce a novel object, the transfer function, and show that…
The distributional single index model is a semiparametric regression model in which the conditional distribution functions $P(Y \leq y | X = x) = F_0(\theta_0(x), y)$ of a real-valued outcome variable $Y$ depend on $d$-dimensional…
Distributional regression aims at estimating the conditional distribution of a targetvariable given explanatory co-variates. It is a crucial tool for forecasting whena precise uncertainty quantification is required. A popular methodology…
Large data sets often require performing distributed statistical estimation, with a full data set split across multiple machines and limited communication between machines. To study such scenarios, we define and study some refinements of…
We study distribution-on-distribution regression problems in which a response distribution depends on multiple distributional predictors. Such settings arise naturally in applications where the outcome distribution is driven by several…
Transfer learning is essential when sufficient data comes from the source domain, with scarce labeled data from the target domain. We develop estimators that achieve minimax linear risk for linear regression problems under distribution…
This paper considers the problem of matrix-variate logistic regression. It derives the fundamental error threshold on estimating low-rank coefficient matrices in the logistic regression problem by obtaining a lower bound on the minimax…
We investigate the estimation of an optimal transport map between probability measures on an infinite-dimensional space and reveal its minimax optimal rate. Optimal transport theory defines distances within a space of probability measures,…
The effects of real-time provision of travel-time information on the behaviour of drivers are considered. The model of Marecek et al. [arXiv:1406.7639, Int. J. Control 88(10), 2015] is extended to consider uncertainty in the response of a…
In transfer learning, we wish to make inference about a target population when we have access to data both from the distribution itself, and from a different but related source distribution. We introduce a flexible framework for transfer…
We consider minimax-optimal designs for the prediction of individual parameters in random coefficient regression models. We focus on the minimax-criterion, which minimizes the "worst case" for the basic criterion with respect to the…
`Distribution regression' refers to the situation where a response Y depends on a covariate P where P is a probability distribution. The model is Y=f(P) + mu where f is an unknown regression function and mu is a random error. Typically, we…
We consider high-dimensional multivariate linear regression models, where the joint distribution of covariates and response variables is a multivariate normal distribution with a bandable covariance matrix. The main goal of this paper is to…