Related papers: Risk Bounds For Distributional Regression

We study the distribution of hard-, soft-, and adaptive soft-thresholding estimators within a linear regression model where the number of parameters k can depend on sample size n and may diverge with n. In addition to the case of known…

We constuct a sequential adaptive procedure for estimating the autoregressive function at a given point in nonparametric autoregression models with Gaussian noise. We make use of the sequential kernel estimators. The optimal adaptive…

Let $i=1,\ldots,N$ index a simple random sample of units drawn from some large population. For each unit we observe the vector of regressors $X_{i}$ and, for each of the $N\left(N-1\right)$ ordered pairs of units, an outcome $Y_{ij}$. The…

In this paper we present a general convex optimization approach for solving high-dimensional multiple response tensor regression problems under low-dimensional structural assumptions. We consider using convex and weakly decomposable…

Most high-dimensional estimation and prediction methods propose to minimize a cost function (empirical risk) that is written as a sum of losses associated to each data point. In this paper we focus on the case of non-convex losses, which is…

We analyze the practices of reservoir computing in the framework of statistical learning theory. In particular, we derive finite sample upper bounds for the generalization error committed by specific families of reservoir computing systems…

Balancing the trade-off between safety and efficiency is of significant importance for path planning under uncertainty. Many risk-aware path planners have been developed to explicitly limit the probability of collision to an acceptable…

This paper studies the distributed adaptiveestimation problems for stochastic large regression modelswith an infinite number of parameters. By constructing a re-cursive local cost function, we propose a novel distributedrecursive least…

We derive generalization error bounds for traditional time-series forecasting models. Our results hold for many standard forecasting tools including autoregressive models, moving average models, and, more generally, linear state-space…

We investigate a data-driven approach to constructing uncertainty sets for robust optimization problems, where the uncertain problem parameters are modeled as random variables whose joint probability distribution is not known. Relying only…

Using only retrospective data, we study the problem of predicting treatment effects for the same treatment/policy implemented in a different location or time period. We propose a distributionally robust estimator that minimizes the…

We consider a regression setting where observations are collected in different environments modeled by different data distributions. The field of out-of-distribution (OOD) generalization aims to design methods that generalize better to test…

A long-standing problem in the construction of asymptotically correct confidence bands for a regression function $m(x)=E[Y|X=x]$, where $Y$ is the response variable influenced by the covariate $X$, involves the situation where $Y$ values…

Nonparametric regression subject to convexity or concavity constraints is increasingly popular in economics, finance, operations research, machine learning, and statistics. However, the conventional convex regression based on the least…

We develop quantile regression models in order to derive risk margin and to evaluate capital in non-life insurance applications. By utilizing the entire range of conditional quantile functions, especially higher quantile levels, we detail…

The problem of adaptive sampling for estimating probability mass functions (pmf) uniformly well is considered. Performance of the sampling strategy is measured in terms of the worst-case mean squared error. A Bayesian variant of the…

While modern large-scale datasets often consist of heterogeneous subpopulations -- for example, multiple demographic groups or multiple text corpora -- the standard practice of minimizing average loss fails to guarantee uniformly low losses…

Averages of proper scoring rules are often used to rank probabilistic forecasts. In many cases, the individual terms in these averages are based on observations and forecasts from different distributions. We show that some of the most…

High-dimensional linear regression has been thoroughly studied in the context of independent and identically distributed data. We propose to investigate high-dimensional regression models for independent but non-identically distributed…

\noindent Randomized nomination sampling (RNS) is a rank-based sampling technique which has been shown to be effective in several nonparametric studies involving environmental and ecological applications. In this paper, we investigate…