Related papers: Distribution-Free Robust Linear Regression
We investigate robust linear regression where data may be contaminated by an oblivious adversary, i.e., an adversary than may know the data distribution but is otherwise oblivious to the realizations of the data samples. This model has been…
We consider the problem of constructing a least conservative estimator of the expected value $\mu$ of a non-negative heavy-tailed random variable. We require that the probability of overestimating the expected value $\mu$ is kept…
We study high-dimensional rank regression when data are distributed across multiple machines and the loss is a non-additive U-statistic, as in convoluted rank regression (CRR). Classical communication-efficient surrogate likelihood (CSL)…
Empirical likelihood serves as a powerful tool for constructing confidence intervals in nonparametric regression and regression discontinuity designs (RDD). The original empirical likelihood framework can be naturally extended to these…
This paper studies the distributed optimization problem under the influence of heavy-tailed gradient noises. Here, a heavy-tailed noise means that the noise does not necessarily satisfy the bounded variance assumption. Instead, it satisfies…
The paper considers the problem of robust estimating a periodic function in a continuous time regression model with dependent disturbances given by a general square integrable semimartingale with unknown distribution. An example of such a…
Estimating extreme quantiles is an important task in many applications, including financial risk management and climatology. More important than estimating the quantile itself is to insure zero coverage error, which implies the quantile…
We revisit heavy-tailed corrupted least-squares linear regression assuming to have a corrupted $n$-sized label-feature sample of at most $\epsilon n$ arbitrary outliers. We wish to estimate a $p$-dimensional parameter $b^*$ given such…
Simplicia-simplicial regression concerns statistical modeling scenarios in which both the predictors and the responses are vectors constrained to lie on the simplex. \cite{fiksel2022} introduced a transformation-free linear regression…
Linear regression is arguably the most widely used statistical method. With fixed regressors and correlated errors, the conventional wisdom is to modify the variance-covariance estimator to accommodate the known correlation structure of the…
Standard sequential inference architectures are compromised by a normalizability crisis when confronted with extreme, structured outliers. By operating on unbounded parameter spaces, state-of-the-art estimators lack the intrinsic geometry…
Motivated by questions about dense (non-sparse) signals in high-dimensional data analysis, we study the unconditional out-of-sample prediction error (predictive risk) associated with three popular linear estimators for high-dimensional…
Distributional reinforcement learning (DRL) enhances the understanding of the effects of the randomness in the environment by letting agents learn the distribution of a random return, rather than its expected value as in standard…
In Regression Discontinuity (RD) design, self-selection leads to different distributions of covariates on two sides of the policy intervention, which essentially violates the continuity of potential outcome assumption. The standard RD…
A fundamental question in the theory of reinforcement learning is: suppose the optimal $Q$-function lies in the linear span of a given $d$ dimensional feature mapping, is sample-efficient reinforcement learning (RL) possible? The recent and…
Modelling multivariate tail dependence is one of the key challenges in extreme-value theory. Multivariate extremes are usually characterized using parametric models, some of which have simpler submodels at the boundary of their parameter…
In this paper we present a novel methodology to perform Bayesian model selection in linear models with heavy-tailed distributions. We consider a finite mixture of distributions to model a latent variable where each component of the mixture…
We address the problem of how to achieve optimal inference in distributed quantile regression without stringent scaling conditions. This is challenging due to the non-smooth nature of the quantile regression (QR) loss function, which…
In several different fields, there is interest in analyzing the upper or lower tail quantile of the underlying distribution rather than mean or center quantile. However, the investigation of the tail quantile is difficult because of data…
We propose a new Bayesian strategy for adaptation to smoothness in nonparametric models based on heavy tailed series priors. We illustrate it in a variety of settings, showing in particular that the corresponding Bayesian posterior…