Related papers: Performance of Empirical Risk Minimization for Lin…

Let $\mathcal{F}$ be a class of measurable functions $f:S\mapsto [0,1]$ defined on a probability space $(S,\mathcal{A},P)$. Given a sample (X_1,...,X_n) of i.i.d. random variables taking values in S with common distribution P, let P_n…

We present a result according to which certain functions of covariance matrices are maximized at scalar multiples of the identity matrix. In a statistical context in which such functions measure loss, this says that the least favourable…

Classical penalized likelihood regression problems deal with the case that the independent variables data are known exactly. In practice, however, it is common to observe data with incomplete covariate information. We are concerned with a…

We present a framework for performing efficient regression in general metric spaces. Roughly speaking, our regressor predicts the value at a new point by computing a Lipschitz extension --- the smoothest function consistent with the…

We consider bounds on the generalization performance of the least-norm linear regressor, in the over-parameterized regime where it can interpolate the data. We describe a sense in which any generalization bound of a type that is commonly…

As data-driven methods are deployed in real-world settings, the processes that generate the observed data will often react to the decisions of the learner. For example, a data source may have some incentive for the algorithm to provide a…

In randomized controlled trials without interference, regression adjustment is widely used to enhance the efficiency of treatment effect estimation. This paper extends this efficiency principle to settings with network interference, where a…

Standard local polynomial estimators of a nonparametric regression function employ a weighted least squares loss function that is tailored to the setting of homoscedastic Gaussian errors. We introduce the outrigger local polynomial…

This article develops a general theory for minimum norm interpolating estimators and regularized empirical risk minimizers (RERM) in linear models in the presence of additive, potentially adversarial, errors. In particular, no conditions on…

In this paper, we study data-dependent generalization error bounds exhibiting a mild dependency on the number of classes, making them suitable for multi-class learning with a large number of label classes. The bounds generally hold for…

We consider generalized linear regression analysis with left-censored covariate due to the lower limit of detection. Complete case analysis by eliminating observations with values below limit of detection yields valid estimates for…

This paper gives two theoretical results on estimating low-rank parameter matrices for linear models with multivariate responses. We first focus on robust parameter estimation of low-rank multi-task learning with heavy-tailed data and…

This paper introduces a new method for testing the statistical significance of estimated parameters in predictive regressions. The approach features a new family of test statistics that are robust to the degree of persistence of the…

Concerning bivariate least squares linear regression, the classical results obtained for extreme structural models in earlier attempts are reviewed using a new formalism in terms of deviation (matrix) traces which, for homoscedastic data,…

In performative prediction, predictions guide decision-making and hence can influence the distribution of future data. To date, work on performative prediction has focused on finding performatively stable models, which are the fixed points…

Penalized likelihood approaches are widely used for high-dimensional regression. Although many methods have been proposed and the associated theory is now well-developed, the relative efficacy of different approaches in finite-sample…

It has been observed that certain loss functions can render deep-learning pipelines robust against flaws in the data. In this paper, we support these empirical findings with statistical theory. We especially show that empirical-risk…

In performative stochastic optimization, decisions can influence the distribution of random parameters, rendering the data-generating process itself decision-dependent. In practice, decision-makers rarely have access to the true…

The problem of estimating the coefficient of bivariate tail dependence is considered here from the robustness point of view; it combines two apparently contradictory theories of robust statistics and extreme value statistics. The usual…

We derive upper bounds for random design linear regression with dependent ($\beta$-mixing) data absent any realizability assumptions. In contrast to the strictly realizable martingale noise regime, no sharp instance-optimal non-asymptotics…