相关论文: Empirical Risk Minimization for Losses without Var…

The empirical covariance matrix is not necessarily the best estimator for the population covariance matrix: we describe a simple method which gives better estimates in two examples. The method models the covariance matrix using truncated…

In this paper, we study convex risk measures with weak optimal transport penalties. In a first step, we show that these risk measures allow for an explicit representation via a nonlinear transform of the loss function. In a second step, we…

In this paper, we study the Empirical Risk Minimization problem in the non-interactive local model of differential privacy. In the case of constant or low dimensionality ($p\ll n$), we first show that if the ERM loss function is $(\infty,…

This paper develops a theory and methodology for estimation of Gini index such that both cost of sampling and estimation error are minimum. Methods in which sample size is fixed in advance, cannot minimize estimation error and sampling cost…

The aim of this paper is to provide several novel upper bounds on the excess risk with a primal focus on classification problems. We suggest two approaches and the obtained bounds are represented via the distribution dependent local…

Conformal risk control (CRC) provides distribution-free guarantees for controlling the expected loss at a user-specified level. Existing theory typically assumes that the loss decreases monotonically with a tuning parameter that governs the…

It is well known that Empirical Risk Minimization (ERM) may attain minimax suboptimal rates in terms of the mean squared error (Birg\'e and Massart, 1993). In this paper, we prove that, under relatively mild assumptions, the suboptimality…

We consider the problem of simulating loss probabilities and conditional excesses for linear asset portfolios under the t-copula model. Although in the literature on market risk management there are papers proposing efficient variance…

Accurate estimates of long-term risk probabilities and their gradients are critical for many stochastic safe control methods. However, computing such risk probabilities in real-time and in unseen or changing environments is challenging.…

This paper introduces ergodic-risk criteria, which capture long-term cumulative risks associated with controlled Markov chains through probabilistic limit theorems--in contrast to existing methods that require assumptions of either finite…

Given a collection of feature maps indexed by a set $\mathcal{T}$, we study the performance of empirical risk minimization (ERM) on regression problems with square loss over the union of the linear classes induced by these feature maps.…

We study prediction and estimation problems using empirical risk minimization, relative to a general convex loss function. We obtain sharp error rates even when concentration is false or is very restricted, for example, in heavy-tailed…

An effective two-stage method for an estimation of parameters of the linear regression is considered. For this purpose we introduce a certain quasi-estimator that, in contrast to usual estimator, produces two alternative estimates. It is…

We introduce a consistent estimator of the extreme value index under random truncation based on a single sample fraction of top observations from truncated and truncation data. We establish the asymptotic normality of the proposed estimator…

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 study the design of portfolios under a minimum risk criterion. The performance of the optimized portfolio relies on the accuracy of the estimated covariance matrix of the portfolio asset returns. For large portfolios, the number of…

In the Mixup training paradigm, a model is trained using convex combinations of data points and their associated labels. Despite seeing very few true data points during training, models trained using Mixup seem to still minimize the…

This paper describes three methods for carrying out non-asymptotic inference on partially identified parameters that are solutions to a class of optimization problems. Applications in which the optimization problems arise include estimation…

In safety-critical applications, machine learning models should generalize well under worst-case distribution shifts, that is, have a small robust risk. Invariance-based algorithms can provably take advantage of structural assumptions on…

Uncertainties from deepening penetration of renewable energy resources have posed critical challenges to the secure and reliable operations of future electric grids. Among various approaches for decision making in uncertain environments,…