相关论文: $\mathscr{H}$-Consistency Estimation Error of Surr…

Recently there are a considerable amount of work devoted to the study of the algorithmic stability and generalization for stochastic gradient descent (SGD). However, the existing stability analysis requires to impose restrictive assumptions…

We consider the a posteriori error analysis of fully discrete approximations of parabolic problems based on conforming $hp$-finite element methods in space and an arbitrary order discontinuous Galerkin method in time. Using an equilibrated…

We obtain estimation error rates and sharp oracle inequalities for regularization procedures of the form \begin{equation*} \hat f \in argmin_{f\in F}\left(\frac{1}{N}\sum_{i=1}^N\ell(f(X_i), Y_i)+\lambda \|f\|\right) \end{equation*} when…

We study the problem of high-dimensional linear regression in a robust model where an $\epsilon$-fraction of the samples can be adversarially corrupted. We focus on the fundamental setting where the covariates of the uncorrupted samples are…

The governing equations of stochastic dynamical systems often become cost-prohibitive for numerical simulation at large scales. Surrogate models of the governing equations, learned from data of the high-fidelity system, are routinely used…

We study confidence intervals based on hard-thresholding, soft-thresholding, and adaptive soft-thresholding in a linear regression model where the number of regressors $k$ may depend on and diverge with sample size $n$. In addition to the…

Many real-world decision problems require solving, again and again, combinatorial optimization instances drawn from a common distribution. A recent line of structured learning methods exploits this regularity by learning policies that pair…

Bayesian regression determines model parameters by minimizing the expected loss, an upper bound to the true generalization error. However, the loss ignores misspecification, where models are imperfect. Parameter uncertainties from Bayesian…

We introduce the notion of consistent error bound functions which provides a unifying framework for error bounds for multiple convex sets. This framework goes beyond the classical Lipschitzian and H\"olderian error bounds and includes…

We consider the problem of learning support vector machines robust to uncertainty. It has been established in the literature that typical loss functions, including the hinge loss, are sensible to data perturbations and outliers, thus…

We establish empirical risk minimization principles for active learning by deriving a family of upper bounds on the generalization error. Aligning with empirical observations, the bounds suggest that superior query algorithms can be…

Data-driven surrogate models offer quick approximations to complex numerical and experimental systems but typically lack uncertainty quantification, limiting their reliability in safety-critical applications. While Bayesian methods provide…

Stochastic unit commitment models typically handle uncertainties in forecast demand by considering a finite number of realizations from a stochastic process model for loads. Accurate evaluations of expectations or higher moments for the…

We present new information-theoretic generalization guarantees through the a novel construction of the "neighboring-hypothesis" matrix and a new family of stability notions termed sample-conditioned hypothesis (SCH) stability. Our approach…

The robustness of risk measures to changes in underlying loss distributions (distributional uncertainty) is of crucial importance in making well-informed decisions. In this paper, we quantify, for the class of distortion risk measures with…

The paper focuses on general properties of parametric minimum contrast estimators. The quality of estimation is measured in terms of the rate function related to the contrast, thus allowing to derive exponential risk bounds invariant with…

We prove that the classic approximation guarantee for the higher-order singular value decomposition (HOSVD) is tight by constructing a tensor for which HOSVD achieves an approximation ratio of $N/(1+\varepsilon)$, for any $\varepsilon > 0$.…

The distributed hypothesis testing problem with full side-information is studied. The trade-off (reliability function) between the two types of error exponents under limited rate is studied in the following way. First, the problem is…

The use of surrogate models instead of computationally expensive simulation codes is very convenient in engineering. Roughly speaking, there are two kinds of surrogate models: the deterministic and the probabilistic ones. These last are…

We study the fundamental problem of estimating the mean of a $d$-dimensional distribution with covariance $\Sigma \preccurlyeq \sigma^2 I_d$ given $n$ samples. When $d = 1$, \cite{catoni} showed an estimator with error $(1+o(1)) \cdot…