论文检索

贝叶斯稳健性：非渐近视角AI 解读

We study the problem of robustly estimating the posterior distribution for the setting where observed data can be contaminated with potentially adversarial outliers. We propose Rob-ULA, a robust variant of the Unadjusted Langevin Algorithm (ULA), and provide a finite-sample analysis of its sampling distribution. In particular, we show that after T=O˜(d/εacc) iterations, we can sample from pT such that dist(pT,p*)≤εacc+O˜(ϵ), where ϵ is the fraction of corruptions and dist…

估计误差的快速收敛率与模型选择的 Oracle 不等式AI 解读

We consider complexity penalization methods for model selection. These methods aim to choose a model to optimally trade off estimation and approximation errors by minimizing the sum of an empirical risk term and a complexity penalty. It is well known that if we use a bound on the maximal deviation between empirical and true risks as a complexity penalty, then the risk of our choice is no more than the approximation error plus twice the complexity penalty. There are many…

局部 Rademacher 复杂度AI 解读

We propose new bounds on the error of learning algorithms in terms of a data-dependent notion of complexity. The estimates we establish give optimal rates and are based on a local and empirical version of Rademacher averages, in the sense that the Rademacher averages are computed from the data, on a subset of functions with small empirical error. We present some applications to classification and prediction with convex function classes, and with kernel classes in particular.

关于提升方法论文的讨论及作者回应AI 解读

Discussions of: "Process consistency for AdaBoost" [Ann. Statist. 32 (2004), no. 1, 13-29] by W. Jiang; "On the Bayes-risk consistency of regularized boosting methods" [ibid., 30-55] by G. Lugosi and N. Vayatis; and "Statistical behavior and consistency of classification methods based on convex risk minimization" [ibid., 56-85] by T. Zhang. Includes rejoinders by the authors.