日期精度：到日 7 篇 · 到月 0 篇 · 到年 0 篇
稳健多元均值估计：截尾均值的最优性
We consider the problem of estimating the mean of a random vector based on i.i.d. observations and adversarial contamination. We introduce a multivariate extension of the trimmed-mean estimator and show its optimal performance under minimal conditions.
L4–L2 范数等价条件下的稳健协方差估计
Let $X$ be a centered random vector taking values in $\mathbb{R}^{d}$ and let $\Sigma=\mathbb{E}(X\otimes X)$ be its covariance matrix. We show that if $X$ satisfies an $L_{4}-L_{2}$ norm equivalence (sometimes referred to as the bounded kurtosis assumption), there is a covariance estimator $\hat{\Sigma}$ that exhibits almost the same performance one would expect had $X$ been a Gaussian vector. The procedure also improves the current state-of-the-art regarding high…
随机向量均值的次高斯估计量
We study the problem of estimating the mean of a random vector $X$ given a sample of $N$ independent, identically distributed points. We introduce a new estimator that achieves a purely sub-Gaussian performance under the only condition that the second moment of $X$ exists. The estimator is based on a novel concept of a multivariate median.
正则化与小球方法之一：稀疏恢复
We obtain bounds on estimation error rates for regularization procedures of the form \begin{equation*}\hat{f}\in\mathop{\operatorname{argmin}}_{f\in F}(\frac{1}{N}\sum_{i=1}^{N}(Y_{i}-f(X_{i}))^{2}+\lambda \Psi(f))\end{equation*} when $\Psi$ is a norm and $F$ is convex. Our approach gives a common framework that may be used in the analysis of learning problems and regularization problems alike. In particular, it sheds some light on the role various notions of sparsity have…
局部参数与全局参数：突破高斯复杂度障碍
We show that if $F$ is a convex class of functions that is $L$-sub-Gaussian, the error rate of learning problems generated by independent noise is equivalent to a fixed point determined by “local” covering estimates of the class (i.e., the covering number at a specific level), rather than by the Gaussian average, which takes into account the structure of $F$ at an arbitrarily small scale. To that end, we establish new sharp upper and lower estimates on the error rate in such…
核学习中的正则化
Under mild assumptions on the kernel, we obtain the best known error rates in a regularized learning scenario taking place in the corresponding reproducing kernel Hilbert space (RKHS). The main novelty in the analysis is a proof that one can use a regularization term that grows significantly slower than the standard quadratic growth in the RKHS norm.
局部 Rademacher 复杂度
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.