每日简报

协方差矩阵特征子空间的假设检验AI 解读

Eigenspaces of covariance matrices play an important role in statistical machine learning, arising in variety of modern algorithms. Quantitatively, it is convenient to describe the eigenspaces in terms of spectral projectors. This work focuses on hypothesis testing for the spectral projectors, both in one- and two-sample scenario. We present new tests, based on a specific matrix norm developed in order to utilize the structure of the spectral projectors. A new resampling…

利用经验贝叶斯学习贝叶斯元先验AI 解读

Adding domain knowledge to a learning system is known to improve results. In multi-parameter Bayesian frameworks, such knowledge is incorporated as a prior. On the other hand, various model parameters can have different learning rates in real-world problems, especially with skewed data. Two often-faced challenges in Operation Management and Management Science applications are the absence of informative priors, and the inability to control parameter learning rates. In this…

非对称性何以有益：非对称扰动低秩矩阵的特征值与特征向量分析AI 解读

This paper is concerned with the interplay between statistical asymmetry and spectral methods. Suppose we are interested in estimating a rank-1 and symmetric matrix $\mathbf{M}^{\star}\in \mathbb{R}^{n\times n}$, yet only a randomly perturbed version $\mathbf{M}$ is observed. The noise matrix $\mathbf{M}-\mathbf{M}^{\star}$ is composed of zero-mean independent (but not necessarily homoscedastic) entries and is, therefore, not symmetric in general. This might arise, for…

持续时间结果下处理效应异质性的非参数检验AI 解读

This article proposes different tests for treatment effect heterogeneity when the outcome of interest, typically a duration variable, may be right-censored. The proposed tests study whether a policy 1) has zero distributional (average) effect for all subpopulations defined by covariate values, and 2) has homogeneous average effect across different subpopulations. The proposed tests are based on two-step Kaplan-Meier integrals and do not rely on parametric distributional…

高维交叉验证 Lasso 的误差界AI 解读

In this paper, we derive non-asymptotic error bounds for the Lasso estimator when the penalty parameter for the estimator is chosen using $K$-fold cross-validation. Our bounds imply that the cross-validated Lasso estimator has nearly optimal rates of convergence in the prediction, $L^2$, and $L^1$ norms. For example, we show that in the model with the Gaussian noise and under fairly general assumptions on the candidate set of values of the penalty parameter, the estimation…