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稀疏主成分半正定松弛的高维分析AI 解读

Principal component analysis (PCA) is a classical method for dimensionality reduction based on extracting the dominant eigenvectors of the sample covariance matrix. However, PCA is well known to behave poorly in the “large p, small n” setting, in which the problem dimension p is comparable to or larger than the sample size n. This paper studies PCA in this high-dimensional regime, but under the additional assumption that the maximal eigenvector is sparse, say, with at most k…

替代损失函数与 f 散度AI 解读

The goal of binary classification is to estimate a discriminant function γ from observations of covariate vectors and corresponding binary labels. We consider an elaboration of this problem in which the covariates are not available directly but are transformed by a dimensionality-reducing quantizer Q. We present conditions on loss functions such that empirical risk minimization yields Bayes consistency when both the discriminant function and the quantizer are estimated.…