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样本扩增的统计复杂性AI 解读

The “sample amplification” problem formalizes the following question: Given n i.i.d. samples drawn from an unknown distribution P, when is it possible to produce a larger set of n+m samples which cannot be distinguished from n+m i.i.d. samples drawn from P? In this work, we provide a firm statistical foundation for this problem by deriving generally applicable amplification procedures, lower bound techniques and connections to existing statistical notions. Our techniques…

基于样本的协方差谱估计AI 解读

We consider the problem of approximating the set of eigenvalues of the covariance matrix of a multivariate distribution (equivalently, the problem of approximating the “population spectrum”), given access to samples drawn from the distribution. We consider this recovery problem in the regime where the sample size is comparable to, or even sublinear in the dimensionality of the distribution. First, we propose a theoretically optimal and computationally efficient algorithm for…