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- W4295247488 abstract "While several papers have investigated computationally and statistically efficient methods for learning Gaussian mixtures, precise minimax bounds for their statistical performance as well as fundamental limits in high-dimensional settings are not well-understood. In this paper, we provide precise information theoretic bounds on the clustering accuracy and sample complexity of learning a mixture of two isotropic Gaussians in high dimensions under small mean separation. If there is a sparse subset of relevant dimensions that determine the mean separation, then the sample complexity only depends on the number of relevant dimensions and mean separation, and can be achieved by a simple computationally efficient procedure. Our results provide the first step of a theoretical basis for recent methods that combine feature selection and clustering." @default.
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- W4295247488 date "2013-06-09" @default.
- W4295247488 modified "2023-10-14" @default.
- W4295247488 title "Minimax Theory for High-dimensional Gaussian Mixtures with Sparse Mean Separation" @default.
- W4295247488 doi "https://doi.org/10.48550/arxiv.1306.2035" @default.
- W4295247488 hasPublicationYear "2013" @default.
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