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math.ST updates on arXiv.org

What is Learnable in Valiant's Theory of the Learnable? 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Statistical Inference using the Morse-Smale Complex
Yen-Chi Chen, Christopher R. Genovese, Larry Wasserman · 2015-06-30 · via math.ST updates on arXiv.org

The Morse-Smale complex of a function $f$ decomposes the sample space into cells where $f$ is increasing or decreasing. When applied to nonparametric density estimation and regression, it provides a way to represent, visualize, and compare multivariate functions. In this paper, we present some statistical results on estimating Morse-Smale complexes. This allows us to derive new results for two existing methods: mode clustering and Morse-Smale regression. We also develop two new methods based on the Morse-Smale complex: a visualization technique for multivariate functions and a two-sample, multivariate hypothesis test.

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