Sensitivity Analysis with Manifolds
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The course of dimensionality is a common problem in statistics and data analysis. Variable sensitivity analysis methods are a well studied and established set of tools designed to overcome these sorts of problems. However, as this work shows, these methods fail to capture relevant features and patterns hidden within the geometry of the enveloping manifold projected into a variable. We propose a sensitivity index that captures and reflects the relevance of distinct variables within a model by focusing at the geometry of their projections.
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