Estimation of first-order sensitivity indices based on symmetric reflected Vietoris-Rips complexes areas

TL;DR

This paper introduces a geometric approach to estimate first-order sensitivity indices of variables by reconstructing the data manifold using symmetric reflected Vietoris-Rips complexes, revealing variable relevance and interactions.

Contribution

The paper presents a novel method that uses Vietoris-Rips complexes and their symmetric reflections to estimate sensitivity indices based on geometric data properties.

Findings

Effective estimation of sensitivity indices through geometric reconstruction.

Ability to detect structural interactions between variables.

Provides insights into the geometric nature of data points.

Abstract

In this paper we estimate the first-order sensitivity index of random variables within a model by reconstructing the embedding manifold of a two-dimensional cloud point. The model assumed has p predictors and a continuous outcome Y . Our method gauges the manifold through a Vietoris-Rips complex with a fixed radius for each variable. With this object, and using the area and its symmetric reflection, we can estimate an index of relevance for each predictor. The index reveals the geometric nature of the data points. Also, given the method used, we can decide whether a pair of non-correlated random variables have some structural pattern in their interaction.