Estimating Mean Dimensionality of Analysis of Variance Decompositions

By Ruixue Liu, Art B. Owen. 2006

175 citations recorded by the source corpus.

Subfields: Numerical Analysis, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/f784b0170fe9c2b37e6d5d4cf731ba178cb3090f

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Numerical Analysis

In Statistics and Probability

Citations in the corpus

Does My Multimodal Model Learn Cross-modal Interactions? It’s Harder to Tell than You Might Think! (2020, methodology): “…gives a general method for computing the projection of a function f onto a set of functions with a specified ANOVA structure (see also Sobol (2001); Liu and Owen (2006)): our algorithmic contributions are to extend the method to multimodal models with d > 1 dimensional outputs, and to prove that…”
Derivative based global sensitivity measures (2014, unknown): “An inequality link is made with an extension of the total Sobol’ sensitivity indices to general sets of variables (called superset importance or total interaction index) proposed by Liu and Owen [20].”
Monte Carlo and Quasi-Monte Carlo Sampling (2009, methodology): “Finally, the ANOVA decomposition framework can be used to characterize functions further by using the concept of dimension distribution introduced in [365] and studied also in [17, 297].”
Two-level Tucker-TT-QTT format for optimized tensor calculus (2012, methodology): “the discretization: the most important components, which can be represented with a low number of parameters are selected and smartly combined to eliminate the errors as far as possible (Sparse Grids, ANOVA decomposition [4, 5, 6, 7], wavelet and multiresolution analysis).”
Construction and Comparison of High-Dimensional Sobol' Generators (2011, methodology): “Owen in Liu and Owen (2006) and independently by Asotsky et al. (2006). These papers contain an important suggestion: for integrands with small average dimension, QMC integrations are superior to MC integrations. Similar conclusions were drawn in Caflisch et al. (1997). This paper introduced the not”