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Hoeffding decomposition of black-box models with dependent inputs
March 8, 2024, 5:43 a.m. | Marouane Il IdrissiEDF R\&D PRISME, IMT, SINCLAIR AI Lab, Nicolas BousquetEDF R\&D PRISME, SINCLAIR AI Lab, LPSM, Fabrice GamboaIMT, Bertrand IoossEDF
stat.ML updates on arXiv.org arxiv.org
Abstract: One of the main challenges for interpreting black-box models is the ability to uniquely decompose square-integrable functions of non-independent random inputs into a sum of functions of every possible subset of variables. However, dealing with dependencies among inputs can be complicated. We propose a novel framework to study this problem, linking three domains of mathematics: probability theory, functional analysis, and combinatorics. We show that, under two reasonable assumptions on the inputs (non-perfect functional dependence and …
abstract arxiv box challenges dependencies every framework functions however independent inputs math.fa math.pr math.st novel random square stat.ml stat.th type variables
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