On the approximation rate of hierarchical mixtures-of-experts for generalized linear models

Wenxin Jiang*, Martin A. Tanner

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

37 Scopus citations

Abstract

We investigate a class of hierarchical mixtures-of-experts (HME) models where generalized linear models with nonlinear mean functions of the form ψ(α + xT β) are mixed. Here ψ(·) is the inverse link function. It is shown that mixtures of such mean functions can approximate a class of smooth functions of the form ψ(h(x)), where h(·) ∈ W2;K (a Sobolev class over [0, 1]s), as the number of experts m in the network increases. An upper bound of the approximation rate is given as O(m-2/s) in Lp norm. This rate can be achieved within the family of HME structures with no more than s-layers, where s is the dimension of the predictor x.

Original languageEnglish (US)
Pages (from-to)1183-1198
Number of pages16
JournalNeural Computation
Volume11
Issue number5
DOIs
StatePublished - Jul 1 1999

ASJC Scopus subject areas

  • Arts and Humanities (miscellaneous)
  • Cognitive Neuroscience

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