## 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 + x^{T} 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(·) ∈ W^{∞}_{2;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 L_{p} 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 language | English (US) |
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Pages (from-to) | 1183-1198 |

Number of pages | 16 |

Journal | Neural Computation |

Volume | 11 |

Issue number | 5 |

DOIs | |

State | Published - Jul 1 1999 |

## ASJC Scopus subject areas

- Arts and Humanities (miscellaneous)
- Cognitive Neuroscience