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Affine Feedforward Stochastic (AFS) Neural Network

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  • Christian Gourieroux

    (University of Toronto, TSE-R - Toulouse School of Economics - UT Capitole - Université Toulouse Capitole - Comue de Toulouse - Communauté d'universités et établissements de Toulouse - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, CREST - Centre de Recherche en Économie et Statistique - ENSAI - Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] - GENES - Groupe des Écoles Nationales d'Économie et Statistique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - ENSAE Paris - École Nationale de la Statistique et de l'Administration Économique - GENES - Groupe des Écoles Nationales d'Économie et Statistique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique)

  • Alain Monfort

    (CREST - Centre de Recherche en Économie et Statistique - ENSAI - Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] - GENES - Groupe des Écoles Nationales d'Économie et Statistique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - ENSAE Paris - École Nationale de la Statistique et de l'Administration Économique - GENES - Groupe des Écoles Nationales d'Économie et Statistique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique)

Abstract

The aim of this paper is to link the machine learning method of multilayer perceptron (MLP) neural network with the classical analysis of stochastic state space models. We consider a special class of state space models with multiple layers based on affine conditional Laplace transforms. This new class of Affine Feedforward Stochastic (AFS) neural network provides closed form recursive formulas for recursive filtering of the state variables of different layers. This approach is suitable for online inference by stochastic gradient ascent optimization and for recursive computation of scores such as backpropagation. The approach is extended to recurrent neural networks and identification issues are discussed.

Suggested Citation

  • Christian Gourieroux & Alain Monfort, 2025. "Affine Feedforward Stochastic (AFS) Neural Network," Working Papers hal-05280003, HAL.
    • Handle: RePEc:hal:wpaper:hal-05280003
    Note: View the original document on HAL open archive server: https://hal.science/hal-05280003v1
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