From Forecast to Decisions in Graphical Models: A Natural Gradient Optimization Approach

25 Pages Posted: 13 Apr 2021

See all articles by Eric Benhamou

Eric Benhamou

Université Paris Dauphine; EB AI Advisory; AI For Alpha

David Saltiel

Université Paris Dauphine; A.I. Square Connect; AI For Alpha

Beatrice Guez

AI For Alpha

Jamal Atif

Université Paris Dauphine

Rida Laraki

Université Paris-Dauphine, PSL Research University

Date Written: March 26, 2021

Abstract

Graphical models and in particular Hidden Markov Models or their continuous space equivalent, the so called Kalman filter model, are a powerful tool to make some inference that can be used in decision making contexts. The estimation of their parameters is usually based on the Expectation Maximization approach as this is a natural statistical way to train them. When used for decision making, it may be more relevant to find parameters that are relevant to our decisions rather than just try to fit the model from a statistical point of view. Hence, we can reformulate the determination of graphical model as an inference problem where the true concern is the quality of the decisions from the forecast given by the model. We show that the resulting optimization problem can be reformulated as an information geometric optimization problem and introduce a natural gradient descent strategy that incorporates additional meta parameters. We show that our approach is a strong alternative to the celebrated EM approach for learning in graphical models. Actually, our natural gradient based strategy leads to learning optimal parameters for the final objective function (which is our decision) without artificially trying to fit a distribution that may not correspond to the real one. We support our theoretical findings with the question of decision in financial markets and show that the learned model performs better than traditional practitioner methods and is less prone to overfitting.

Suggested Citation

Benhamou, Eric and Saltiel, David and Guez, Beatrice and Atif, Jamal and Laraki, Rida, From Forecast to Decisions in Graphical Models: A Natural Gradient Optimization Approach (March 26, 2021). Université Paris-Dauphine Research Paper No. 3813403, Available at SSRN: https://ssrn.com/abstract=3813403 or http://dx.doi.org/10.2139/ssrn.3813403

Eric Benhamou (Contact Author)

Université Paris Dauphine ( email )

Place du Maréchal de Tassigny
Paris, Cedex 16 75775
France

EB AI Advisory ( email )

35 Boulevard d'Inkermann
Neuilly sur Seine, 92200
France

AI For Alpha ( email )

35 boulevard d'Inkermann
Neuilly sur Seine, 92200
France

David Saltiel

Université Paris Dauphine ( email )

Place du Maréchal de Tassigny
Paris, Cedex 16 75775
France

A.I. Square Connect ( email )

35 Boulevard d'Inkermann
Neuilly sur Seine, 92200
France

AI For Alpha ( email )

35 boulevard d'Inkermann
Neuilly sur Seine, 92200
France

Beatrice Guez

AI For Alpha ( email )

35 boulevard d'Inkermann
Neuilly sur Seine, 92200
France

Jamal Atif

Université Paris Dauphine ( email )

Place du Maréchal de Tassigny
Paris, Cedex 16 75775
France

Rida Laraki

Université Paris-Dauphine, PSL Research University ( email )

Place du Maréchal de Lattre de Tassigny
Paris, 75016
France

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