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Open AccessArticle

Learning from Both Experts and Data

1
CMAP Ecole Polytechnique, Institut Polytechnique de Paris, 91128 Palaiseau, France
2
XPop, Inria Saclay, 91120 Palaiseau, France
3
School of Medecine, Université Paris-Descartes, 75006 Paris, France
*
Author to whom correspondence should be addressed.
Entropy 2019, 21(12), 1208; https://doi.org/10.3390/e21121208
Received: 29 October 2019 / Revised: 29 November 2019 / Accepted: 6 December 2019 / Published: 10 December 2019
(This article belongs to the Section Information Theory, Probability and Statistics)
In this work, we study the problem of inferring a discrete probability distribution using both expert knowledge and empirical data. This is an important issue for many applications where the scarcity of data prevents a purely empirical approach. In this context, it is common to rely first on an a priori from initial domain knowledge before proceeding to an online data acquisition. We are particularly interested in the intermediate regime, where we do not have enough data to do without the initial a priori of the experts, but enough to correct it if necessary. We present here a novel way to tackle this issue, with a method providing an objective way to choose the weight to be given to experts compared to data. We show, both empirically and theoretically, that our proposed estimator is always more efficient than the best of the two models (expert or data) within a constant. View Full-Text
Keywords: maximum entropy; mixing expert and data; Kullback–Leibler centroid maximum entropy; mixing expert and data; Kullback–Leibler centroid
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Besson, R.; Le Pennec, E.; Allassonnière, S. Learning from Both Experts and Data. Entropy 2019, 21, 1208.

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