Learning from Both Experts and Data

Abstract

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 initial domain knowledge a priori 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 expert 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.

EXplainable Neural-Symbolic Learning (X-NeSyL) methodology to fuse deep learning representations with expert knowledge graphs: the MonuMAI cultural heritage use case

“…When it comes to learning from both experts and data, theoretical and empirical studies show that it is always more efficient to learn from both than using the best of two models. [10] confirm this by combining expert knowledge -in the form of marginal probabilities and rules-with empirical data and apply it to learning the probability distribution of the different combinations of symptoms of a given disease. This approach is useful in cases when there is not enough data to learn without experts, but enough to correct them if needed.…”

Approximate Bayesian Inference

“…Such distributions were also well known in game theory and in prediction with expert advice since the 1990s [ 53 , 54 ]. We refer to the book [ 55 ], the recent work [ 56 ], and to connected problems such as bandits [ 57 , 58 ].…”