Causal discovery for fuzzy rule learning
Résumé
Fuzzy rules induction algorithms are usually based on statistical criteria such as correlation or on examples covering.
Although these algorithms can be efficient to predict the outputs, some studies also aim to provide insight about the mechanism that links inputs and outputs.
In our work, we focus on allying fuzzy logic, which is a suitable model for human-like information, and causality, which is a key concept for humans to generate knowledge from observations and also to build explanations. If a fuzzy premise causes a fuzzy consequence, then acting on the fuzzy premise will have an impact on the fuzzy consequence. This is not necessarily the case for common fuzzy rules based on correlation. Indeed, correlations may be due to some latent common cause of fuzzy premise and consequence, thus acting on the fuzzy premise will have no impact on the fuzzy consequence.
This article proposes an approach to construct a set of causality-based fuzzy rules from crisp observational data. The idea is to identify causal relationships on the set of fuzzified inputs and outputs by well-known constraints-based causal discovery algorithms such as Peter-Clark and Fast Causal Inference. The causal discovery algorithms are combined with entropy-based conditional independent testing that avoids making hypotheses on the data distribution.
Experiments are conducted to evaluate our approach in terms of ability to recover causal relationships between fuzzy sets in the presence of a latent common cause. The results illustrate the interest of our approach compared to a correlation-based approach and state-of-the-art approaches.
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