Abstract
The pervasive presence of artificial intelligence (AI) in our everyday life has nourished the pursuit of explainable AI. Since the dawn of AI, logic has been widely used to express, in a human-friendly fashion, the internal process that led an (intelligent) system to deliver a specific output. In this paper, we take a step forward in this direction by introducing a novel family of kernels, called Propositional kernels, that construct feature spaces that are easy to interpret. Specifically, Propositional Kernel functions compute the similarity between two binary vectors in a feature space composed of logical propositions of a fixed form. The Propositional kernel framework improves upon the recent Boolean kernel framework by providing more expressive kernels. In addition to the theoretical definitions, we also provide an algorithm (and the source code) to efficiently construct any propositional kernel. An extensive empirical evaluation shows the effectiveness of Propositional kernels on several artificial and benchmark categorical data sets.
Highlights
Explainable Artificial Intelligence has become a hot topic in the current research [1,2]
Before diving into the details of how to compute Propositional kernels, we show the limitations of the Boolean kernel framework [8], and how Propositional kernels overcome them
We proposed a novel family of kernels, dubbed Propositional kernels, for categorical data
Summary
Explainable Artificial Intelligence has become a hot topic in the current research [1,2]. Like SVMs [4,5,6], typically work on an implicitly defined feature space by resorting to the well-known kernel trick The use of such an implicit representation clearly harms the interpretability of the resulting model. Given binary-valued input data, a possible approach to make SVM more interpretable consists of defining features that are easy to interpret, for example, features that are logical rules over the input To this end, recently, a novel Boolean kernel (BK) framework has been proposed [8]. We provide a mathematical definition for all possible binary logical operations as well as a general procedure to compose base Propositional kernels to form any propositional kernel This “composability” makes Propositional kernels highly expressive, much more than BKs. In the experimental section, we evaluate the effectiveness of these new kernels on several artificial and benchmark categorical data sets.
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