Reijo Jaakkola

Reijo Jaakkola, Tomi Janhunen, Antti Kuusisto et al.

We conceptualize explainability in terms of logic and formula size, giving a number of related definitions of explainability in a very general setting. Our main interest is the so-called special explanation problem which aims to explain the truth value of an input formula in an input model. The explanation is a formula of minimal size that (1) agrees with the input formula on the input model and (2) transmits the involved truth value to the input formula globally, i.e., on every model. As an important example case, we study propositional logic in this setting and show that the special explainability problem is complete for the second level of the polynomial hierarchy. We also provide an implementation of this problem in answer set programming and investigate its capacity in relation to explaining answers to the n-queens and dominating set problems.

Reijo Jaakkola, Tomi Janhunen, Antti Kuusisto et al.

We investigate explainability via short Boolean formulas in the data model based on unary relations. As an explanation of length k, we take a Boolean formula of length k that minimizes the error with respect to the target attribute to be explained. We first provide novel quantitative bounds for the expected error in this scenario. We then also demonstrate how the setting works in practice by studying three concrete data sets. In each case, we calculate explanation formulas of different lengths using an encoding in Answer Set Programming. The most accurate formulas we obtain achieve errors similar to other methods on the same data sets. However, due to overfitting, these formulas are not necessarily ideal explanations, so we use cross validation to identify a suitable length for explanations. By limiting to shorter formulas, we obtain explanations that avoid overfitting but are still reasonably accurate and also, importantly, human interpretable.

Tobias Geibinger, Reijo Jaakkola, Antti Kuusisto et al.

We define several canonical problems related to contrastive explanations, each answering a question of the form ''Why P but not Q?''. The problems compute causes for both P and Q, explicitly comparing their differences. We investigate the basic properties of our definitions in the setting of propositional logic. We show, inter alia, that our framework captures a cardinality-minimal version of existing contrastive explanations in the literature. Furthermore, we provide an extensive analysis of the computational complexities of the problems. We also implement the problems for CNF-formulas using answer set programming and present several examples demonstrating how they work in practice.

Reijo Jaakkola, Tomi Janhunen, Antti Kuusisto et al.

We present a novel approach for graph classification based on tabularizing graph data via variants of the Weisfeiler-Leman algorithm and then applying methods for tabular data. We investigate a comprehensive class of Weisfeiler-Leman variants obtained by modifying the underlying logical framework and establish a precise theoretical characterization of their expressive power. We then test two selected variants on twelve benchmark datasets that span a range of different domains. The experiments demonstrate that our approach matches the accuracy of state-of-the-art graph neural networks and graph kernels while being more time or memory efficient, depending on the dataset. We also briefly discuss directly extracting interpretable modal logic formulas from graph datasets.

Reijo Jaakkola, Tomi Janhunen, Antti Kuusisto et al.

Interpretability and explainability are among the most important challenges of modern artificial intelligence, being mentioned even in various legislative sources. In this article, we develop a method for extracting immediately human interpretable classifiers from tabular data. The classifiers are given in the form of short Boolean formulas built with propositions that can either be directly extracted from categorical attributes or dynamically computed from numeric ones. Our method is implemented using Answer Set Programming. We investigate seven datasets and compare our results to ones obtainable by state-of-the-art classifiers for tabular data, namely, XGBoost and random forests. Over all datasets, the accuracies obtainable by our method are similar to the reference methods. The advantage of our classifiers in all cases is that they are very short and immediately human intelligible as opposed to the black-box nature of the reference methods.

Reijo Jaakkola, Tomi Janhunen, Antti Kuusisto et al.

We introduce a method for computing immediately human interpretable yet accurate classifiers from tabular data. The classifiers obtained are short Boolean formulas, computed via first discretizing the original data and then using feature selection coupled with a very fast algorithm for producing the best possible Boolean classifier for the setting. We demonstrate the approach via 12 experiments, obtaining results with accuracies comparable to ones obtained via random forests, XGBoost, and existing results for the same datasets in the literature. In most cases, the accuracy of our method is in fact similar to that of the reference methods, even though the main objective of our study is the immediate interpretability of our classifiers. We also prove a new result on the probability that the classifier we obtain from real-life data corresponds to the ideally best classifier with respect to the background distribution the data comes from.