Multivariate time series classification is an ubiquitous and widely studied problem. Due to their strong generalization capability, neural networks are suitable for this problem, but their intrinsic black-box nature often limits their applicability. Temporal decision trees are a relevant alternative to neural networks for the same task regarding classification performances while attaining higher levels of transparency and interpretability. In this work, we approach the problem of hybridizing these two techniques, and present three independent, natural hybridization solutions to study if, and in what measure, both the ability of neural networks to capture complex temporal patterns and the transparency and flexibility of temporal decision trees can be leveraged. To this end, we provide initial experimental results for several tasks in a binary classification setting, showing that our proposed neural-symbolic hybridization schemata may be a step towards accurate and interpretable models.

Symbolic learning is the subfield of machine learning concerned with learning predictive models with knowledge represented in logical form, such as decision tree and decision list models. Ensemble learning methods, such as random forests, are usually deployed to improve the performance of decision trees; unfortunately, interpreting tree ensembles is challenging. In order to deal with unstructured (e.g., temporal or spatial) data, moreover, decision trees and random forests have been recently generalized to the use of modal logics, which are harder to interpret than their propositional counterpart. Recently, a methodology for extracting simple rules from propositional random forests, based on a sequence of optimization steps, was proposed. In this work, we generalize this approach along two directions: from propositional to modal logic and from a sequence of optimization steps to a single multi-objective optimization problem. Even if confined to the temporal domain, our experimental results, based on open-source implementations and public data, show that our method is robust and able to extract small, accurate, and informative decision lists even for complex classification problems.

Symbolic learning is the logic-based approach to machine learning. The mission of symbolic learning is to provide algorithms and methodologies to extract logical information from data and express it in an interpretable way. In the context of temporal data, interval temporal logic has been recently proposed as a suitable tool for symbolic learning, specifically via the design of an interval temporal logic decision tree extraction algorithm. Building on it, we study here its natural generalization to interval temporal random forests, mimicking the corresponding schema at the propositional level. Interval temporal random forests turn out to be a very performing multivariate time series classification method, which, despite the introduction of a functional component, are still logically interpretable to some extent. We apply this method to the problem of diagnosing COVID-19 based on the time series that emerge from cough and breath recording of positive versus negative subjects. Our experiment show that our models achieve very high accuracies and sensitivities, often superior to those achieved by classical methods on the same data. Although other recent approaches to the same problem (based on different and more numerous data) show even better statistical results, our solution is the first logic-based, interpretable, and explainable one.