Interval Temporal Random Forests with an Application to COVID-19 Diagnosis

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

Neural-Symbolic Temporal Decision Trees for Multivariate Time Series Classification

Multivariate time series classification is a widely known problem, and its applications are ubiquitous. Due to their strong generalization capability, neural networks have been proven to be very powerful for the task, but their applicability is often limited by their intrinsic black-box nature. Recently, temporal decision trees have been shown to be a serious alternative to neural networks for the same task in terms of classification performances, while attaining higher levels of transparency and interpretability. In this work, we propose an initial approach to neural-symbolic temporal decision trees, that is, an hybrid method that leverages on both the ability of neural networks of capturing temporal patterns and the flexibility of temporal decision trees of taking decisions on intervals based on (possibly, externally computed) temporal features. While based on a proof-of-concept implementation, in our experiments on public datasets, neural-symbolic temporal decision trees show promising results

On Coarser Interval Temporal Logics

The primary characteristic of interval temporal logic is that intervals, rather than points, are taken as the primitive ontological entities. Given their generally bad computational behavior of interval temporal logics, several techniques exist to produce decidable and computationally affordable temporal logics based on intervals. In this paper we take inspiration from Golumbic and Shamir’s coarser interval algebras, which generalize the classical Allen’s Interval Algebra, in order to define two previously unknown variants of Halpern and Shoham’s logic (HS) based on coarser relations. We prove that, perhaps surprisingly, the satisfiability problem for the coarsest of the two variants, namely HS3, not only is decidable, but PSpace-complete in the finite/discrete case, and PSpace-hard in any other case; besides proving its complexity bounds, we implement a tableau-based satisfiability checker for it and test it against a systematically generated benchmark. Our results are strengthened by showing that not all coarser-than-Allen’s relations are a guarantee of decidability, as we prove that the second variant, namely HS 7, remains undecidable in all interesting cases

Implementation of a Tableau-Based Satisfiability Checker for HS3

Although there exist several decidable fragments of Halpern and Shoham's interval temporal logic HS, the computational complexity of their satisfiability problem tend to be generally high. Recently, the fragment HS3 of HS, based on coarser-than-Allen's relations, has been introduced, and it has been proven to be not only decidable, but also relatively efficient. In this paper we describe an implementation of a tableau-based satisfiability checker for HS3 interpreted in the class of all finite linear order

Feature and Language Selection in Temporal Symbolic Regression for Interpretable Air Quality Modelling

Air quality modelling that relates meteorological, car traffic, and pollution data is a fundamental problem, approached in several different ways in the recent literature. In particular, a set of such data sampled at a specific location and during a specific period of time can be seen as a multivariate time series, and modelling the values of the pollutant concentrations can be seen as a multivariate temporal regression problem. In this paper, we propose a new method for symbolic multivariate temporal regression, and we apply it to several data sets that contain real air quality data from the city of Wrocław (Poland). Our experiments show that our approach is superior to classical, especially symbolic, ones, both in statistical performances and the interpretability of the results

Towards Interval Temporal Logic Rule-Based Classification

Supervised classification is one of the main computational tasks of modern Artificial Intelligence, and it is used to automatically extract an underlying theory from a set of already classified instances. The available learning schemata are mostly limited to static instances, in which the temporal component of the information is absent, neglected, or abstracted into atemporal data, and purely, native temporal classification is still largely unexplored. In this paper, we propose a temporal rulebased classifier based on interval temporal logic, that is able to learn a classification model for multivariate classified (abstracted) time series, and we discuss some implementation issues

On coarser interval temporal logics

The primary characteristic of interval temporal logic is that intervals, rather than points, are taken as the primitive ontological entities. Given their generally bad computational behavior of interval temporal logics, several techniques exist to produce decidable and computationally affordable temporal logics based on intervals. In this paper we take inspiration from Golumbic and Shamir's coarser interval algebras, which generalize the classical Allen's Interval Algebra, in order to define two previously unknown variants of Halpern and Shoham's logic (HS) based on coarser relations. We prove that, perhaps surprisingly, the satisfiability problem for the coarsest of the two variants, namely , not only is decidable, but PSpace-complete in the finite/discrete case, and PSpace-hard in any other case; besides proving its complexity bounds, we implement a tableau-based satisfiability checker for it and test it against a systematically generated benchmark. Our results are strengthened by showing that not all coarser-than-Allen's relations are a guarantee of decidability, as we prove that the second variant, namely , remains undecidable in all interesting cases

Data-driven precision determination of the material budget in ALICE

International audienceThe knowledge of the material budget with a high precision is fundamental for measurements of direct photon production using the photon conversion method due to its direct impact on the total systematic uncertainty. Moreover, it influences many aspects of the charged-particle reconstruction performance. In this article, two procedures to determine data-driven corrections to the material-budget description in ALICE simulation software are developed. One is based on the precise knowledge of the gas composition in the Time Projection Chamber. The other is based on the robustness of the ratio between the produced number of photons and charged particles, to a large extent due to the approximate isospin symmetry in the number of produced neutral and charged pions. Both methods are applied to ALICE data allowing for a reduction of the overall material budget systematic uncertainty from 4.5% down to 2.5%. Using these methods, a locally correct material budget is also achieved. The two proposed methods are generic and can be applied to any experiment in a similar fashion