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In this paper we focus on the opacity issue of sub-symbolic machine learning predictors by promoting two complementary activities, namely, symbolic knowledge extraction (SKE) and injection (SKI) from and into sub-symbolic predictors. We consider as symbolic any language being intelligible and interpretable for both humans and computers. Accordingly, we propose general meta-models for both SKE and SKI, along with two taxonomies for the classification of SKE and SKI methods. By adopting an explainable artificial intelligence (XAI) perspective, we highlight how such methods can be exploited to mitigate the aforementioned opacity issue. Our taxonomies are attained by surveying and classifying existing methods from the literature, following a systematic approach, and by generalising the results of previous surveys targeting specific sub-topics of either SKE or SKI alone. More precisely, we analyse 132 methods for SKE and 117 methods for SKI, and we categorise them according to their purpose, operation, expected input/output data and predictor types. For each method, we also indicate the presence/lack of runnable software implementations. Our work may be of interest for data scientists aiming at selecting the most adequate SKE/SKI method for their needs, and also work as suggestions for researchers interested in filling the gaps of the current state of the art, as well as for developers willing to implement SKE/SKI-based technologies.

In clinical practice, decision-making relies heavily on established protocols, often formalised as rules. Concurrently, Machine Learning (ML) models, trained on clinical data, aspire to integrate into medical decision-making processes. However, despite the growing number of ML applications, their adoption into clinical practice remains limited. Two critical concerns arise, relevant to the notions of consistency and continuity of care: (a) accuracy - the ML model, albeit more accurate, might introduce errors that would not have occurred by applying the protocol; (b) interpretability - ML models operating as black boxes might make predictions based on relationships that contradict established clinical knowledge. In this context, the literature suggests using ML models integrating domain knowledge for improved accuracy and interpretability. However, there is a lack of appropriate metrics for comparing ML models with clinical rules in addressing these challenges. Accordingly, in this article, we first propose metrics to assess the accuracy of ML models with respect to the established protocol. Secondly, we propose an approach to measure the distance of explanations provided by two rule sets, with the goal of comparing the explanation similarity between clinical rule-based systems and rules extracted from ML models. The approach is validated on the Pima Indians Diabetes dataset by training two neural networks - one exclusively on data, and the other integrating a clinical protocol. Our findings demonstrate that the integrated ML model achieves comparable performance to that of a fully data-driven model while exhibiting superior accuracy relative to the clinical protocol, ensuring enhanced continuity of care. Furthermore, we show that our integrated model provides explanations for predictions that align more closely with the clinical protocol compared to the data-driven model.

Context. Galactic cosmic rays (GCRs) and solar particles with energies greater than tens of MeV penetrate spacecraft and instruments hosted aboard space missions. The Solar Orbiter Metis coronagraph is aimed at observing the solar corona in both visible (VL) and ultraviolet (UV) light. Particle tracks are observed in the Metis images of the corona. An algorithm has been implemented in the Metis processing electronics to detect the VL image pixels crossed by cosmic rays. This algorithm was initially enabled for the VL instrument only, since the process of separating the particle tracks in the UV images has proven to be very challenging. Aims. We study the impact of the overall bulk of particles of galactic and solar origin on the Metis coronagraph images. We discuss the effects of the increasing solar activity after the Solar Orbiter mission launch on the secondary particle production in the spacecraft. Methods. We compared Monte Carlo simulations of GCRs crossing or interacting in the Metis VL CMOS sensor to observations gathered in 2020 and 2022. We also evaluated the impact of solar energetic particle events of different intensities on the Metis images. Results. The study of the role of abundant and rare cosmic rays in firing pixels in the Metis VL images of the corona allows us to estimate the efficiency of the algorithm applied for cosmic-ray track removal from the images and to demonstrate that the instrument performance had remained unchanged during the first two years of the Solar Orbiter operations. The outcome of this work can be used to estimate the Solar Orbiter instrument's deep charging and the order of magnitude for energetic particles crossing the images of Metis and other instruments such as STIX and EUI., Comment: 8 pages, 6 figures

In this work we study the potentialities of machine learning models in reconstructing the solar wind speed observations gathered in the first Lagrangian point by the ACE satellite in 2016--2017 using as input data galactic cosmic-ray flux variations measured with particle detectors hosted onboard the LISA Pathfinder mission also orbiting around L1 during the same years. We show that ensemble models composed of heterogeneous weak regressors are able to outperform weak regressors in terms of predictive accuracy. Machine learning and other powerful predictive algorithms open a window on the possibility of substituting dedicated instrumentation with software models acting as surrogates for diagnostics of space missions such as LISA and space weather science., Comment: Submitted to Environmental Modelling & Software

The characteristics of a hydrogenated amorphous silicon (a-Si:H) detector are presented here for monitoring in space solar flares and the evolution of large energetic proton events up to hundreds of MeV. The a-Si:H presents an excellent radiation hardness and finds application in harsh radiation environments for medical purposes, for particle beam characterization and in space weather science and applications. The critical flux detection threshold for solar X rays, soft gamma rays, electrons and protons is discussed in detail., Comment: 32 pages, 13 figures, submitted to Experimental Astronomy

As opaque decision systems are being increasingly adopted in almost any application field, issues about their lack of transparency and human readability are a concrete concern for end-users. Amongst existing proposals to associate human-interpretable knowledge with accurate predictions provided by opaque models, there are rule extraction techniques, capable of extracting symbolic knowledge out of an opaque model. However, how to assess the level of readability of the extracted knowledge quantitatively is still an open issue. Finding such a metric would be the key, for instance, to enable automatic comparison between a set of different knowledge representations, paving the way for the development of parameter autotuning algorithms for knowledge extractors. In this paper we discuss the need for such a metric as well as the criticalities of readability assessment and evaluation, taking into account the most common knowledge representations while highlighting the most puzzling issues., Comment: 2nd International Workshop on Explainable AI in Finance (XAI-FIN 2022)

Opaque models belonging to the machine learning world are ever more exploited in the most different application areas. These models, acting as black boxes (BB) from the human perspective, cannot be entirely trusted if the application is critical unless there exists a method to extract symbolic and human-readable knowledge out of them. In this paper we analyse a recurrent design adopted by symbolic knowledge extractors for BB regressors - that is, the creation of rules associated with hypercubic input space regions. We argue that this kind of partitioning may lead to suboptimal solutions when the data set at hand is high-dimensional or does not satisfy symmetric constraints. We then propose a (deep) clustering-based approach to be performed before symbolic knowledge extraction to achieve better performance with data sets of any kind., Comment: Third Workshop on Explainable Logic-Based Knowledge Representation (XLoKR2022)

Machine learning models are nowadays ubiquitous in space missions, performing a wide variety of tasks ranging from the prediction of multivariate time series through the detection of specific patterns in the input data. Adopted models are usually deep neural networks or other complex machine learning algorithms providing predictions that are opaque, i.e., human users are not allowed to understand the rationale behind the provided predictions. Several techniques exist in the literature to combine the impressive predictive performance of opaque machine learning models with human-intelligible prediction explanations, as for instance the application of symbolic knowledge extraction procedures. In this paper are reported the results of different knowledge extractors applied to an ensemble predictor capable of reproducing cosmic-ray data gathered on board the LISA Pathfinder space mission. A discussion about the readability/fidelity trade-off of the extracted knowledge is also presented.

Cubic gold-platinum free-falling test masses (TMs) constitute the mirrors of future LISA and LISA-like interferometers for low-frequency gravitational wave detection in space. High-energy particles of Galactic and solar origin charge the TMs and thus induce spurious electrostatic and magnetic forces that limit the sensitivity of these interferometers. Prelaunch Monte Carlo simulations of the TM charging were carried out for the LISA Pathfinder (LPF) mission, that was planned to test the LISA instrumentation. Measurements and simulations were compared during the mission operations. The measured net TM charging agreed with simulation estimates, while the charging noise was three to four times higher. We aim to bridge the gap between LPF TM charging noise simulations and observations. New Monte Carlo simulations of the LPF TM charging due to both Galactic and solar particles were carried out with the FLUKA/LEI toolkit. This allowed propagating low-energy electrons down to a few electronvolt. These improved FLUKA/LEI simulations agree with observations gathered during the mission operations within statistical and Monte Carlo errors. The charging noise induced by Galactic cosmic rays is about one thousand charges per second. This value increases to tens of thousands charges per second during solar energetic particle events. Similar results are expected for the LISA TM charging., Comment: 11 pages, 9 figures

Galactic cosmic-ray (GCR) flux short-term variations ($<$1 month) in the inner heliosphere are mainly associated with the passage of high-speed solar wind streams (HSS) and interplanetary (IP) counterparts of coronal mass ejections (ICMEs). Data gathered with a particle detector flown on board the ESA LISA Pathfinder (LPF) spacecraft, during the declining part of the solar cycle 24 (February 2016 - July 2017) around the Lagrange point L1, have allowed to study the characteristics of recurrent cosmic-ray flux modulations above 70 MeV n$^{-1}$. %These modulations are observed when the solar wind speed is $>$ 400 km s$^{-1}$ and/or the IP magnetic field intensity $>$ 10 nT. It is shown that the amplitude and evolution of individual modulations depend in a unique way on both IP plasma parameters and particle flux intensity before HSS and ICMEs transit. By comparing the LPF data with those gathered contemporaneously with the magnetic spectrometer experiment AMS-02 on board the International Space Station and with those of Earth polar neutron monitors, the GCR flux modulation was studied at different energies during recurrent short-term variations. It is also aimed to set the near real-time particle observation requirements to disentangle the role of long and short-term variations of the GCR flux to evaluate the performance of high-sensitivity instruments in space such as the future interferometers for gravitational wave detection. Finally, the association between recurrent GCR flux variation observations in L1 and weak to moderate geomagnetic activity in 2016-2017 is discussed. Short-term recurrent GCR flux variations are good proxies of recurrent geomagnetic activity when the B$_z$ component of the IP magnetic field is directed northern.