Expectation Maximization in Deep Probabilistic Logic Programming

Probabilistic Logic Programming (PLP) combines logic and probability for representing and reasoning over domains with uncertainty. Hierarchical probability Logic Programming (HPLP) is a recent language of PLP whose clauses are hierarchically organized forming a deep neural network or arithmetic circuit. Inference in HPLP is done by circuit evaluation and learning is therefore cheaper than any generic PLP language. We present in this paper an Expectation Maximization algorithm, called Expectation Maximization Parameter learning for HIerarchical Probabilistic Logic programs (EMPHIL), for learning HPLP parameters. The algorithm converts an arithmetic circuit into a Bayesian network and performs the belief propagation algorithm over the corresponding factor graph

Neural-Symbolic Ensemble Learning for early-stage prediction of critical state of Covid-19 patients

Recently, Artificial Intelligence (AI) and Machine Learning (ML) have been successfully applied to many domains of interest including medical diagnosis. Due to the availability of a large quantity of data, it is possible to build reliable AI systems that assist humans in making decisions. The recent Covid-19 pandemic quickly spread over the world causing serious health problems and severe economic and social damage. Computer scientists are actively working together with doctors on different ML models to diagnose Covid-19 patients using Computed Tomography (CT) scans and clinical data. In this work, we propose a neural-symbolic system that predicts if a Covid-19 patient arriving at the hospital will end in a critical condition. The proposed system relies on Deep 3D Convolutional Neural Networks (3D-CNNs) for analyzing lung CT scans of Covid-19 patients, Decision Trees (DTs) for predicting if a Covid-19 patient will eventually pass away by analyzing its clinical data, and a neural system that integrates the previous ones using Hierarchical Probabilistic Logic Programs (HPLPs). Predicting if a Covid-19 patient will end in a critical condition is useful for managing the limited number of intensive care at the hospital. Moreover, knowing early that a Covid-19 patient could end in serious conditions allows doctors to gain early knowledge on patients and provide special treatment to those predicted to finish in critical conditions. The proposed system, entitled Neural HPLP, obtains good performance in terms of area under the receiver operating characteristic and precision curves with values of about 0.96 for both metrics. Therefore, with Neural HPLP, it is possible not only to efficiently predict if Covid-19 patients will end in severe conditions but also possible to provide an explanation of the prediction. This makes Neural HPLP explainable, interpretable, and reliable. Graphical abstract Representation of Neural HPLP. From top to bottom, the two different types of data collected from the same patient and used in this project are represented. This data feeds the two different machine learning systems and the integration of the two systems using Hierarchical Probabilistic Logic Program

Explainable Deep Learning

Il grande successo che il Deep Learning ha ottenuto in ambiti strategici per la nostra società quali l'industria, la difesa, la medicina etc., ha portanto sempre più realtà a investire ed esplorare l'utilizzo di questa tecnologia. Ormai si possono trovare algoritmi di Machine Learning e Deep Learning quasi in ogni ambito della nostra vita. Dai telefoni, agli elettrodomestici intelligenti fino ai veicoli che guidiamo. Quindi si può dire che questa tecnologia pervarsiva è ormai a contatto con le nostre vite e quindi dobbiamo confrontarci con essa. Da questo nasce l’eXplainable Artificial Intelligence o XAI, uno degli ambiti di ricerca che vanno per la maggiore al giorno d'oggi in ambito di Deep Learning e di Intelligenza Artificiale. Il concetto alla base di questo filone di ricerca è quello di rendere e/o progettare i nuovi algoritmi di Deep Learning in modo che siano affidabili, interpretabili e comprensibili all'uomo. Questa necessità è dovuta proprio al fatto che le reti neurali, modello matematico che sta alla base del Deep Learning, agiscono come una scatola nera, rendendo incomprensibile all'uomo il ragionamento interno che compiono per giungere ad una decisione. Dato che stiamo delegando a questi modelli matematici decisioni sempre più importanti, integrandole nei processi più delicati della nostra società quali, ad esempio, la diagnosi medica, la guida autonoma o i processi di legge, è molto importante riuscire a comprendere le motivazioni che portano questi modelli a produrre determinati risultati. Il lavoro presentato in questa tesi consiste proprio nello studio e nella sperimentazione di algoritmi di Deep Learning integrati con tecniche di Intelligenza Artificiale simbolica. Questa integrazione ha un duplice scopo: rendere i modelli più potenti, consentendogli di compiere ragionamenti o vincolandone il comportamento in situazioni complesse, e renderli interpretabili. La tesi affronta due macro argomenti: le spiegazioni ottenute grazie all'integrazione neuro-simbolica e lo sfruttamento delle spiegazione per rendere gli algoritmi di Deep Learning più capaci o intelligenti. Il primo macro argomento si concentra maggiormente sui lavori svolti nello sperimentare l'integrazione di algoritmi simbolici con le reti neurali. Un approccio è stato quelli di creare un sistema per guidare gli addestramenti delle reti stesse in modo da trovare la migliore combinazione di iper-parametri per automatizzare la progettazione stessa di queste reti. Questo è fatto tramite l'integrazione di reti neurali con la Programmazione Logica Probabilistica (PLP) che consente di sfruttare delle regole probabilistiche indotte dal comportamento delle reti durante la fase di addestramento o ereditate dall'esperienza maturata dagli esperti del settore. Queste regole si innescano allo scatenarsi di un problema che il sistema rileva durate l'addestramento della rete. Questo ci consente di ottenere una spiegazione di cosa è stato fatto per migliorare l'addestramento una volta identificato un determinato problema. Un secondo approccio è stato quello di far cooperare sistemi logico-probabilistici con reti neurali per la diagnosi medica da fonti di dati eterogenee. La seconda tematica affrontata in questa tesi tratta lo sfruttamento delle spiegazioni che possiamo ottenere dalle rete neurali. In particolare, queste spiegazioni sono usate per creare moduli di attenzione che aiutano a vincolare o a guidare le reti neurali portandone ad avere prestazioni migliorate. Tutti i lavori sviluppati durante il dottorato e descritti in questa tesi hanno portato alle pubblicazioni elencate nel Capitolo 14.2.The great success that Machine and Deep Learning has achieved in areas that are strategic for our society such as industry, defence, medicine, etc., has led more and more realities to invest and explore the use of this technology. Machine Learning and Deep Learning algorithms and learned models can now be found in almost every area of our lives. From phones to smart home appliances, to the cars we drive. So it can be said that this pervasive technology is now in touch with our lives, and therefore we have to deal with it. This is why eXplainable Artificial Intelligence or XAI was born, one of the research trends that are currently in vogue in the field of Deep Learning and Artificial Intelligence. The idea behind this line of research is to make and/or design the new Deep Learning algorithms so that they are interpretable and comprehensible to humans. This necessity is due precisely to the fact that neural networks, the mathematical model underlying Deep Learning, act like a black box, making the internal reasoning they carry out to reach a decision incomprehensible and untrustable to humans. As we are delegating more and more important decisions to these mathematical models, it is very important to be able to understand the motivations that lead these models to make certain decisions. This is because we have integrated them into the most delicate processes of our society, such as medical diagnosis, autonomous driving or legal processes. The work presented in this thesis consists in studying and testing Deep Learning algorithms integrated with symbolic Artificial Intelligence techniques. This integration has a twofold purpose: to make the models more powerful, enabling them to carry out reasoning or constraining their behaviour in complex situations, and to make them interpretable. The thesis focuses on two macro topics: the explanations obtained through neuro-symbolic integration and the exploitation of explanations to make the Deep Learning algorithms more capable or intelligent. The neuro-symbolic integration was addressed twice, by experimenting with the integration of symbolic algorithms with neural networks. A first approach was to create a system to guide the training of the networks themselves in order to find the best combination of hyper-parameters to automate the design of these networks. This is done by integrating neural networks with Probabilistic Logic Programming (PLP). This integration makes it possible to exploit probabilistic rules tuned by the behaviour of the networks during the training phase or inherited from the experience of experts in the field. These rules are triggered when a problem occurs during network training. This generates an explanation of what was done to improve the training once a particular issue was identified. A second approach was to make probabilistic logic systems cooperate with neural networks for medical diagnosis on heterogeneous data sources. The second topic addressed in this thesis concerns the exploitation of explanations. In particular, the explanations one can obtain from neural networks are used in order to create attention modules that help in constraining and improving the performance of neural networks. All works developed during the PhD and described in this thesis have led to the publications listed in Chapter 14.2

Deep probabilistic logic programming

Probabilistic logic programming under the distribution semantics has been very useful in machine learning. However, inference is expensive so machine learning algorithms may turn out to be slow. In this paper we consider a restriction of the language called hierarchical PLP in which clauses and predicates are hierarchically organized. In this case the language becomes truth-functional and inference reduces to the evaluation of formulas in the product fuzzy logic. Programs in this language can also be seen as arithmetic circuits or deep neural networks and inference can be reperformed quickly when the parameters change. Learning can then be performed by EM or backpropagation