Riccardo Guidotti

AI
h-index63
27papers
6,649citations
Novelty43%
AI Score49

27 Papers

AIOct 30, 2023
Explainable Artificial Intelligence (XAI) 2.0: A Manifesto of Open Challenges and Interdisciplinary Research Directions

Luca Longo, Mario Brcic, Federico Cabitza et al.

As systems based on opaque Artificial Intelligence (AI) continue to flourish in diverse real-world applications, understanding these black box models has become paramount. In response, Explainable AI (XAI) has emerged as a field of research with practical and ethical benefits across various domains. This paper not only highlights the advancements in XAI and its application in real-world scenarios but also addresses the ongoing challenges within XAI, emphasizing the need for broader perspectives and collaborative efforts. We bring together experts from diverse fields to identify open problems, striving to synchronize research agendas and accelerate XAI in practical applications. By fostering collaborative discussion and interdisciplinary cooperation, we aim to propel XAI forward, contributing to its continued success. Our goal is to put forward a comprehensive proposal for advancing XAI. To achieve this goal, we present a manifesto of 27 open problems categorized into nine categories. These challenges encapsulate the complexities and nuances of XAI and offer a road map for future research. For each problem, we provide promising research directions in the hope of harnessing the collective intelligence of interested stakeholders.

CLNov 15, 2023
Social Bias Probing: Fairness Benchmarking for Language Models

Marta Marchiori Manerba, Karolina Stańczak, Riccardo Guidotti et al. · eth-zurich

While the impact of social biases in language models has been recognized, prior methods for bias evaluation have been limited to binary association tests on small datasets, limiting our understanding of bias complexities. This paper proposes a novel framework for probing language models for social biases by assessing disparate treatment, which involves treating individuals differently according to their affiliation with a sensitive demographic group. We curate SoFa, a large-scale benchmark designed to address the limitations of existing fairness collections. SoFa expands the analysis beyond the binary comparison of stereotypical versus anti-stereotypical identities to include a diverse range of identities and stereotypes. Comparing our methodology with existing benchmarks, we reveal that biases within language models are more nuanced than acknowledged, indicating a broader scope of encoded biases than previously recognized. Benchmarking LMs on SoFa, we expose how identities expressing different religions lead to the most pronounced disparate treatments across all models. Finally, our findings indicate that real-life adversities faced by various groups such as women and people with disabilities are mirrored in the behavior of these models.

AIJan 18, 2023
Boosting Synthetic Data Generation with Effective Nonlinear Causal Discovery

Martina Cinquini, Fosca Giannotti, Riccardo Guidotti

Synthetic data generation has been widely adopted in software testing, data privacy, imbalanced learning, and artificial intelligence explanation. In all such contexts, it is crucial to generate plausible data samples. A common assumption of approaches widely used for data generation is the independence of the features. However, typically, the variables of a dataset depend on one another, and these dependencies are not considered in data generation leading to the creation of implausible records. The main problem is that dependencies among variables are typically unknown. In this paper, we design a synthetic dataset generator for tabular data that can discover nonlinear causalities among the variables and use them at generation time. State-of-the-art methods for nonlinear causal discovery are typically inefficient. We boost them by restricting the causal discovery among the features appearing in the frequent patterns efficiently retrieved by a pattern mining algorithm. We design a framework for generating synthetic datasets with known causalities to validate our proposal. Broad experimentation on many synthetic and real datasets with known causalities shows the effectiveness of the proposed method.

IVJan 18, 2023
Exemplars and Counterexemplars Explanations for Image Classifiers, Targeting Skin Lesion Labeling

Carlo Metta, Riccardo Guidotti, Yuan Yin et al.

Explainable AI consists in developing mechanisms allowing for an interaction between decision systems and humans by making the decisions of the formers understandable. This is particularly important in sensitive contexts like in the medical domain. We propose a use case study, for skin lesion diagnosis, illustrating how it is possible to provide the practitioner with explanations on the decisions of a state of the art deep neural network classifier trained to characterize skin lesions from examples. Our framework consists of a trained classifier onto which an explanation module operates. The latter is able to offer the practitioner exemplars and counterexemplars for the classification diagnosis thus allowing the physician to interact with the automatic diagnosis system. The exemplars are generated via an adversarial autoencoder. We illustrate the behavior of the system on representative examples.

QUANT-PHDec 13, 2022
Quantum Clustering with k-Means: a Hybrid Approach

Alessandro Poggiali, Alessandro Berti, Anna Bernasconi et al.

Quantum computing is a promising paradigm based on quantum theory for performing fast computations. Quantum algorithms are expected to surpass their classical counterparts in terms of computational complexity for certain tasks, including machine learning. In this paper, we design, implement, and evaluate three hybrid quantum k-Means algorithms, exploiting different degree of parallelism. Indeed, each algorithm incrementally leverages quantum parallelism to reduce the complexity of the cluster assignment step up to a constant cost. In particular, we exploit quantum phenomena to speed up the computation of distances. The core idea is that the computation of distances between records and centroids can be executed simultaneously, thus saving time, especially for big datasets. We show that our hybrid quantum k-Means algorithms can be more efficient than the classical version, still obtaining comparable clustering results.

AIAug 29, 2023
Ensemble of Counterfactual Explainers

Riccardo Guidotti, Salvatore Ruggieri

In eXplainable Artificial Intelligence (XAI), several counterfactual explainers have been proposed, each focusing on some desirable properties of counterfactual instances: minimality, actionability, stability, diversity, plausibility, discriminative power. We propose an ensemble of counterfactual explainers that boosts weak explainers, which provide only a subset of such properties, to a powerful method covering all of them. The ensemble runs weak explainers on a sample of instances and of features, and it combines their results by exploiting a diversity-driven selection function. The method is model-agnostic and, through a wrapping approach based on autoencoders, it is also data-agnostic.

LGJun 12, 2023
A Protocol for Continual Explanation of SHAP

Andrea Cossu, Francesco Spinnato, Riccardo Guidotti et al.

Continual Learning trains models on a stream of data, with the aim of learning new information without forgetting previous knowledge. Given the dynamic nature of such environments, explaining the predictions of these models can be challenging. We study the behavior of SHAP values explanations in Continual Learning and propose an evaluation protocol to robustly assess the change of explanations in Class-Incremental scenarios. We observed that, while Replay strategies enforce the stability of SHAP values in feedforward/convolutional models, they are not able to do the same with fully-trained recurrent models. We show that alternative recurrent approaches, like randomized recurrent models, are more effective in keeping the explanations stable over time.

LGNov 29, 2023
A Bag of Receptive Fields for Time Series Extrinsic Predictions

Francesco Spinnato, Riccardo Guidotti, Anna Monreale et al.

High-dimensional time series data poses challenges due to its dynamic nature, varying lengths, and presence of missing values. This kind of data requires extensive preprocessing, limiting the applicability of existing Time Series Classification and Time Series Extrinsic Regression techniques. For this reason, we propose BORF, a Bag-Of-Receptive-Fields model, which incorporates notions from time series convolution and 1D-SAX to handle univariate and multivariate time series with varying lengths and missing values. We evaluate BORF on Time Series Classification and Time Series Extrinsic Regression tasks using the full UEA and UCR repositories, demonstrating its competitive performance against state-of-the-art methods. Finally, we outline how this representation can naturally provide saliency and feature-based explanations.

AIDec 10, 2022
Causality-Aware Local Interpretable Model-Agnostic Explanations

Martina Cinquini, Riccardo Guidotti

A main drawback of eXplainable Artificial Intelligence (XAI) approaches is the feature independence assumption, hindering the study of potential variable dependencies. This leads to approximating black box behaviors by analyzing the effects on randomly generated feature values that may rarely occur in the original samples. This paper addresses this issue by integrating causal knowledge in an XAI method to enhance transparency and enable users to assess the quality of the generated explanations. Specifically, we propose a novel extension to a widely used local and model-agnostic explainer, which encodes explicit causal relationships within the data surrounding the instance being explained. Extensive experiments show that our approach overcomes the original method in terms of faithfully replicating the black-box model's mechanism and the consistency and reliability of the generated explanations.

AISep 28, 2024
Bridging the Gap in Hybrid Decision-Making Systems

Federico Mazzoni, Roberto Pellungrini, Riccardo Guidotti

We introduce BRIDGET, a novel human-in-the-loop system for hybrid decision-making, aiding the user to label records from an un-labeled dataset, attempting to ``bridge the gap'' between the two most popular Hybrid Decision-Making paradigms: those featuring the human in a leading position, and the other with a machine making most of the decisions. BRIDGET understands when either a machine or a human user should be in charge, dynamically switching between two statuses. In the different statuses, BRIDGET still fosters the human-AI interaction, either having a machine learning model assuming skeptical stances towards the user and offering them suggestions, or towards itself and calling the user back. We believe our proposal lays the groundwork for future synergistic systems involving a human and a machine decision-makers.

LGMar 28, 2025
MASCOTS: Model-Agnostic Symbolic COunterfactual explanations for Time Series

Dawid Płudowski, Francesco Spinnato, Piotr Wilczyński et al.

Counterfactual explanations provide an intuitive way to understand model decisions by identifying minimal changes required to alter an outcome. However, applying counterfactual methods to time series models remains challenging due to temporal dependencies, high dimensionality, and the lack of an intuitive human-interpretable representation. We introduce MASCOTS, a method that leverages the Bag-of-Receptive-Fields representation alongside symbolic transformations inspired by Symbolic Aggregate Approximation. By operating in a symbolic feature space, it enhances interpretability while preserving fidelity to the original data and model. Unlike existing approaches that either depend on model structure or autoencoder-based sampling, MASCOTS directly generates meaningful and diverse counterfactual observations in a model-agnostic manner, operating on both univariate and multivariate data. We evaluate MASCOTS on univariate and multivariate benchmark datasets, demonstrating comparable validity, proximity, and plausibility to state-of-the-art methods, while significantly improving interpretability and sparsity. Its symbolic nature allows for explanations that can be expressed visually, in natural language, or through semantic representations, making counterfactual reasoning more accessible and actionable.

HCMar 8, 2025
A Frank System for Co-Evolutionary Hybrid Decision-Making

Federico Mazzoni, Riccardo Guidotti, Alessio Malizia

We introduce Frank, a human-in-the-loop system for co-evolutionary hybrid decision-making aiding the user to label records from an un-labeled dataset. Frank employs incremental learning to ``evolve'' in parallel with the user's decisions, by training an interpretable machine learning model on the records labeled by the user. Furthermore, Frank advances state-of-the-art approaches by offering inconsistency controls, explanations, fairness checks, and bad-faith safeguards simultaneously. We evaluate our proposal by simulating the users' behavior with various levels of expertise and reliance on Frank's suggestions. The experiments show that Frank's intervention leads to improvements in the accuracy and the fairness of the decisions.

LGNov 20, 2025
Causal Synthetic Data Generation in Recruitment

Andrea Iommi, Antonio Mastropietro, Riccardo Guidotti et al.

The importance of Synthetic Data Generation (SDG) has increased significantly in domains where data quality is poor or access is limited due to privacy and regulatory constraints. One such domain is recruitment, where publicly available datasets are scarce due to the sensitive nature of information typically found in curricula vitae, such as gender, disability status, or age. % This lack of accessible, representative data presents a significant obstacle to the development of fair and transparent machine learning models, particularly ranking algorithms that require large volumes of data to effectively learn how to recommend candidates. In the absence of such data, these models are prone to poor generalisation and may fail to perform reliably in real-world scenarios. % Recent advances in Causal Generative Models (CGMs) offer a promising solution. CGMs enable the generation of synthetic datasets that preserve the underlying causal relationships within the data, providing greater control over fairness and interpretability in the data generation process. % In this study, we present a specialised SDG method involving two CGMs: one modelling job offers and the other modelling curricula. Each model is structured according to a causal graph informed by domain expertise. We use these models to generate synthetic datasets and evaluate the fairness of candidate rankings under controlled scenarios that introduce specific biases.

AINov 10, 2025
Evaluating Online Moderation Via LLM-Powered Counterfactual Simulations

Giacomo Fidone, Lucia Passaro, Riccardo Guidotti

Online Social Networks (OSNs) widely adopt content moderation to mitigate the spread of abusive and toxic discourse. Nonetheless, the real effectiveness of moderation interventions remains unclear due to the high cost of data collection and limited experimental control. The latest developments in Natural Language Processing pave the way for a new evaluation approach. Large Language Models (LLMs) can be successfully leveraged to enhance Agent-Based Modeling and simulate human-like social behavior with unprecedented degree of believability. Yet, existing tools do not support simulation-based evaluation of moderation strategies. We fill this gap by designing a LLM-powered simulator of OSN conversations enabling a parallel, counterfactual simulation where toxic behavior is influenced by moderation interventions, keeping all else equal. We conduct extensive experiments, unveiling the psychological realism of OSN agents, the emergence of social contagion phenomena and the superior effectiveness of personalized moderation strategies.

AIOct 23, 2025
Towards the Formalization of a Trustworthy AI for Mining Interpretable Models explOiting Sophisticated Algorithms

Riccardo Guidotti, Martina Cinquini, Marta Marchiori Manerba et al.

Interpretable-by-design models are crucial for fostering trust, accountability, and safe adoption of automated decision-making models in real-world applications. In this paper we formalize the ground for the MIMOSA (Mining Interpretable Models explOiting Sophisticated Algorithms) framework, a comprehensive methodology for generating predictive models that balance interpretability with performance while embedding key ethical properties. We formally define here the supervised learning setting across diverse decision-making tasks and data types, including tabular data, time series, images, text, transactions, and trajectories. We characterize three major families of interpretable models: feature importance, rule, and instance based models. For each family, we analyze their interpretability dimensions, reasoning mechanisms, and complexity. Beyond interpretability, we formalize three critical ethical properties, namely causality, fairness, and privacy, providing formal definitions, evaluation metrics, and verification procedures for each. We then examine the inherent trade-offs between these properties and discuss how privacy requirements, fairness constraints, and causal reasoning can be embedded within interpretable pipelines. By evaluating ethical measures during model generation, this framework establishes the theoretical foundations for developing AI systems that are not only accurate and interpretable but also fair, privacy-preserving, and causally aware, i.e., trustworthy.

LGJul 31, 2025
An Interpretable Data-Driven Unsupervised Approach for the Prevention of Forgotten Items

Luca Corbucci, Javier Alejandro Borges Legrottaglie, Francesco Spinnato et al.

Accurately identifying items forgotten during a supermarket visit and providing clear, interpretable explanations for recommending them remains an underexplored problem within the Next Basket Prediction (NBP) domain. Existing NBP approaches typically only focus on forecasting future purchases, without explicitly addressing the detection of unintentionally omitted items. This gap is partly due to the scarcity of real-world datasets that allow for the reliable estimation of forgotten items. Furthermore, most current NBP methods rely on black-box models, which lack transparency and limit the ability to justify recommendations to end users. In this paper, we formally introduce the forgotten item prediction task and propose two novel interpretable-by-design algorithms. These methods are tailored to identify forgotten items while offering intuitive, human-understandable explanations. Experiments on a real-world retail dataset show our algorithms outperform state-of-the-art NBP baselines by 10-15% across multiple evaluation metrics.

LGMay 3, 2025
Fair Clustering with Clusterlets

Mattia Setzu, Riccardo Guidotti

Given their widespread usage in the real world, the fairness of clustering methods has become of major interest. Theoretical results on fair clustering show that fairness enjoys transitivity: given a set of small and fair clusters, a trivial centroid-based clustering algorithm yields a fair clustering. Unfortunately, discovering a suitable starting clustering can be computationally expensive, rather complex or arbitrary. In this paper, we propose a set of simple \emph{clusterlet}-based fuzzy clustering algorithms that match single-class clusters, optimizing fair clustering. Matching leverages clusterlet distance, optimizing for classic clustering objectives, while also regularizing for fairness. Empirical results show that simple matching strategies are able to achieve high fairness, and that appropriate parameter tuning allows to achieve high cohesion and low overlap.

LGApr 29, 2025
Explanations Go Linear: Interpretable and Individual Latent Encoding for Post-hoc Explainability

Simone Piaggesi, Riccardo Guidotti, Fosca Giannotti et al.

Post-hoc explainability is essential for understanding black-box machine learning models. Surrogate-based techniques are widely used for local and global model-agnostic explanations but have significant limitations. Local surrogates capture non-linearities but are computationally expensive and sensitive to parameters, while global surrogates are more efficient but struggle with complex local behaviors. In this paper, we present ILLUME, a flexible and interpretable framework grounded in representation learning, that can be integrated with various surrogate models to provide explanations for any black-box classifier. Specifically, our approach combines a globally trained surrogate with instance-specific linear transformations learned with a meta-encoder to generate both local and global explanations. Through extensive empirical evaluations, we demonstrate the effectiveness of ILLUME in producing feature attributions and decision rules that are not only accurate but also robust and faithful to the black-box, thus providing a unified explanation framework that effectively addresses the limitations of traditional surrogate methods.

AIMar 21, 2025
Interpretable Machine Learning for Oral Lesion Diagnosis through Prototypical Instances Identification

Alessio Cascione, Mattia Setzu, Federico A. Galatolo et al.

Decision-making processes in healthcare can be highly complex and challenging. Machine Learning tools offer significant potential to assist in these processes. However, many current methodologies rely on complex models that are not easily interpretable by experts. This underscores the need to develop interpretable models that can provide meaningful support in clinical decision-making. When approaching such tasks, humans typically compare the situation at hand to a few key examples and representative cases imprinted in their memory. Using an approach which selects such exemplary cases and grounds its predictions on them could contribute to obtaining high-performing interpretable solutions to such problems. To this end, we evaluate PivotTree, an interpretable prototype selection model, on an oral lesion detection problem, specifically trying to detect the presence of neoplastic, aphthous and traumatic ulcerated lesions from oral cavity images. We demonstrate the efficacy of using such method in terms of performance and offer a qualitative and quantitative comparison between exemplary cases and ground-truth prototypes selected by experts.

CVNov 22, 2021
Explainable Deep Image Classifiers for Skin Lesion Diagnosis

Carlo Metta, Andrea Beretta, Riccardo Guidotti et al.

A key issue in critical contexts such as medical diagnosis is the interpretability of the deep learning models adopted in decision-making systems. Research in eXplainable Artificial Intelligence (XAI) is trying to solve this issue. However, often XAI approaches are only tested on generalist classifier and do not represent realistic problems such as those of medical diagnosis. In this paper, we analyze a case study on skin lesion images where we customize an existing XAI approach for explaining a deep learning model able to recognize different types of skin lesions. The explanation is formed by synthetic exemplar and counter-exemplar images of skin lesion and offers the practitioner a way to highlight the crucial traits responsible for the classification decision. A survey conducted with domain experts, beginners and unskilled people proof that the usage of explanations increases the trust and confidence in the automatic decision system. Also, an analysis of the latent space adopted by the explainer unveils that some of the most frequent skin lesion classes are distinctly separated. This phenomenon could derive from the intrinsic characteristics of each class and, hopefully, can provide support in the resolution of the most frequent misclassifications by human experts.

AIFeb 25, 2021
Benchmarking and Survey of Explanation Methods for Black Box Models

Francesco Bodria, Fosca Giannotti, Riccardo Guidotti et al.

The widespread adoption of black-box models in Artificial Intelligence has enhanced the need for explanation methods to reveal how these obscure models reach specific decisions. Retrieving explanations is fundamental to unveil possible biases and to resolve practical or ethical issues. Nowadays, the literature is full of methods with different explanations. We provide a categorization of explanation methods based on the type of explanation returned. We present the most recent and widely used explainers, and we show a visual comparison among explanations and a quantitative benchmarking.

LGJan 19, 2021
GLocalX -- From Local to Global Explanations of Black Box AI Models

Mattia Setzu, Riccardo Guidotti, Anna Monreale et al.

Artificial Intelligence (AI) has come to prominence as one of the major components of our society, with applications in most aspects of our lives. In this field, complex and highly nonlinear machine learning models such as ensemble models, deep neural networks, and Support Vector Machines have consistently shown remarkable accuracy in solving complex tasks. Although accurate, AI models often are "black boxes" which we are not able to understand. Relying on these models has a multifaceted impact and raises significant concerns about their transparency. Applications in sensitive and critical domains are a strong motivational factor in trying to understand the behavior of black boxes. We propose to address this issue by providing an interpretable layer on top of black box models by aggregating "local" explanations. We present GLocalX, a "local-first" model agnostic explanation method. Starting from local explanations expressed in form of local decision rules, GLocalX iteratively generalizes them into global explanations by hierarchically aggregating them. Our goal is to learn accurate yet simple interpretable models to emulate the given black box, and, if possible, replace it entirely. We validate GLocalX in a set of experiments in standard and constrained settings with limited or no access to either data or local explanations. Experiments show that GLocalX is able to accurately emulate several models with simple and small models, reaching state-of-the-art performance against natively global solutions. Our findings show how it is often possible to achieve a high level of both accuracy and comprehensibility of classification models, even in complex domains with high-dimensional data, without necessarily trading one property for the other. This is a key requirement for a trustworthy AI, necessary for adoption in high-stakes decision making applications.

CVJan 27, 2020
Black Box Explanation by Learning Image Exemplars in the Latent Feature Space

Riccardo Guidotti, Anna Monreale, Stan Matwin et al.

We present an approach to explain the decisions of black box models for image classification. While using the black box to label images, our explanation method exploits the latent feature space learned through an adversarial autoencoder. The proposed method first generates exemplar images in the latent feature space and learns a decision tree classifier. Then, it selects and decodes exemplars respecting local decision rules. Finally, it visualizes them in a manner that shows to the user how the exemplars can be modified to either stay within their class, or to become counter-factuals by "morphing" into another class. Since we focus on black box decision systems for image classification, the explanation obtained from the exemplars also provides a saliency map highlighting the areas of the image that contribute to its classification, and areas of the image that push it into another class. We present the results of an experimental evaluation on three datasets and two black box models. Besides providing the most useful and interpretable explanations, we show that the proposed method outperforms existing explainers in terms of fidelity, relevance, coherence, and stability.

LGOct 22, 2018
On The Stability of Interpretable Models

Riccardo Guidotti, Salvatore Ruggieri

Interpretable classification models are built with the purpose of providing a comprehensible description of the decision logic to an external oversight agent. When considered in isolation, a decision tree, a set of classification rules, or a linear model, are widely recognized as human-interpretable. However, such models are generated as part of a larger analytical process. Bias in data collection and preparation, or in model's construction may severely affect the accountability of the design process. We conduct an experimental study of the stability of interpretable models with respect to feature selection, instance selection, and model selection. Our conclusions should raise awareness and attention of the scientific community on the need of a stability impact assessment of interpretable models.

AIJun 26, 2018
Open the Black Box Data-Driven Explanation of Black Box Decision Systems

Dino Pedreschi, Fosca Giannotti, Riccardo Guidotti et al.

Black box systems for automated decision making, often based on machine learning over (big) data, map a user's features into a class or a score without exposing the reasons why. This is problematic not only for lack of transparency, but also for possible biases hidden in the algorithms, due to human prejudices and collection artifacts hidden in the training data, which may lead to unfair or wrong decisions. We introduce the local-to-global framework for black box explanation, a novel approach with promising early results, which paves the road for a wide spectrum of future developments along three dimensions: (i) the language for expressing explanations in terms of highly expressive logic-based rules, with a statistical and causal interpretation; (ii) the inference of local explanations aimed at revealing the logic of the decision adopted for a specific instance by querying and auditing the black box in the vicinity of the target instance; (iii), the bottom-up generalization of the many local explanations into simple global ones, with algorithms that optimize the quality and comprehensibility of explanations.

AIMay 28, 2018
Local Rule-Based Explanations of Black Box Decision Systems

Riccardo Guidotti, Anna Monreale, Salvatore Ruggieri et al.

The recent years have witnessed the rise of accurate but obscure decision systems which hide the logic of their internal decision processes to the users. The lack of explanations for the decisions of black box systems is a key ethical issue, and a limitation to the adoption of machine learning components in socially sensitive and safety-critical contexts. %Therefore, we need explanations that reveals the reasons why a predictor takes a certain decision. In this paper we focus on the problem of black box outcome explanation, i.e., explaining the reasons of the decision taken on a specific instance. We propose LORE, an agnostic method able to provide interpretable and faithful explanations. LORE first leans a local interpretable predictor on a synthetic neighborhood generated by a genetic algorithm. Then it derives from the logic of the local interpretable predictor a meaningful explanation consisting of: a decision rule, which explains the reasons of the decision; and a set of counterfactual rules, suggesting the changes in the instance's features that lead to a different outcome. Wide experiments show that LORE outperforms existing methods and baselines both in the quality of explanations and in the accuracy in mimicking the black box.

CYFeb 6, 2018
A Survey Of Methods For Explaining Black Box Models

Riccardo Guidotti, Anna Monreale, Salvatore Ruggieri et al.

In the last years many accurate decision support systems have been constructed as black boxes, that is as systems that hide their internal logic to the user. This lack of explanation constitutes both a practical and an ethical issue. The literature reports many approaches aimed at overcoming this crucial weakness sometimes at the cost of scarifying accuracy for interpretability. The applications in which black box decision systems can be used are various, and each approach is typically developed to provide a solution for a specific problem and, as a consequence, delineating explicitly or implicitly its own definition of interpretability and explanation. The aim of this paper is to provide a classification of the main problems addressed in the literature with respect to the notion of explanation and the type of black box system. Given a problem definition, a black box type, and a desired explanation this survey should help the researcher to find the proposals more useful for his own work. The proposed classification of approaches to open black box models should also be useful for putting the many research open questions in perspective.