Salvatore Ruggieri

Jose M. Alvarez, Kristen M. Scott, Salvatore Ruggieri et al.

In uses of pre-trained machine learning models, it is a known issue that the target population in which the model is being deployed may not have been reflected in the source population with which the model was trained. This can result in a biased model when deployed, leading to a reduction in model performance. One risk is that, as the population changes, certain demographic groups will be under-served or otherwise disadvantaged by the model, even as they become more represented in the target population. The field of domain adaptation proposes techniques for a situation where label data for the target population does not exist, but some information about the target distribution does exist. In this paper we contribute to the domain adaptation literature by introducing domain-adaptive decision trees (DADT). We focus on decision trees given their growing popularity due to their interpretability and performance relative to other more complex models. With DADT we aim to improve the accuracy of models trained in a source domain (or training data) that differs from the target domain (or test data). We propose an in-processing step that adjusts the information gain split criterion with outside information corresponding to the distribution of the target population. We demonstrate DADT on real data and find that it improves accuracy over a standard decision tree when testing in a shifted target population. We also study the change in fairness under demographic parity and equal opportunity. Results show an improvement in fairness with the use of DADT.

Jose M. Alvarez, Salvatore Ruggieri

We present counterfactual situation testing (CST), a causal data mining framework for detecting discrimination in classifiers. CST aims to answer in an actionable and meaningful way the intuitive question "what would have been the model outcome had the individual, or complainant, been of a different protected status?" It extends the legally-grounded situation testing of Thanh et al. (2011) by operationalizing the notion of fairness given the difference using counterfactual reasoning. For any complainant, we find and compare similar protected and non-protected instances in the dataset used by the classifier to construct a control and test group, where a difference between the decision outcomes of the two groups implies potential individual discrimination. Unlike situation testing, which builds both groups around the complainant, we build the test group on the complainant's counterfactual generated using causal knowledge. The counterfactual is intended to reflect how the protected attribute when changed affects the seemingly neutral attributes used by the classifier, which is taken for granted in many frameworks for discrimination. Under CST, we compare similar individuals within each group but dissimilar individuals across both groups due to the possible difference between the complainant and its counterfactual. Evaluating our framework on two classification scenarios, we show that it uncovers a greater number of cases than situation testing, even when the classifier satisfies the counterfactual fairness condition of Kusner et al. (2017).

Andrea Pugnana, Salvatore Ruggieri

Selective classification (or classification with a reject option) pairs a classifier with a selection function to determine whether or not a prediction should be accepted. This framework trades off coverage (probability of accepting a prediction) with predictive performance, typically measured by distributive loss functions. In many application scenarios, such as credit scoring, performance is instead measured by ranking metrics, such as the Area Under the ROC Curve (AUC). We propose a model-agnostic approach to associate a selection function to a given probabilistic binary classifier. The approach is specifically targeted at optimizing the AUC. We provide both theoretical justifications and a novel algorithm, called AUCROSS, to achieve such a goal. Experiments show that our method succeeds in trading-off coverage for AUC, improving over existing selective classification methods targeted at optimizing accuracy.

Carlos Mougan, Laura State, Antonio Ferrara et al.

Liberalism-oriented political philosophy reasons that all individuals should be treated equally independently of their protected characteristics. Related work in machine learning has translated the concept of \emph{equal treatment} into terms of \emph{equal outcome} and measured it as \emph{demographic parity} (also called \emph{statistical parity}). Our analysis reveals that the two concepts of equal outcome and equal treatment diverge; therefore, demographic parity does not faithfully represent the notion of \emph{equal treatment}. We propose a new formalization for equal treatment by (i) considering the influence of feature values on predictions, such as computed by Shapley values decomposing predictions across its features, (ii) defining distributions of explanations, and (iii) comparing explanation distributions between populations with different protected characteristics. We show the theoretical properties of our notion of equal treatment and devise a classifier two-sample test based on the AUC of an equal treatment inspector. We study our formalization of equal treatment on synthetic and natural data. We release \texttt{explanationspace}, an open-source Python package with methods and tutorials.

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.

Xuan Zhao, Klaus Broelemann, Salvatore Ruggieri et al.

We introduce an innovative approach to enhancing the empirical risk minimization (ERM) process in model training through a refined reweighting scheme of the training data to enhance fairness. This scheme aims to uphold the sufficiency rule in fairness by ensuring that optimal predictors maintain consistency across diverse sub-groups. We employ a bilevel formulation to address this challenge, wherein we explore sample reweighting strategies. Unlike conventional methods that hinge on model size, our formulation bases generalization complexity on the space of sample weights. We discretize the weights to improve training speed. Empirical validation of our method showcases its effectiveness and robustness, revealing a consistent improvement in the balance between prediction performance and fairness metrics across various experiments.

Xuan Zhao, Klaus Broelemann, Salvatore Ruggieri et al.

The importance of achieving fairness in machine learning models cannot be overstated. Recent research has pointed out that fairness should be examined from a causal perspective, and several fairness notions based on the on Pearl's causal framework have been proposed. In this paper, we construct a reweighting scheme of datasets to address causal fairness. Our approach aims at mitigating bias by considering the causal relationships among variables and incorporating them into the reweighting process. The proposed method adopts two neural networks, whose structures are intentionally used to reflect the structures of a causal graph and of an interventional graph. The two neural networks can approximate the causal model of the data, and the causal model of interventions. Furthermore, reweighting guided by a discriminator is applied to achieve various fairness notions. Experiments on real-world datasets show that our method can achieve causal fairness on the data while remaining close to the original data for downstream tasks.

Jose M. Alvarez, Antonio Mastropietro, Salvatore Ruggieri

We investigate the role of the initial screening order (ISO) in candidate screening. The ISO refers to the order in which the screener searches the candidate pool when selecting $k$ candidates. Today, it is common for the ISO to be the product of an information access system, such as an online platform or a database query. The ISO has been largely overlooked in the literature, despite its impact on the optimality and fairness of the selected $k$ candidates, especially under a human screener. We define two problem formulations describing the search behavior of the screener given an ISO: the best-$k$, where it selects the top $k$ candidates; and the good-$k$, where it selects the first good-enough $k$ candidates. To study the impact of the ISO, we introduce a human-like screener and compare it to its algorithmic counterpart, where the human-like screener is conceived to be inconsistent over time. Our analysis, in particular, shows that the ISO, under a human-like screener solving for the good-$k$ problem, hinders individual fairness despite meeting group fairness, and hampers the optimality of the selected $k$ candidates. This is due to position bias, where a candidate's evaluation is affected by its position within the ISO. We report extensive simulated experiments exploring the parameters of the best-$k$ and good-$k$ problems for both screeners. Our simulation framework is flexible enough to account for multiple candidate screening tasks, being an alternative to running real-world procedures.

Andrea Pugnana, Lorenzo Perini, Jesse Davis et al.

With the increasing deployment of machine learning models in many socially sensitive tasks, there is a growing demand for reliable and trustworthy predictions. One way to accomplish these requirements is to allow a model to abstain from making a prediction when there is a high risk of making an error. This requires adding a selection mechanism to the model, which selects those examples for which the model will provide a prediction. The selective classification framework aims to design a mechanism that balances the fraction of rejected predictions (i.e., the proportion of examples for which the model does not make a prediction) versus the improvement in predictive performance on the selected predictions. Multiple selective classification frameworks exist, most of which rely on deep neural network architectures. However, the empirical evaluation of the existing approaches is still limited to partial comparisons among methods and settings, providing practitioners with little insight into their relative merits. We fill this gap by benchmarking 18 baselines on a diverse set of 44 datasets that includes both image and tabular data. Moreover, there is a mix of binary and multiclass tasks. We evaluate these approaches using several criteria, including selective error rate, empirical coverage, distribution of rejected instance's classes, and performance on out-of-distribution instances. The results indicate that there is not a single clear winner among the surveyed baselines, and the best method depends on the users' objectives.

Jose M. Alvarez, Salvatore Ruggieri

We present counterfactual situation testing (CST), a causal data mining framework for detecting individual discrimination in a dataset of classifier decisions. CST answers the question ``what would have been the model outcome had the individual, or complainant, been of a different protected status?'' It extends the legally-grounded situation testing (ST) of Thanh et al. (2011) by operationalizing the notion of "fairness given the difference" via counterfactual reasoning. ST finds for each complainant similar protected and non-protected instances in the dataset; constructs, respectively, a control and test group; and compares the groups such that a difference in model outcomes implies a potential case of individual discrimination. CST, instead, avoids this idealized comparison by establishing the test group on the complainant's generated counterfactual, which reflects how the protected attribute when changed influences other seemingly neutral attributes of the complainant. Under CST we test for discrimination for each complainant by comparing similar individuals within the control and test group but dissimilar individuals across these groups. We consider single (e.g.,~gender) and multidimensional (e.g.,~gender and race) discrimination testing. For multidimensional discrimination we study multiple and intersectional discrimination and, as feared by legal scholars, find evidence that the former fails to account for the latter kind. Using a k-nearest neighbor implementation, we showcase CST on synthetic and real data. Experimental results show that CST uncovers a higher number of cases than ST, even when the model is counterfactually fair. CST, in fact, extends counterfactual fairness (CF) of Kusner et al. (2017) by equipping CF with confidence intervals, which we report for all experiments.

Martina Cinquini, Isacco Beretta, Salvatore Ruggieri et al.

In this paper, we focus on estimating the causal effect of an intervention over time on a dynamical system. To that end, we formally define causal interventions and their effects over time on discrete-time stochastic processes (DSPs). Then, we show under which conditions the equilibrium states of a DSP, both before and after a causal intervention, can be captured by a structural causal model (SCM). With such an equivalence at hand, we provide an explicit mapping from vector autoregressive models (VARs), broadly applied in econometrics, to linear, but potentially cyclic and/or affected by unmeasured confounders, SCMs. The resulting causal VAR framework allows us to perform causal inference over time from observational time series data. Our experiments on synthetic and real-world datasets show that the proposed framework achieves strong performance in terms of observational forecasting while enabling accurate estimation of the causal effect of interventions on dynamical systems. We demonstrate, through a case study, the potential practical questions that can be addressed using the proposed causal VAR framework.

Jose M. Alvarez, Salvatore Ruggieri

Testing for individual discrimination involves deriving a profile, the comparator, similar to the one making the discrimination claim, the complainant, based on a protected attribute, such as race or gender, and comparing their decision outcomes. The complainant-comparator pair is central to discrimination testing. Most discrimination testing tools rely on this pair to establish evidence for discrimination. In this work we revisit the role of the comparator in discrimination testing. We first argue for the inherent causal modeling nature of deriving the comparator. We then introduce a two-kinds classification for the comparator: the ceteris paribus, or``with all else equal,'' (CP) comparator and the mutatis mutandis, or ``with the appropriate adjustments being made,'' (MM) comparator. The CP comparator is the standard comparator, representing an idealized comparison for establishing discrimination as it aims for a complainant-comparator pair that only differs on membership to the protected attribute. As an alternative to it, we define the MM comparator, which requires that the comparator represents the``what would have been of'' the complainant without the effects of the protected attribute on the non-protected attributes. Under the MM comparator, the complainant-comparator pair can be dissimilar in terms of the non-protected attributes, departing from an idealized comparison. Notably, the MM comparator is a more complex kind of comparator and its implementation offers an impactful venue for machine learning methods. We illustrate these two comparators and their impact on discrimination testing using a real-world example.

Laura State, Alejandra Bringas Colmenarejo, Andrea Beretta et al.

Explainable AI (XAI) provides methods to understand non-interpretable machine learning models. However, we have little knowledge about what legal experts expect from these explanations, including their legal compliance with, and value against European Union legislation. To close this gap, we present the Explanation Dialogues, an expert focus study to uncover the expectations, reasoning, and understanding of legal experts and practitioners towards XAI, with a specific focus on the European General Data Protection Regulation. The study consists of an online questionnaire and follow-up interviews, and is centered around a use-case in the credit domain. We extract both a set of hierarchical and interconnected codes using grounded theory, and present the standpoints of the participating experts towards XAI. We find that the presented explanations are hard to understand and lack information, and discuss issues that can arise from the different interests of the data controller and subject. Finally, we present a set of recommendations for developers of XAI methods, and indications of legal areas of discussion. Among others, recommendations address the presentation, choice, and content of an explanation, technical risks as well as the end-user, while we provide legal pointers to the contestability of explanations, transparency thresholds, intellectual property rights as well as the relationship between involved parties.

Mattia Setzu, Salvatore Ruggieri

Decision Trees are accessible, interpretable, and well-performing classification models. A plethora of variants with increasing expressiveness has been proposed in the last forty years. We contrast the two families of univariate DTs, whose split functions partition data through axis-parallel hyperplanes, and multivariate DTs, whose splits instead partition data through oblique hyperplanes. The latter include the former, hence multivariate DTs are in principle more powerful. Surprisingly enough, however, univariate DTs consistently show comparable performances in the literature. We analyze the reasons behind this, both with synthetic and real-world benchmark datasets. Our research questions test whether the pre-processing phase of removing correlation among features in datasets has an impact on the relative performances of univariate vs multivariate DTs. We find that existing benchmark datasets are likely biased towards favoring univariate DTs.

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.

Antonio Ferrara, Andrea Pugnana, Francesco Bonchi et al.

Ranking systems influence decision-making in high-stakes domains like health, education, and employment, where they can have substantial economic and social impacts. This makes the integration of safety mechanisms essential. One such mechanism is $\textit{abstention}$, which enables algorithmic decision-making system to defer uncertain or low-confidence decisions to human experts. While abstention have been predominantly explored in the context of classification tasks, its application to other machine learning paradigms remains underexplored. In this paper, we introduce a novel method for abstention in pairwise learning-to-rank tasks. Our approach is based on thresholding the ranker's conditional risk: the system abstains from making a decision when the estimated risk exceeds a predefined threshold. Our contributions are threefold: a theoretical characterization of the optimal abstention strategy, a model-agnostic, plug-in algorithm for constructing abstaining ranking models, and a comprehensive empirical evaluations across multiple datasets, demonstrating the effectiveness of our approach.

Jose M. Alvarez, Salvatore Ruggieri

Perception occurs when individuals interpret the same information differently. It is a known cognitive phenomenon with implications for bias in human decision-making. Perception, however, remains understudied in machine learning (ML). This is problematic as modern decision flows, whether partially or fully automated by ML applications, always involve human experts. For instance, how might we account for cases in which two experts interpret differently the same deferred instance or explanation from a ML model? Addressing this and similar questions requires first a formulation of perception, particularly, in a manner that integrates with ML-enabled decision flows. In this work, we present a first approach to modeling perception causally. We define perception under causal reasoning using structural causal models (SCMs). Our approach formalizes individual experience as additional causal knowledge that comes with and is used by the expert decision-maker in the form of a SCM. We define two kinds of probabilistic causal perception: structural and parametrical. We showcase our framework through a series of examples of modern decision flows. We also emphasize the importance of addressing perception in fair ML, discussing relevant fairness implications and possible applications.

Laura State, Salvatore Ruggieri, Franco Turini

Explaining opaque Machine Learning (ML) models is an increasingly relevant problem. Current explanation in AI (XAI) methods suffer several shortcomings, among others an insufficient incorporation of background knowledge, and a lack of abstraction and interactivity with the user. We propose REASONX, an explanation method based on Constraint Logic Programming (CLP). REASONX can provide declarative, interactive explanations for decision trees, which can be the ML models under analysis or global/local surrogate models of any black-box model. Users can express background or common sense knowledge using linear constraints and MILP optimization over features of factual and contrastive instances, and interact with the answer constraints at different levels of abstraction through constraint projection. We present here the architecture of REASONX, which consists of a Python layer, closer to the user, and a CLP layer. REASONX's core execution engine is a Prolog meta-program with declarative semantics in terms of logic theories.

Laura State, Salvatore Ruggieri, Franco Turini

Many high-performing machine learning models are not interpretable. As they are increasingly used in decision scenarios that can critically affect individuals, it is necessary to develop tools to better understand their outputs. Popular explanation methods include contrastive explanations. However, they suffer several shortcomings, among others an insufficient incorporation of background knowledge, and a lack of interactivity. While (dialogue-like) interactivity is important to better communicate an explanation, background knowledge has the potential to significantly improve their quality, e.g., by adapting the explanation to the needs of the end-user. To close this gap, we present REASONX, an explanation tool based on Constraint Logic Programming (CLP). REASONX provides interactive contrastive explanations that can be augmented by background knowledge, and allows to operate under a setting of under-specified information, leading to increased flexibility in the provided explanations. REASONX computes factual and constrative decision rules, as well as closest constrative examples. It provides explanations for decision trees, which can be the ML models under analysis, or global/local surrogate models of any ML model. While the core part of REASONX is built on CLP, we also provide a program layer that allows to compute the explanations via Python, making the tool accessible to a wider audience. We illustrate the capability of REASONX on a synthetic data set, and on a a well-developed example in the credit domain. In both cases, we can show how REASONX can be flexibly used and tailored to the needs of the user.

Carlos Mougan, Jose M. Alvarez, Salvatore Ruggieri et al.

Past research has demonstrated that the explicit use of protected attributes in machine learning can improve both performance and fairness. Many machine learning algorithms, however, cannot directly process categorical attributes, such as country of birth or ethnicity. Because protected attributes frequently are categorical, they must be encoded as features that can be input to a chosen machine learning algorithm, e.g.\ support vector machines, gradient boosting decision trees or linear models. Thereby, encoding methods influence how and what the machine learning algorithm will learn, affecting model performance and fairness. This work compares the accuracy and fairness implications of the two most well-known encoding methods: \emph{one-hot encoding} and \emph{target encoding}. We distinguish between two types of induced bias that may arise from these encoding methods and may lead to unfair models. The first type, \textit{irreducible bias}, is due to direct group category discrimination, and the second type, \textit{reducible bias}, is due to the large variance in statistically underrepresented groups. We investigate the interaction between categorical encodings and target encoding regularization methods that reduce unfairness. Furthermore, we consider the problem of intersectional unfairness that may arise when machine learning best practices improve performance measures by encoding several categorical attributes into a high-cardinality feature.

Fabrizio Lillo, Salvatore Ruggieri

We study the problem of estimating the total number of searches (volume) of queries in a specific domain, which were submitted to a search engine in a given time period. Our statistical model assumes that the distribution of searches follows a Zipf's law, and that the observed sample volumes are biased accordingly to three possible scenarios. These assumptions are consistent with empirical data, with keyword research practices, and with approximate algorithms used to take counts of query frequencies. A few estimators of the parameters of the distribution are devised and experimented, based on the nature of the empirical/simulated data. For continuous data, we recommend using nonlinear least square regression (NLS) on the top-volume queries, where the bound on the volume is obtained from the well-known Clauset, Shalizi and Newman (CSN) estimation of power-law parameters. For binned data, we propose using a Chi-square minimization approach restricted to the top-volume queries, where the bound is obtained by the binned version of the CSN method. Estimations are then derived for the total number of queries and for the total volume of the population, including statistical error bounds. We apply the methods on the domain of recipes and cooking queries searched in Italian in 2017. The observed volumes of sample queries are collected from Google Trends (continuous data) and SearchVolume (binned data). The estimated total number of queries and total volume are computed for the two cases, and the results are compared and discussed.

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.

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.

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.

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.