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.

This paper surveys Machine Learning approaches to build predictive models that know what they don't know. The consequential action of this knowledge can consist of abstaining from providing an output (rejection), deferring to another model (dynamic model selection), deferring to a human expert (learning to defer), or informing the user (uncertainty estimation). We formally state the problems each approach solves and point to key references. We discuss open issues that deserve investigation from the scientific community.

Deferring systems extend supervised Machine Learning (ML) models with the possibility to defer predictions to human experts. However, evaluating the impact of a deferring strategy on system accuracy is still an overlooked area. This paper fills this gap by evaluating deferring systems through a causal lens. We link the potential outcomes framework for causal inference with deferring systems, which allows to identify the causal impact of the deferring strategy on predictive accuracy. We distinguish two scenarios. In the first one, we have access to both the human and ML model predictions for the deferred instances. Here, we can identify the individual causal effects for deferred instances and the aggregates of them. In the second one, only human predictions are available for the deferred instances. Here, we can resort to regression discontinuity design to estimate a local causal effect. We evaluate our approach on synthetic and real datasets for seven deferring systems from the literature.

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.

As machine learning models enable decisions once performed only by humans, it is central to develop tools that assess the fairness of such models. Notably, within high-stake settings like hiring and lending, these tools must be able to detect potentially discriminatory models. 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.

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. Code is available at https://github.com/zhaoxuan00707/Reweighting_for_sufficiency.

Abstract Recent years have witnessed the rise of accurate but obscure classification models that hide the logic of their internal decision processes. Explaining the decision taken by a black-box classifier on a specific input instance is therefore of striking interest. We propose a local rule-based model-agnostic explanation method providing stable and actionable explanations. An explanation consists of a factual logic rule, stating the reasons for the black-box decision, and a set of actionable counterfactual logic rules, proactively suggesting the changes in the instance that lead to a different outcome. Explanations are computed from a decision tree that mimics the behavior of the black-box locally to the instance to explain. The decision tree is obtained through a bagging-like approach that favors stability and fidelity: first, an ensemble of decision trees is learned from neighborhoods of the instance under investigation; then, the ensemble is merged into a single decision tree. Neighbor instances are synthetically generated through a genetic algorithm whose fitness function is driven by the black-box behavior. Experiments show that the proposed method advances the state-of-the-art towards a comprehensive approach that successfully covers stability and actionability of factual and counterfactual explanations.

Selective classification (also known as classification with reject option) conservatively extends a classifier with a selection function to determine whether or not a prediction should be accepted (i.e., trusted, used, deployed). This is a highly relevant issue in socially sensitive tasks, such as credit scoring. State-of-the-art approaches rely on Deep Neural Networks (DNNs) that train at the same time both the classifier and the selection function. These approaches are model-specific and computationally expensive. We propose a model-agnostic approach, as it can work with any base probabilistic binary classification algorithm, and it can be scalable to large tabular datasets if the base classifier is so. The proposed algorithm, called SCROSS, exploits a cross-fitting strategy and theoretical results for quantile estimation to build the selection function. Experiments on real-world data show that SCROSS improves over existing methods.

There is a fast-growing literature in addressing the fairness of AI models (fair-AI), with a continuous stream of new conceptual frameworks, methods, and tools. How much can we trust them? How much do they actually impact society? We take a critical focus on fair-AI and survey issues, simplifications, and mistakes that researchers and practitioners often underestimate, which in turn can undermine the trust on fair-AI and limit its contribution to society. In particular, we discuss the hyper-focus on fairness metrics and on optimizing their average performances. We instantiate this observation by discussing the Yule's effect of fair-AI tools: being fair on average does not imply being fair in contexts that matter. We conclude that the use of fair-AI methods should be complemented with the design, development, and verification practices that are commonly summarized under the umbrella of trustworthy AI.

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: one-hot encoding and 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, irreducible bias, is due to direct group category discrimination and the second type, 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.

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.

We describe the design, the architecture, and the evaluation of the Leasing Score Prediction (LSP) system - a credit scoring and credit rating system for the leasing sector deployed at the Italian association of leasing companies. Due to its challenging objectives, the design and complexity of the LSP system represent a unique contribution to the best practices in the field. We cover requirements by managers, users, and regulations about rigorous backtesting, statistical validation, calibration, explainability, robustness and uncertainty self-assessment. LSP relies on a machine learning model trained on a mixture of data distributions contributed by many associated leasing companies. We describe the technical solutions adopted and report on their performance evaluation, including the management of the data shifts due to the COVID-19 pandemic.

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.

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.

Abstract We present xspells, a model-agnostic local approach for explaining the decisions of black box models in classification of short texts. The explanations provided consist of a set of exemplar sentences and a set of counter-exemplar sentences. The former are examples classified by the black box with the same label as the text to explain. The latter are examples classified with a different label (a form of counter-factuals). Both are close in meaning to the text to explain, and both are meaningful sentences – albeit they are synthetically generated. xspells generates neighbors of the text to explain in a latent space using Variational Autoencoders for encoding text and decoding latent instances. A decision tree is learned from randomly generated neighbors, and used to drive the selection of the exemplars and counter-exemplars. Moreover, diversity of counter-exemplars is modeled as an optimization problem, solved by a greedy algorithm with theoretical guarantee. We report experiments on three datasets showing that xspells outperforms the well-known lime method in terms of quality of explanations, fidelity, diversity, and usefulness, and that is comparable to it in terms of stability.

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 ofrecipes and cookingqueries 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.

Abstract We present xspells, a model-agnostic local approach for explaining the decisions of a black box model for sentiment classification of short texts. The explanations provided consist of a set of exemplar sentences and a set of counter-exemplar sentences. The former are examples classified by the black box with the same label as the text to explain. The latter are examples classified with a different label (a form of counter-factuals). Both are close in meaning to the text to explain, and both are meaningful sentences – albeit they are synthetically generated. xspells generates neighbors of the text to explain in a latent space using Variational Autoencoders for encoding text and decoding latent instances. A decision tree is learned from randomly generated neighbors, and used to drive the selection of the exemplars and counter-exemplars. We report experiments on two datasets showing that xspells outperforms the well-known lime method in terms of quality of explanations, fidelity, and usefulness, and that is comparable to it in terms of stability.

Black box AI 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 inherited by the algorithms from human prejudices and collection artifacts hidden in the training data, which may lead to unfair or wrong decisions. We focus on the urgent open challenge of how to construct meaningful explanations of opaque AI/ML systems, introducing the local-toglobal framework for black box explanation, articulated along three lines: (i) the language for expressing explanations in terms of logic rules, with statistical and causal interpretation; (ii) the inference of local explanations for revealing the decision rationale for a specific case, by auditing the black box in the vicinity of the target instance; (iii), the bottom-up generalization of many local explanations into simple global ones, with algorithms that optimize for quality and comprehensibility. We argue that the local-first approach opens the door to a wide variety of alternative solutions along different dimensions: a variety of data sources (relational, text, images, etc.), a variety of learning problems (multi-label classification, regression, scoring, ranking), a variety of languages for expressing meaningful explanations, a variety of means to audit a black box.

Segregation is the separation of social groups in the physical or in the online world. Segregation discovery consists of finding contexts of segregation. In the modern digital society, discovering segregation is challenging, due to the large amount and the variety of social data. We present a tool in support of segregation discovery from relational and graph data. The SCube system builds on attributed graph clustering and frequent itemset mining. It offers to the analyst a multi-dimensional segregation data cube for exploratory data analysis. The demonstration first guides the audience through the relevant social science concepts. Then, it focuses on scenarios around case studies of gender occupational segregation. Two real and large datasets about the boards of directors of Italian and Estonian companies will be explored in search of segregation contexts. The architecture of the SCube system and its computational efficiency challenges and solutions are discussed.

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.

We study the problem of estimating the total volume of queries of a specific domain, which were submitted to the Google search engine in a given time period. Our statistical model assumes a Zipf's law distribution of the population in the reference domain, and a non-uniform or noisy sampling of queries. Parameters of the distribution are estimated using nonlinear least square regression. Estimations with errors are then derived for the total number of queries and for the total number of searches (volume). We apply the method on the recipes and cooking domain, where a sample of queries is collected by crawling popular Italian websites specialized on this domain. The relative volumes of queries in the sample are computed using Google Trends, and transformed to absolute frequencies after estimating a scaling factor. Our model estimates that the volume of Italian recipes and cooking queries submitted to Google in 2017 and with at least 10 monthly searches consists of 7.2B searches.

The search space for the feature selection problem in decision tree learning is the lattice of subsets of the available features. We design an exact enumeration procedure of the subsets of features that lead to all and only the distinct decision trees built by a greedy top-down decision tree induction algorithm. The procedure stores, in the worst case, a number of trees linear in the number of features. By exploiting a further pruning of the search space, we design a complete procedure for finding $\delta$-acceptable feature subsets, which depart by at most $\delta$ from the best estimated error over any feature subset. Feature subsets with the best estimated error are called best feature subsets. Our results apply to any error estimator function, but experiments are mainly conducted under the wrapper model, in which the misclassification error over a search set is used as an estimator. The approach is also adapted to the design of a computational optimization of the sequential backward elimination heuristic, extending its applicability to large dimensional datasets. The procedures of this paper are implemented in a multi-core data parallel C++ system. We investigate experimentally the properties and limitations of the procedures on a collection of 20 benchmark datasets, showing that oversearching increases both overfitting and instability.

We introduce a framework for the data-driven analysis of social segregation of minority groups, and challenge it on a complex scenario. The framework builds on quantitative measures of segregation, called segregation indexes, proposed in the social science literature. The segregation discovery problem is introduced, which consists of searching sub-groups of population and minorities for which a segregation index is above a minimum threshold. A search algorithm is devised that solves the segregation problem by computing a multi-dimensional data cube that can be explored by the analyst. The machinery underlying the search algorithm relies on frequent itemset mining concepts and tools. The framework is challenged on a cases study in the context of company networks. We analyse segregation on the grounds of sex and age for directors in the boards of the Italian companies. The network includes 2.15M companies and 3.63M directors.

Attributed graphs model real networks by enriching their nodes with attributes accounting for properties. Several techniques have been proposed for partitioning these graphs into clusters that are homogeneous with respect to both semantic attributes and to the structure of the graph. However, time and space complexities of state of the art algorithms limit their scalability to medium-sized graphs. We propose SToC (for Semantic-Topological Clustering), a fast and scalable algorithm for partitioning large attributed graphs. The approach is robust, being compatible both with categorical and with quantitative attributes, and it is tailorable, allowing the user to weight the semantic and topological components. Further, the approach does not require the user to guess in advance the number of clusters. SToC relies on well known approximation techniques such as bottom-k sketches, traditional graph-theoretic concepts, and a new perspective on the composition of heterogeneous distance measures. Experimental results demonstrate its ability to efficiently compute high-quality partitions of large scale attributed graphs.

The search space for the feature selection problem in decision tree learning is the lattice of subsets of the available features. We provide an exact enumeration procedure of the subsets that lead to all and only the distinct decision trees. The procedure can be adopted to prune the search space of complete and heuristics search methods in wrapper models for feature selection. Based on this, we design a computational optimization of the sequential backward elimination heuristics with a performance improvement of up to 100X.

We present a framework for the analysis of corporate governance problems using network science and graph algorithms on ownership networks. In such networks, nodes model companies/shareholders and edges model shares owned. Inspired by the widespread pyramidal organization of corporate groups of companies, we model ownership networks as layered graphs, and exploit the layered structure to design feasible and efficient solutions to three key problems of corporate governance. The first one is the long-standing problem of computing direct and indirect ownership (integrated ownership problem). The other two problems are introduced here: computing direct and indirect dividends (dividend problem), and computing the group of companies controlled by a parent shareholder (corporate group problem). We conduct an extensive empirical analysis of the Italian ownership network, which, with its 3.9M nodes, is 30× the largest network studied so far.

We introduce a framework for a data-driven analysis of segregation of minority groups in social networks, and challenge it on a complex scenario. The framework builds on quantitative measures of segregation, called segregation indexes, proposed in the social science literature. The segregation discovery problem consists of searching sub-graphs and sub-groups for which a reference segregation index is above a minimum threshold. A search algorithm is devised that solves the segregation problem. The framework is challenged on the analysis of segregation of social groups in the boards of directors of the real and large network of Italian companies connected through shared directors. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

SUMMARY The whole computer hardware industry embraced the multi‐core. The extreme optimisation of sequential algorithms is then no longer sufficient to squeeze the real machine power, which can be only exploited via thread‐level parallelism. Decision tree algorithms exhibit natural concurrency that makes them suitable to be parallelised. This paper presents an in‐depth study of the parallelisation of an implementation of the C4.5 algorithm for multi‐core architectures. We characterise elapsed time lower bounds for the forms of parallelisations adopted and achieve close to optimal performance. Our implementation is based on the FastFlow parallel programming environment, and it requires minimal changes to the original sequential code. Copyright © 2013 John Wiley & Sons, Ltd.

The current availability of efficient algorithms for decision tree induction makes intricate post-processing techniques worth to be investigated both for efficiency and effectiveness. We study the simplification operator of subtree replacement, also known as grafting, originally implemented in the C4.5 system. We present a parametric bottom-up algorithm integrating grafting with the standard pruning operator, and analyze its complexity in terms of the number of nodes visited. Immediate instances of the parametric algorithm include extensions of error based, reduced error, minimum error, and pessimistic error pruning. Experimental results show that the computational cost of grafting is paid off by statistically significant smaller trees without accuracy loss.

With the support of the legally-grounded methodology of situation testing, we tackle the problems of discrimination discovery and prevention from a dataset of historical decisions by adopting a variant of k-NN classification. A tuple is labeled as discriminated if we can observe a significant difference of treatment among its neighbors belonging to a protected-by-law group and its neighbors not belonging to it. Discrimination discovery boils down to extracting a classification model from the labeled tuples. Discrimination prevention is tackled by changing the decision value for tuples labeled as discriminated before training a classifier. The approach of this paper overcomes legal weaknesses and technical limitations of existing proposals.

Concise representations of frequent itemsets sacrifice readability and direct interpretability by a data analyst of the concise patterns extracted. In this paper, we introduce an extension of itemsets, called regular, with an immediate semantics and interpretability, and a conciseness comparable to closed itemsets. Regular itemsets allow for specifying that an item may or may not be present; that any subset of an itemset may be present; and that any non-empty subset of an itemset may be present. We devise a procedure, called RegularMine, for mining a set of regular itemsets that is a concise representation of frequent itemsets. The procedure computes a covering, in terms of regular itemsets, of the frequent itemsets in the class of equivalence of a closed one. We report experimental results on several standard dense and sparse datasets that validate the proposed approach.

Discrimination discovery in databases consists in finding unfair practices against minorities which are hidden in a dataset of historical decisions. The DCUBE system implements the approach of [5], which is based on classification rule extraction and analysis, by centering the analysis phase around an Oracle database. The proposed demonstration guides the audience through the legal issues about discrimination hidden in data, and through several legally-grounded analyses to unveil discriminatory situations. The SIGMOD attendees will freely pose complex discrimination analysis queries over the database of extracted classification rules, once they are presented with the database relational schema, a few ad-hoc functions and procedures, and several snippets of SQL queries for discrimination discovery.

In the context of civil rights law, discrimination refers to unfair or unequal treatment of people based on membership to a category or a minority, without regard to individual merit. Discrimination in credit, mortgage, insurance, labor market, and education has been investigated by researchers in economics and human sciences. With the advent of automatic decision support systems, such as credit scoring systems, the ease of data collection opens several challenges to data analysts for the fight against discrimination. In this article, we introduce the problem of discovering discrimination through data mining in a dataset of historical decision records, taken by humans or by automatic systems. We formalize the processes of direct and indirect discrimination discovery by modelling protected-by-law groups and contexts where discrimination occurs in a classification rule based syntax. Basically, classification rules extracted from the dataset allow for unveiling contexts of unlawful discrimination, where the degree of burden over protected-by-law groups is formalized by an extension of the lift measure of a classification rule. In direct discrimination, the extracted rules can be directly mined in search of discriminatory contexts. In indirect discrimination, the mining process needs some background knowledge as a further input, for example, census data, that combined with the extracted rules might allow for unveiling contexts of discriminatory decisions. A strategy adopted for combining extracted classification rules with background knowledge is called an inference model. In this article, we propose two inference models and provide automatic procedures for their implementation. An empirical assessment of our results is provided on the German credit dataset and on the PKDD Discovery Challenge 1999 financial dataset.

We present a type system for linear constraints over the reals intended for reasoning about the input-output directionality of variables. Types model the properties of definiteness, range width or approximation, lower and upper bounds of variables in a linear constraint. Several proof procedures are presented for inferring the type of a variable and for checking validity of type assertions. We rely on theory and tools for linear programming problems, linear algebra, parameterized polyhedra and negative constraints. An application of the type system is proposed in the context of the static analysis of constraint logic programs. Type assertions are at the basis of the extension of well-moding from pure logic programming. The proof procedures (both for type assertion validity and for well-moding) are implemented and their computational complexity is discussed. We report experimental results demonstrating the efficiency in practice of the proposed approach.

Automatic Decision Support Systems (DSS) are widely adopted for screening purposes in socially sensitive tasks, including access to credit, mortgage, insurance, labor market and other benefits. While less arbitrary decisions can potentially be guaranteed, automatic DSS can still be discriminating in the socially negative sense of resulting in unfair or unequal treatment of people. We present a reference model for finding (prima facie) evidence of discrimination in automatic DSS which is driven by a few key legal concepts. First, frequent classification rules are extracted from the set of decisions taken by the DSS over an input pool dataset. Key legal concepts are then used to drive the analysis of the set of classification rules, with the aim of discovering patterns of discrimination. We present an implementation, called LP2DD, of the overall reference model integrating induction, through data mining classification rule extraction, and deduction, through a computational logic implementation of the analytical tools.

Discrimination in social sense (e.g., against minorities and disadvantaged groups) is the subject of many laws worldwide, and it has been extensively studied in the social and economic sciences. We tackle the problem of determining, given a dataset of historical decision records, a precise measure of the degree of discrimination suffered by a given group (e.g., an etnic minority) in a given context (e.g., a geographic area) with respect to the decision (e.g. credit denial). In our approach, this problem is rephrased in a classification rule based setting, and a collection of quantitative measures of discrimination is introduced, on the basis of existing norms and regulations. The measures are defined as functions of the contingency table of a classification rule, and their statistical significance is assessed, relying on a large body of statistical inference methods for proportions. Based on this basic method, we are then able to address the more general problems of: (1) unveiling all discriminatory decision patterns hidden in the historical data, combining discrimination analysis with association rule mining, (2) unveiling discrimination in classifiers that learn over training data biased by discriminatory decisions, and (3) in the case of rule-based classifiers, sanitizing discriminatory rules by correcting their confidence. Our approach is validated on the German credit dataset and on the CPAR classifier.

In the context of civil rights law, discrimination refers to unfair or unequal treatment of people based on membership to a category or a minority, without regard to individual merit. Rules extracted from databases by data mining techniques, such as classification or association rules, when used for decision tasks such as benefit or credit approval, can be discriminatory in the above sense. In this paper, the notion of discriminatory classification rules is introduced and studied. Providing a guarantee of non-discrimination is shown to be a non trivial task. A naive approach, like taking away all discriminatory attributes, is shown to be not enough when other background knowledge is available. Our approach leads to a precise formulation of the redlining problem along with a formal result relating discriminatory rules with apparently safe ones by means of background knowledge. An empirical assessment of the results on the German credit dataset is also provided.

YaDT is a from-scratch main-memory implementation of the C4.5-like decision tree algorithm. Our presentation would be focused on the design principles that allowed for obtaining an extremely efficient system. Experimental results are reported comparing YaDT with Weka, dti, Xelopes and (E)C4.5.

The Constraint Logic Programming (CLP) Scheme merges logic programming with constraint solving over predefined domains. In this article, we study proof methods for universal left termination of constraint logic programs. We provide a sound and complete characterization of left termination for ideal CLP languages which generalizesacceptabilityof logic programs. The characterization is then refined to the notion ofpartial acceptability, which is well suited for automatic modular inference. We describe a theoretical framework for automation of the approach, which is implemented. For nonideal CLP languages and without any assumption on their incomplete constraint solvers, even the most basic sound termination criterion from logic programming does not lift. We focus on a specific system, namely CLP(R), by proposing some additional conditions that make (partial) acceptability sound.

We present an analytic evaluation of the runtime behavior of the C4.5 algorithm which highlights some efficiency improvements. Based on the analytic evaluation, we have implemented a more efficient version of the algorithm, called EC4.5. It improves on C4.5 by adopting the best among three strategies for computing the information gain of continuous attributes. All the strategies adopt a binary search of the threshold in the whole training set starting from the local threshold computed at a node. The first strategy computes the local threshold using the algorithm of C4.5, which, in particular, sorts cases by means of the quicksort method. The second strategy also uses the algorithm of C4.5, but adopts a counting sort method. The third strategy calculates the local threshold using a main-memory version of the RainForest algorithm, which does not need sorting. Our implementation computes the same decision trees as C4.5 with a performance gain of up to five times.

Termination of logic programs depends critically on the selection rule, i.e. the rule that determines which atom is selected in each resolution step. In this article, we classify programs (and queries) according to the selection rules for which they terminate. This is a survey and unified view on different approaches in the literature. For each class, we present a sufficient, for most classes even necessary, criterion for determining that a program is in that class. We study six classes: a program strongly terminates if it terminates for all selection rules; a program input terminates if it terminates for selection rules which only select atoms that are sufficiently instantiated in their input positions, so that these arguments do not get instantiated any further by the unification; a program local delay terminates if it terminates for local selection rules which only select atoms that are bounded w.r.t. an appropriate level mapping; a program left-terminates if it terminates for the usual left-to-right selection rule; a program ∃-terminates if there exists a selection rule for which it terminates; finally, a program has bounded nondeterminism if it only has finitely many refutations. We propose a semantics-preserving transformation from programs with bounded nondeterminism into strongly terminating programs. Moreover, by unifying different formalisms and making appropriate assumptions, we are able to establish a formal hierarchy between the different classes.

A novel approach to the verification of meta-interpreters is introduced. We apply a general purpose verification method for logic programs to the case study of Vanilla and other logic meta-interpreters. We extend the standard notion of declarative correctness, and design a criterion for proving correctness of meta-interpreters in a general sense, including amalgamated and reflective meta-interpreters. The contribution of this paper can be summarized as follows: under certain natural assumptions, all interesting verification properties lift up from the object program to the metaprogram, including partial correctness, termination, absence of errors, call patterns persistence, correct instances of queries, computed instances of queries. Interestingly, it is possible to establish these results on the basis of purely declarative reasoning, using the mentioned proof method. We believe that the obtained results illustrate the broad applicability of the adopted verification principles.