Andrea Pugnana

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.

Andrea Pugnana, Carlos Mougan, Dan Saattrup Nielsen

With the wide adoption of machine learning techniques, requirements have evolved beyond sheer high performance, often requiring models to be trustworthy. A common approach to increase the trustworthiness of such systems is to allow them to refrain from predicting. Such a framework is known as selective prediction. While selective prediction for classification tasks has been widely analyzed, the problem of selective regression is understudied. This paper presents a novel approach to selective regression that utilizes model-agnostic non-parametric uncertainty estimation. Our proposed framework showcases superior performance compared to state-of-the-art selective regressors, as demonstrated through comprehensive benchmarking on 69 datasets. Finally, we use explainable AI techniques to gain an understanding of the drivers behind selective regression. We implement our selective regression method in the open-source Python package doubt and release the code used to reproduce our experiments.

Cesare Barbera, Lorenzo Perini, Giovanni De Toni et al.

Accurate and well-calibrated Machine Learning (ML) models are mandatory in high-stakes settings, yet effective multiclass calibration remains challenging: global approaches assume calibration errors are homogeneous across the latent space, while local methods often rely on latent-space dimensionality reduction, which leads to information loss. To address these issues, we propose a compositional approach to multiclass calibration, where region-specific calibration maps are constructed from shared codeword-dependent factors. We instantiate this idea via Vector Quantization (VQ), which induces a structured partition of the representation space, and an indexed parameterization of Dirichlet concentrations that enables parameter sharing across regions. Our approach learns heterogeneous calibration maps that generalize well even to sparse regions of the latent space. Experiments on benchmark datasets show significant improvements in local calibration while maintaining competitive global calibration and predictive performance.

Samuele Bortolotti, Emanuele Marconato, Andrea Pugnana et al.

Neuro-Symbolic Concept-based Models (NeSy-CBMs) are a family of architectures that integrate neural networks with symbolic reasoning for enhanced reliability in high-stakes applications. They work by first extracting high-level concepts from the input and then inferring a task label from these compatibly with given logical constraints. Yet, their label and concept predictions can be overconfident, making it difficult for stakeholders to gauge when the model's decisions can be trusted. We address this issue by integrating ideas from Conformal Prediction (CP), a framework providing rigorous, distribution-free coverage guarantees. We formalize three desiderata -- consistency, coverage, and conciseness -- that any conformal method for NeSy-CBMs should satisfy, and show that existing approaches fall short of at least one. We then introduce COCOCO, a post-hoc framework that conformalizes concepts and labels jointly and reconciles them via a single deduction-abduction revision step. COCOCO satisfies all three desiderata, retains distribution-free coverage, is robust to imperfect knowledge and supports user-specified size budgets. Our experiments on 8 data sets highlight how COCOCO compares favorably against competitors and natural baselines in terms of performance and set size.

Luca Stradiotti, Laurens Devos, Anna Monreale et al.

Multi-horizon time-series forecasting involves simultaneously making predictions for a consecutive sequence of subsequent time steps. This task arises in many application domains, such as healthcare and finance, where mispredictions can have a high cost and reduce trust. The learning with abstention framework tackles these problems by allowing a model to abstain from offering a prediction when it is at an elevated risk of making a misprediction. Unfortunately, existing abstention strategies are ill-suited for the multi-horizon setting: they target problems where a model offers a single prediction for each instance. Hence, they ignore the structured and correlated nature of the predictions offered by a multi-horizon forecaster. We formalize the problem of learning with abstention for multi-horizon forecasting setting and show that its structured nature admits a richer set of abstention problems. Concretely, we propose three natural notions of how a model could abstain for multi-horizon forecasting. We theoretically analyze each problem to derive the optimal abstention strategy and propose an algorithm that implements it. Extensive evaluation on 24 datasets shows that our proposed algorithms significantly outperforms existing baselines.

Nicola Debole, Andrea Passerini, Stefano Teso et al.

Concept-bottleneck models (CBMs) are neural classifiers that compute predictions from high-level concepts extracted from the input. CBMs ensure stakeholders can understand the concepts -- and the predictions they entail -- by learning these from concept-level annotations, which are however seldom available. Recent CBM architectures work around this issue by obtaining annotations from Vision-Language Models (VLMs). While greatly broadening applicability, doing so can yield lower quality concepts and therefore less interpretable models. We strike for a middle ground by introducing Vision-plus-Human-guided CBM (VH-CBM), a hybrid approach that exploits both VLMs and a small amount of dense annotations. VH-CBM employs a Gaussian Process in the VLM's embedding space, which captures useful global information about the target domain, to propagate the expert's supervision to any target data point. Our empirical evaluation shows how VH-CBM predicts more accurate concepts than VLM-guided CBMs even when annotating as little as 1% of the data, while sporting better concept calibration and supporting active learning.

Cesare Barbera, Lorenzo Perini, Giovanni De Toni et al.

Developing trustworthy Machine Learning (ML) models requires their predicted probabilities to be well-calibrated, meaning they should reflect true-class frequencies. Among calibration notions in multiclass classification, strong calibration is the most stringent, as it requires all predicted probabilities to be simultaneously calibrated across all classes. However, existing approaches to multiclass calibration lack a notion of distance among inputs, which makes them vulnerable to proximity bias: predictions in sparse regions of the feature space are systematically miscalibrated. This is especially relevant in high-stakes settings, such as healthcare, where the sparse instances are exactly those most at risk of biased treatment. In this work, we address this main shortcoming by introducing a local perspective on multiclass calibration. First, we formally define multiclass local calibration and establish its relationship with strong calibration. Second, we theoretically analyze the pitfalls of existing evaluation metrics when applied to multiclass local calibration. Third, we propose a practical method for enhancing local calibration in Neural Networks, which enforces alignment between predicted probabilities and local estimates of class frequencies using the Jensen-Shannon distance. Finally, we empirically validate our approach against existing multiclass calibration techniques.

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.

Andrea Pugnana, Riccardo Massidda, Francesco Giannini et al.

Concept Bottleneck Models (CBMs) are machine learning models that improve interpretability by grounding their predictions on human-understandable concepts, allowing for targeted interventions in their decision-making process. However, when intervened on, CBMs assume the availability of humans that can identify the need to intervene and always provide correct interventions. Both assumptions are unrealistic and impractical, considering labor costs and human error-proneness. In contrast, Learning to Defer (L2D) extends supervised learning by allowing machine learning models to identify cases where a human is more likely to be correct than the model, thus leading to deferring systems with improved performance. In this work, we gain inspiration from L2D and propose Deferring CBMs (DCBMs), a novel framework that allows CBMs to learn when an intervention is needed. To this end, we model DCBMs as a composition of deferring systems and derive a consistent L2D loss to train them. Moreover, by relying on a CBM architecture, DCBMs can explain why defer occurs on the final task. Our results show that DCBMs achieve high predictive performance and interpretability at the cost of deferring more to humans.

Daphne Lenders, Andrea Pugnana, Roberto Pellungrini et al.

Abstaining classifiers have the option to refrain from providing a prediction for instances that are difficult to classify. The abstention mechanism is designed to trade off the classifier's performance on the accepted data while ensuring a minimum number of predictions. In this setting, often fairness concerns arise when the abstention mechanism solely reduces errors for the majority groups of the data, resulting in increased performance differences across demographic groups. While there exist a bunch of methods that aim to reduce discrimination when abstaining, there is no mechanism that can do so in an explainable way. In this paper, we fill this gap by introducing Interpretable and Fair Abstaining Classifier IFAC, an algorithm that can reject predictions both based on their uncertainty and their unfairness. By rejecting possibly unfair predictions, our method reduces error and positive decision rate differences across demographic groups of the non-rejected data. Since the unfairness-based rejections are based on an interpretable-by-design method, i.e., rule-based fairness checks and situation testing, we create a transparent process that can empower human decision-makers to review the unfair predictions and make more just decisions for them. This explainable aspect is especially important in light of recent AI regulations, mandating that any high-risk decision task should be overseen by human experts to reduce discrimination risks.

Andrea Pugnana, Giovanni De Toni, Cesare Barbera et al.

Developing decision-support systems that complement human performance in classification tasks remains an open challenge. A popular approach, Learning to Defer (LtD), allows a Machine Learning (ML) model to pass difficult cases to a human expert. However, LtD treats humans and ML models as mutually exclusive decision-makers, restricting the expert contribution to mere predictions. To address this limitation, we propose Learning to Ask (LtA), a new framework that handles both when and how to incorporate expert input in an ML model. LtA is based on a two-part architecture: a standard ML model and an enriched model trained with additional expert human feedback, with a formally optimal strategy for selecting when to query the enriched model. We provide two practical implementations of LtA: a sequential approach, which trains the models in stages, and a joint approach, which optimises them simultaneously. For the latter, we design surrogate losses with realisable-consistency guarantees. Our experiments with synthetic and real expert data demonstrate that LtA provides a more flexible and powerful foundation for effective human-AI collaboration.

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.