arXiv subjects

Marouane Il Idrissi

Publications and source records attributed to Marouane Il Idrissi.

8 recordsLinked to original sources

arXiv2025

Beyond Shapley Values: Cooperative Games for the Interpretation of Machine Learning Models

Cooperative game theory has become a cornerstone of post-hoc interpretability in machine learning, largely through the use of Shapley values. Yet, despite their widespread adoption, Shapley-based methods often rest on axiomatic justifications whose relevance to feature attribution remains debatable. In this paper, we revisit cooperative game theory from an interpretability perspective and argue for a broader and more principled use of its tools. We highlight two general families of efficient allocations, the Weber and Harsanyi sets, that extend beyond Shapley values and offer richer interpretative flexibility. We present an accessible overview of these allocation schemes, clarify the distinction between value functions and aggregation rules, and introduce a three-step blueprint for constructing reliable and theoretically-grounded feature attributions. Our goal is to move beyond fixed axioms and provide the XAI community with a coherent framework to design attribution methods that are both meaningful and robust to shifting methodological trends.

stat.ML↗

arXiv2025

Unveil Sources of Uncertainty: Feature Contribution to Conformal Prediction Intervals

Cooperative game theory methods, notably Shapley values, have significantly enhanced machine learning (ML) interpretability. However, existing explainable AI (XAI) frameworks mainly attribute average model predictions, overlooking predictive uncertainty. This work addresses that gap by proposing a novel, model-agnostic uncertainty attribution (UA) method grounded in conformal prediction (CP). By defining cooperative games where CP interval properties-such as width and bounds-serve as value functions, we systematically attribute predictive uncertainty to input features. Extending beyond the traditional Shapley values, we use the richer class of Harsanyi allocations, and in particular the proportional Shapley values, which distribute attribution proportionally to feature importance. We propose a Monte Carlo approximation method with robust statistical guarantees to address computational feasibility, significantly improving runtime efficiency. Our comprehensive experiments on synthetic benchmarks and real-world datasets demonstrate the practical utility and interpretative depth of our approach. By combining cooperative game theory and conformal prediction, we offer a rigorous, flexible toolkit for understanding and communicating predictive uncertainty in high-stakes ML applications.

cs.AI↗

arXiv2024

Hoeffding decomposition of black-box models with dependent inputs

Performing an additive decomposition of arbitrary functions of random elements is paramount for global sensitivity analysis and, therefore, the interpretation of black-box models. The well-known seminal work of Hoeffding characterized the summands in such a decomposition in the particular case of mutually independent inputs. Going beyond the framework of independent inputs has been an ongoing challenge in the literature. Existing solutions have so far required constraining assumptions or suffer from a lack of interpretability. In this paper, we generalize Hoeffding's decomposition for dependent inputs under very mild conditions. For that purpose, we propose a novel framework to handle dependencies based on probability theory, functional analysis, and combinatorics. It allows for characterizing two reasonable assumptions on the dependence structure of the inputs: non-perfect functional dependence and non-degenerate stochastic dependence. We then show that any square-integrable, real-valued function of random elements respecting these two assumptions can be uniquely additively decomposed and offer a characterization of the summands using oblique projections. We then introduce and discuss the theoretical properties and practical benefits of the sensitivity indices that ensue from this decomposition. Finally, the decomposition is analytically illustrated on bivariate functions of Bernoulli inputs.

math.FA↗

arXiv2023

Shapley effects and proportional marginal effects for global sensitivity analysis: application to computed tomography scan organ dose estimation

Concerns have been raised about possible cancer risks after exposure to computed tomography (CT) scans in childhood. The health effects of ionizing radiation are then estimated from the absorbed dose to the organs of interest which is calculated, for each CT scan, from dosimetric numerical models, like the one proposed in the NCICT software. Given that a dosimetric model depends on input parameters which are most often uncertain, the calculation of absorbed doses is inherently uncertain. A current methodological challenge in radiation epidemiology is thus to be able to account for dose uncertainty in risk estimation. A preliminary important step can be to identify the most influential input parameters implied in dose estimation, before modelling and accounting for their related uncertainty in radiation-induced health risks estimates. In this work, a variance-based global sensitivity analysis was performed to rank by influence the uncertain input parameters of the NCICT software implied in brain and red bone marrow doses estimation, for four classes of CT examinations. Two recent sensitivity indices, especially adapted to the case of dependent input parameters, were estimated, namely: the Shapley effects and the Proportional Marginal Effects (PME). This provides a first comparison of the respective behavior and usefulness of these two indices on a real medical application case. The conclusion is that Shapley effects and PME are intrinsically different, but complementary. Interestingly, we also observed that the proportional redistribution property of the PME allowed for a clearer importance hierarchy between the input parameters.

stat.AP↗

arXiv2023

On the coalitional decomposition of parameters of interest

Understanding the behavior of a black-box model with probabilistic inputs can be based on the decomposition of a parameter of interest (e.g., its variance) into contributions attributed to each coalition of inputs (i.e., subsets of inputs). In this paper, we produce conditions for obtaining unambiguous and interpretable decompositions of very general parameters of interest. This allows to recover known decompositions, holding under weaker assumptions than stated in the literature.

math.ST↗

arXiv2022

Proportional marginal effects for global sensitivity analysis

Performing (variance-based) global sensitivity analysis (GSA) with dependent inputs has recently benefited from cooperative game theory concepts.By using this theory, despite the potential correlation between the inputs, meaningful sensitivity indices can be defined via allocation shares of the model output's variance to each input. The ``Shapley effects'', i.e., the Shapley values transposed to variance-based GSA problems, allowed for this suitable solution. However, these indices exhibit a particular behavior that can be undesirable: an exogenous input (i.e., which is not explicitly included in the structural equations of the model) can be associated with a strictly positive index when it is correlated to endogenous inputs. In the present work, the use of a different allocation, called the ``proportional values'' is investigated. A first contribution is to propose an extension of this allocation, suitable for variance-based GSA. Novel GSA indices are then proposed, called the ``proportional marginal effects'' (PME). The notion of exogeneity is formally defined in the context of variance-based GSA, and it is shown that the PME allow the distinction of exogenous variables, even when they are correlated to endogenous inputs. Moreover, their behavior is compared to the Shapley effects on analytical toy-cases and more realistic use-cases.

math.ST↗

arXiv2022

Quantile-constrained Wasserstein projections for robust interpretability of numerical and machine learning models

Robustness studies of black-box models is recognized as a necessary task for numerical models based on structural equations and predictive models learned from data. These studies must assess the model's robustness to possible misspecification of regarding its inputs (e.g., covariate shift). The study of black-box models, through the prism of uncertainty quantification (UQ), is often based on sensitivity analysis involving a probabilistic structure imposed on the inputs, while ML models are solely constructed from observed data. Our work aim at unifying the UQ and ML interpretability approaches, by providing relevant and easy-to-use tools for both paradigms. To provide a generic and understandable framework for robustness studies, we define perturbations of input information relying on quantile constraints and projections with respect to the Wasserstein distance between probability measures, while preserving their dependence structure. We show that this perturbation problem can be analytically solved. Ensuring regularity constraints by means of isotonic polynomial approximations leads to smoother perturbations, which can be more suitable in practice. Numerical experiments on real case studies, from the UQ and ML fields, highlight the computational feasibility of such studies and provide local and global insights on the robustness of black-box models to input perturbations.

math.OC↗

arXiv2021

Developments and applications of Shapley effects to reliability-oriented sensitivity analysis with correlated inputs

Reliability-oriented sensitivity analysis methods have been developed for understanding the influence of model inputs relative to events which characterize the failure of a system (e.g., a threshold exceedance of the model output). In this field, the target sensitivity analysis focuses primarily on capturing the influence of the inputs on the occurrence of such a critical event. This paper proposes new target sensitivity indices, based on the Shapley values and called "target Shapley effects", allowing for interpretable sensitivity measures under dependent inputs. Two algorithms (one based on Monte Carlo sampling, and a given-data algorithm based on a nearest-neighbors procedure) are proposed for the estimation of these target Shapley effects based on the $\ell^2$ norm. Additionally, the behavior of these target Shapley effects are theoretically and empirically studied through various toy-cases. Finally, the application of these new indices in two real-world use-cases (a river flood model and a COVID-19 epidemiological model) is discussed.

math.ST↗