Christophe A. N. Biscio

Martin V. Vejling, Christophe A. N. Biscio, Adrien Mazoyer et al.

Uncertainty quantification is essential in high-stakes machine learning tasks. However, one of the principled solutions, conformal prediction, faces challenges under limited local calibration data, privacy constraints, and data heterogeneity. In multi-agent settings, existing works do not simultaneously and satisfactorily address these challenges with guarantees either limited to averages across agents or losing validity in heterogeneous settings. Hence, we propose personalized federated weighted conformal prediction (PFWCP), a framework that combines local density ratio weighting with weighted quantile aggregation to correct for heterogeneity while preserving privacy. The method yields asymptotically valid marginal and calibration-conditional coverage guarantees for each participating agent and supports protocols with one-shot communication. Theoretical analysis presents an adjustment to the coverage variance, governed by an effective sample size expression, which is necessary in the context of weighted conformal prediction, and experiments on synthetic and real datasets show improved calibration quality over state-of-the-art federated conformal baselines.

Martin V. Vejling, Shashi Raj Pandey, Christophe A. N. Biscio et al.

The amount of quality data in many machine learning tasks is limited to what is available locally to data owners. The set of quality data can be expanded through trading or sharing with external data agents. However, data buyers need quality guarantees before purchasing, as external data may be contaminated or irrelevant to their specific learning task. Previous works primarily rely on distributional assumptions about data from different agents, relegating quality checks to post-hoc steps involving costly data valuation procedures. We propose a distribution-free, contamination-aware data-sharing framework that identifies external data agents whose data is most valuable for model personalization. To achieve this, we introduce novel two-sample testing procedures, grounded in rigorous theoretical foundations for conformal outlier detection, to determine whether an agent's data exceeds a contamination threshold. The proposed tests, termed conformal data contamination tests, remain valid under arbitrary contamination levels while enabling false discovery rate control via the Benjamini-Hochberg procedure. Empirical evaluations across diverse collaborative learning scenarios demonstrate the robustness and effectiveness of our approach. Overall, the conformal data contamination test distinguishes itself as a generic procedure for aggregating data with statistically rigorous quality guarantees.

Ottmar Cronie, Mehdi Moradi, Christophe A. N. Biscio

This paper presents the first general (supervised) statistical learning framework for point processes in general spaces. Our approach is based on the combination of two new concepts, which we define in the paper: i) bivariate innovations, which are measures of discrepancy/prediction-accuracy between two point processes, and ii) point process cross-validation (CV), which we here define through point process thinning. The general idea is to carry out the fitting by predicting CV-generated validation sets using the corresponding training sets; the prediction error, which we minimise, is measured by means of bivariate innovations. Having established various theoretical properties of our bivariate innovations, we study in detail the case where the CV procedure is obtained through independent thinning and we apply our statistical learning methodology to three typical spatial statistical settings, namely parametric intensity estimation, non-parametric intensity estimation and Papangelou conditional intensity fitting. Aside from deriving theoretical properties related to these cases, in each of them we numerically show that our statistical learning approach outperforms the state of the art in terms of mean (integrated) squared error.