On one hand, the knowledge learned from public data is implicitly transferred into the private model.

An increasingly common setting in machine learning involves multiple parties, each with their own data, who want to jointly make predictions on future test points. Agents wish to benefit from the collective expertise of the full set of agents to make better predictions than they would individually, but may not be willing to release labeled data or model parameters.

The $ρ$-posterior framework provides universal Bayesian estimation with explicit contamination rates and optimal convergence guarantees, but has remained computationally difficult due to an optimization over reference distributions that precludes intractable posterior computation. We develop a PAC-Bayesian framework that recovers these theoretical guarantees through temperature-dependent Gibbs posteriors, deriving finite-sample oracle inequalities with explicit rates and introducing tractable variational approximations that inherit the robustness properties of exact $ρ$-posteriors. Numerical experiments demonstrate that this approach achieves theoretical contamination rates while remaining computationally feasible, providing the first practical implementation of $ρ$-posterior inference with rigorous finite-sample guarantees.

Decision trees are powerful machine learning algorithms, widely used in fields such as economics and medicine for their simplicity and interpretability. However, decision trees such as CART are prone to overfitting, especially when grown deep or the sample size is small. Conventional methods to reduce overfitting include pre-pruning and post-pruning, which constrain the growth of uninformative branches. In this paper, we propose a complementary approach by introducing a covariance-driven splitting criterion for regression trees (CovRT). This method is more robust to overfitting than the empirical risk minimization criterion used in CART, as it produces more balanced and stable splits and more effectively identifies covariates with true signals. We establish an oracle inequality of CovRT and prove that its predictive accuracy is comparable to that of CART in high-dimensional settings. We find that CovRT achieves superior prediction accuracy compared to CART in both simulations and real-world tasks.

The rise of powerful generative models has sparked concerns over data authenticity. While detection methods have been extensively developed for images and text, the case of tabular data, despite its ubiquity, has been largely overlooked. Yet, detecting synthetic tabular data is especially challenging due to its heterogeneous structure and unseen formats at test time. We address the underexplored task of detecting synthetic tabular data ''in the wild'', i.e. when the detector is deployed on tables with variable and previously unseen schemas. We introduce a novel datum-wise transformer architecture that significantly outperforms the only previously published baseline, improving both AUC and accuracy by 7 points. By incorporating a table-adaptation component, our model gains an additional 7 accuracy points, demonstrating enhanced robustness. This work provides the first strong evidence that detecting synthetic tabular data in real-world conditions is feasible, and demonstrates substantial improvements over previous approaches. Following acceptance of the paper, we are finalizing the administrative and licensing procedures necessary for releasing the source code. This extended version will be updated as soon as the release is complete.

Quantifying uncertainty in deep regression models is important both for understanding the confidence of the model and for safe decision-making in high-risk domains. Existing approaches that yield prediction intervals overlook distributional information, neglecting the effect of multimodal or asymmetric distributions on decision-making. Similarly, full or approximated Bayesian methods, while yielding the predictive posterior density, demand major modifications to the model architecture and retraining. We introduce MCNF, a novel post hoc uncertainty quantification method that produces both prediction intervals and the full conditioned predictive distribution. MCNF operates on top of the underlying trained predictive model; thus, no predictive model retraining is needed. We provide experimental evidence that the MCNF-based uncertainty estimate is well calibrated, is competitive with state-of-the-art uncertainty quantification methods, and provides richer information for downstream decision-making tasks.

Finally, we illustrate how our framework can be used for exploratory data analysis.

We introduce chefs' random tables (CRTs), a new class of non-trigonometric random features (RFs) to approximate Gaussian and softmax-kernels.

An increasingly common setting in machine learning involves multiple parties, each with their own data, who want to jointly make predictions on future test points. Agents wish to benefit from the collective expertise of the full set of agents to make better predictions than they would individually, but may not be willing to release labeled data or model parameters.