Luben M. C. Cabezas

Conformal prediction methods create prediction bands with distribution-free guarantees but do not explicitly capture epistemic uncertainty, which can lead to overconfident predictions in data-sparse regions. Although recent conformal scores have been developed to address this limitation, they are typically designed for specific tasks, such as regression or quantile regression. Moreover, they rely on particular modeling choices for epistemic uncertainty, restricting their applicability. We introduce EPICSCORE, a model-agnostic approach that enhances any conformal score by explicitly integrating epistemic uncertainty. Leveraging Bayesian techniques such as Gaussian Processes, Monte Carlo Dropout, or Bayesian Additive Regression Trees, EPICSCORE adaptively expands predictive intervals in regions with limited data while maintaining compact intervals where data is abundant. As with any conformal method, it preserves finite-sample marginal coverage. Additionally, it also achieves asymptotic conditional coverage. Experiments demonstrate its good performance compared to existing methods. Designed for compatibility with any Bayesian model, but equipped with distribution-free guarantees, EPICSCORE provides a general-purpose framework for uncertainty quantification in prediction problems.

We propose methods for the analysis of hierarchical clustering that fully use the multi-resolution structure provided by a dendrogram. Specifically, we propose a loss for choosing between clustering methods, a feature importance score and a graphical tool for visualizing the segmentation of features in a dendrogram. Current approaches to these tasks lead to loss of information since they require the user to generate a single partition of the instances by cutting the dendrogram at a specified level. Our proposed methods, instead, use the full structure of the dendrogram. The key insight behind the proposed methods is to view a dendrogram as a phylogeny. This analogy permits the assignment of a feature value to each internal node of a tree through an evolutionary model. Real and simulated datasets provide evidence that our proposed framework has desirable outcomes and gives more insights than state-of-art approaches. We provide an R package that implements our methods.

In predictive modeling, quantifying prediction uncertainty is crucial for reliable decision-making. Traditional conformal inference methods provide marginally valid predictive regions but often produce non-adaptive intervals when naively applied to regression, potentially biasing applications. Recent advances using quantile regressors or conditional density estimators improve adaptability but are typically tied to specific prediction models, limiting their ability to quantify uncertainty around arbitrary models. Similarly, methods based on partitioning the feature space adopt sub-optimal strategies, failing to consistently measure predictive uncertainty across the feature space, especially in adversarial examples. This paper introduces a model-agnostic family of methods to calibrate prediction intervals for regression with local coverage guarantees. By leveraging regression trees and Random Forests, our approach constructs data-adaptive partitions of the feature space to approximate conditional coverage, enhancing the accuracy and scalability of prediction intervals. Our methods outperform established benchmarks on simulated and real-world datasets. They are implemented in the Python package clover, which integrates seamlessly with the scikit-learn interface for practical application.