Anytime-valid, Bayes-assisted,Prediction-Powered Inference

Given a large pool of unlabelled data and a smaller amount of labels, prediction-powered inference (PPI) leverages machine learning predictions to increase the statistical efficiency of standard confidence interval procedures based solely on labelled data, while preserving their fixed-time validity. In this paper, we extend the PPI framework to the sequential setting, where labelled and unlabelled datasets grow over time. Exploiting Ville's inequality and the method of mixtures, we propose prediction-powered confidence sequence procedures that are valid uniformly over time and naturally accommodate prior knowledge on the quality of the predictions to further boost efficiency. We carefully illustrate the design choices behind our method and demonstrate its effectiveness in real and synthetic examples.

Rapidly Varying Completely Random Measures for Modeling Extremely Sparse Networks

Completely random measures (CRMs) are fundamental to Bayesian nonparametric models, with applications in clustering, feature allocation, and network analysis. A key quantity of interest is the Laplace exponent, whose asymptotic behavior determines how the random structures scale. When the Laplace exponent grows nearly linearly - known as rapid variation - the induced models exhibit approximately linear growth in the number of clusters, features, or edges with sample size or network nodes. This regime is especially relevant for modeling sparse networks, yet existing CRM constructions lack tractability under rapid variation. We address this by introducing a new class of CRMs with index of variation $\alpha\in(0,1]$, defined as mixtures of stable or generalized gamma processes. These models offer interpretable parameters, include well-known CRMs as limiting cases, and retain analytical tractability through a tractable Laplace exponent and simple size-biased representation. We analyze the asymptotic properties of this CRM class and apply it to the Caron-Fox framework for sparse graphs. The resulting models produce networks with near-linear edge growth, aligning with empirical evidence from large-scale networks. Additionally, we present efficient algorithms for simulation and posterior inference, demonstrating practical advantages through experiments on real-world sparse network datasets.