3 papers
stat.ML2025
Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data
Anastasis Kratsios, Tin Sum Cheng, Daniel Roy
At its core, machine learning seeks to train models that reliably generalize beyond noisy observations; however, the theoretical vacuum in which state-of-the-art universal approxim…
math.PR2023
de Finetti's theorem and the existence of regular conditional distributions and strong laws on exchangeable algebras
Peter Potaptchik, Daniel M. Roy, David Schrittesser
We show the following generalizations of the de Finetti--Hewitt--Savage theorem: Given an exchangeable sequence of random elements, the sequence is conditionally i.i.d. if and only…
math.PR2016
A characterization of product-form exchangeable feature probability functions
Marco Battiston, Stefano Favaro, Daniel M. Roy +1
We characterize the class of exchangeable feature allocations assigning probability to a feature allocation of individuals, display…