4 papers
Random Graphs by Product Random Measures
Caleb Bastian, Herschel Rabitz
A natural representation of random graphs is the random measure. The collection of product random measures, their transformations, and non-negative test functions forms a general r…
Uncertainty Quantification by Random Measures and Fields
Caleb Deen Bastian, Herschel Rabitz
We present a general framework for uncertainty quantification that is a mosaic of interconnected models. We define global first and second order structural and correlative sensitiv…
High Dimensional Model Representation as a Glass Box in Supervised Machine Learning
Caleb Deen Bastian, Herschel Rabitz
Prediction and explanation are key objects in supervised machine learning, where predictive models are known as black boxes and explanatory models are known as glass boxes. Explana…
Throwing Stones and Collecting Bones: Looking for Poisson-like Random Measures
Caleb Deen Bastian, Grzegorz A. Rempala
We show that in a broad class of random counting measures one may identify only three that are rescaled versions of themselves when restricted to a subspace. These are Poisson, bin…