Characterising intractable high-dimensional random variables is one of the fundamental challenges in stochastic computation. The recent surge transport maps offers a mathematical foundation and new insights for tackling this challenge by coupling with tractable reference variables. This paper generalises functional tensor-train approximation inverse Rosenblatt recently developed Dolgov et al. (...

Linear threshold units (LTUs) were originally proposed as models of biological neurons. They were widely studied in the context of the perceptron (Rosenblatt, 1962). Due to the difficulties of finding a general algorithm for networks with hidden nodes, they never passed into general use. In this work we derive an algorithm in the context of probabilistic models and show how it may be applied in...

A goodness of fit test for copulas based on Rosenblatt’s transformation is investigated. This test performs well if the marginal distribution functions are known and are used in the test statistic. If the marginal distribution functions are unknown and are replaced by their empirical estimates, then the test’s properties change significantly. This is shown in detail by simulation for special ca...

1. Abstract For the performance measure approach (PMA) of RBDO, a transformation between the input random variables and the standard normal random variables is required to carry out the inverse reliability analysis. Since the transformation uses the joint cumulative density function (CDF) of input variables, the joint CDF should be known before carrying out RBDO. In many industrial RBDO problem...

electrical detection Sebastian Sorgenfrei, Inanc Meric, Sarbajit Banerjee, Austin Akey, Sami Rosenblatt, Irving P. Herman, and Kenneth L. Shepard Department of Electrical Engineering, Columbia University, New York, New York 10027, USA Department of Chemistry, University of Buffalo, Buffalo, New York 14260-3000, USA Department of Applied Physics and Applied Mathematics, Columbia University, New ...

This paper explores the relationship between the day of the week on which a survey respondent is interviewed and their self-reported job satisfaction and mental health scores using from the first ten years of the British Household Panel Survey. Evidence presented here confirms that self-reported levels of job satisfaction and subjective levels of mental distress systematically vary according to...