Predicting Regression Probability Distributions with Imperfect Data Through Optimal Transformations
Abstract
The goal of regression analysis is to predict the value of a numeric outcome variable y given a vector of joint values of other (predictor) variables x. Usually a particular x-vector does not specify a repeatable value for y, but rather a probability distribution of possible y--values, p(y|x). This distribution has a location, scale and shape, all of which can depend on x, and are needed to infer likely values for y given x. Regression methods usually assume that training data y-values are perfect numeric realizations from some well behaived p(y|x). Often actual training data y-values are discrete, truncated and/or arbitrary censored. Regression procedures based on an optimal transformation strategy are presented for estimating location, scale and shape of p(y|x) as general functions of x, in the possible presence of such imperfect training data. In addition, validation diagnostics are presented to ascertain the quality of the solutions.
Keywords
Cite
@article{arxiv.2001.10102,
title = {Predicting Regression Probability Distributions with Imperfect Data Through Optimal Transformations},
author = {Jerome H. Friedman},
journal= {arXiv preprint arXiv:2001.10102},
year = {2020}
}
Comments
33 pages, 19 figures