Semi-automated Parameterization of a Probabilistic Model Using Logistic Regression - A Tutorial

Many practical situations require some modeling of uncertainty, and often, this means speaking about events whose likelihood to occur is conveniently expressible by probability parameters, say, a scalar 0 ≤  p  ≤ 1 . The semantics of such values can be arbitrarily complex, ranging from simple probabilities, up to conditional likelihoods, or factors of mere subjective interpretation, such as hyper-parameters in Bayesian models. This chapter addresses the often untold story of how to find a value for a generic probability parameter p , or a whole set of such parameters. The simplicity of embodying opaque background dynamics in the mantle of uncertainty, brought into a model by a parameter p , is often bought at the challenge for the user of a model to find a good value for it. This tutorial is a step-by-step guidance through the idea of finding values for probability parameters “by examples.” Provided that a parameter p refers to the likelihood of an event to occur, or conditionally occur under certain settings of other parameters, we describe how to use logistic regression, as an instance of machine learning, to parameterize models using sets of examples. The method is explained in the R programming language and demonstrated along a running showcase application.