# Colloquium - Grudic

Regression and Classification Models with Probabilistic Confidence Estimates
Gregory Grudic
Department of Computer Science
2/26/2004
3:30pm-4:30pm

Most regression and classification models output only a predicted target value or class, and make no attempt to give a probabilistic confidence estimate for the output. However, in many applications, it is important to have such estimates. Consider a medical diagnosis problem where the goal is to predict whether a patient has a disease given a set of symptoms or tests. Here a YES or NO decision is not nearly as useful as a probabilistic estimate of how likely it is the patient has the disease -- if it is highly likely that the patient has cancer, perhaps she should be treated immediately, otherwise more tests might be in order. In fact, the general framework of reasoning under uncertainty using utility functions is based on having good estimates of such conditional classification probabilities. Similarly, in regression, it is much more useful to know the probability that future values fall within some interval, than to have a single predicted value.

We propose a probabilistic regression and classification framework for basis function models, which includes widely used kernel methods such as Support Vector Machines. In the case of regression, we present a theoretical framework for obtaining point specific estimates of the probability that the true output is within some user specified range. In the case of classification, our framework estimates the point specific probability that the predicted class is the true class. We make minimal distribution assumptions, and no specific distributions (e.g. no Gaussian or other distributions) are assumed. We show that, under appropriate assumptions, as the number of training examples increases, the probability estimates approach the true values. Experimental results show that our framework can give better probability estimates than those obtained with algorithms that make specific distribution assumptions, such as Gaussian Process Regression and Support Vector Machine classification with probabilistic outputs.

Finally, we outline two new important applications of probabilistic models. The first is based on recently gathered clinical data, where the goal is to use machine learning algorithms to identify the presence of serious heart disease in children. We show that probabilistic classification models can be used to give accurate estimates of the probability that a child has congenital heart disease, using only an electronic stethoscope sensor. In the second application we outline the use of probabilistic regression and classification models for end-to-end learning of complex robotic tasks.

Department of Computer Science