Proper likelihood ratio based ROC curves for general binary classification problems

09/03/2018
by   M. Gasparini, et al.
0

Everybody writes that ROC curves, a very common tool in binary classification problems, should be optimal, and in particular concave, non-decreasing and above the 45-degree line. Everybody uses ROC curves, theoretical and especially empirical, which are not so. This work is an attempt to correct this schizophrenic behavior. Optimality stems from the Neyman-Pearson lemma, which prescribes using likelihood-ratio based ROC curves. Starting from there, we give the most general definition of a likelihood-ratio based classification procedure, which encompasses finite, continuous and even more complex data types. We point out a strict relationship with a general notion of concentration of two probability measures. We give some nontrivial examples of situations with non-monotone and non-continuous likelihood ratios. Finally, we propose the ROC curve of a likelihood ratio based Gaussian kernel flexible Bayes classifier as a proper default alternative to the usual empirical ROC curve.

READ FULL TEXT
research
01/24/2018

Threadable Curves

We define a plane curve to be threadable if it can rigidly pass through ...
research
04/30/2013

G2 Transition curve using Quartic Bezier Curve

A method to construct transition curves using a family of the quartic Be...
research
04/06/2023

U-Statistics Based Jackknife Empirical Likelihood Tests for the Generalized Lorenz Curves

A Lorenz curve is a graphical representation of the distribution of inco...
research
11/29/2019

ROC movies – a new generalization to a popular classic

Throughout science and technology, receiver operating characteristic (RO...
research
05/05/2019

Decision Making with Machine Learning and ROC Curves

The Receiver Operating Characteristic (ROC) curve is a representation of...
research
03/19/2021

The Shape of Learning Curves: a Review

Learning curves provide insight into the dependence of a learner's gener...
research
05/24/2019

Optimizing Shallow Networks for Binary Classification

Data driven classification that relies on neural networks is based on op...

Please sign up or login with your details

Forgot password? Click here to reset