10: One Sample Goodness-of-Fit Tests for the Distribution-of-Distances

Music City Center 

In this work we propose a class of goodness-of-fit tests for testing if the marginal distribution of a vector of pairwise distances follows a specified distribution or family of distributions. These tests are used in forensic science for deciding if a certain known-source distribution is reasonable for deciding if an object arose from a specified source. Forensic science consists of many few-shot learning problems, where there are few objects per source, with a large number of sources. This class of tests is designed to deal with the small sample sizes per source (class), and the dependency arising from the pairwise comparisons.

Unlike in standard goodness-of-fit tests with a fixed distribution, there is one free parameter that accounts for the dependencies between the pairwise comparisons. We will focus on strategies for estimating this nuisance parameter and the effect that different estimation strategies (REML, super efficient MLE, where sample size n acts as n-choose-2) have on the resulting Type 1 and Type 2 errors, using Monte Carlo simulation. We will also look at the theoretical differences of the estimation strategies for this goodness-of-fit test.

Goodness-of-fit test

Maximum likelihood estimation

Distribution of distances

Manifold learning 

IMS