Michael Puthawala

Beomsu Kim, Michael Puthawala, Jong Chul Ye et al.

In this work, we propose to study the global geometrical properties of generative models. We introduce a new Riemannian metric to assess the similarity between any two data points. Importantly, our metric is agnostic to the parametrization of the generative model and requires only the evaluation of its data likelihood. Moreover, the metric leads to the conceptual definition of generative distances and generative geodesics, whose computation can be done efficiently in the data space. Their approximations are proven to converge to their true values under mild conditions. We showcase three proof-of-concept applications of this global metric, including clustering, data visualization, and data interpolation, thus providing new tools to support the geometrical understanding of generative models.

Cole Patten, Christopher Saunders, Michael Puthawala

We used contrastive neural networks to learn useful similarity scores between the 144 cartridge casings in the NBIDE dataset, under the common-but-unknown source paradigm. The common-but-unknown source problem is a problem archetype in forensics where the question is whether two objects share a common source (e.g. were two cartridge casings fired from the same firearm). Similarity scores are often used to interpret evidence under this paradigm. We directly compared our results to a state-of-the-art algorithm, Congruent Matching Cells (CMC). When trained on the E3 dataset of 2967 cartridge casings, contrastive learning achieved an ROC AUC of 0.892. The CMC algorithm achieved 0.867. We also conducted an ablation study where we varied the neural network architecture; specifically, the network's width or depth. The ablation study showed that contrastive network performance results are somewhat robust to the network architecture. This work was in part motivated by the use of similarity scores attained via contrastive learning for standard evidence interpretation methods such as score-based likelihood ratios.