Matthew W. Hahn

Benjamin K. Rosenzweig, Matthew W. Hahn

Inferring the phylogenetic relationships among a sample of organisms is a fundamental problem in modern biology. While distance-based hierarchical clustering algorithms achieved early success on this task, these have been supplanted by Bayesian and maximum likelihood search procedures based on complex models of molecular evolution. In this work we describe minimal neural network architectures that can approximate classic phylogenetic distance functions and the properties required to learn distances under a variety of molecular evolutionary models. In contrast to model-based inference (and recently proposed model-free convolutional and transformer networks), these architectures have a small computational footprint and are scalable to large numbers of taxa and molecular characters. The learned distance functions generalize well and, given an appropriate training dataset, achieve results comparable to state-of-the art inference methods.

Ruiyu Yang, Yuxiang Jiang, Scott Mathews et al.

We propose a new class of metrics on sets, vectors, and functions that can be used in various stages of data mining, including exploratory data analysis, learning, and result interpretation. These new distance functions unify and generalize some of the popular metrics, such as the Jaccard and bag distances on sets, Manhattan distance on vector spaces, and Marczewski-Steinhaus distance on integrable functions. We prove that the new metrics are complete and show useful relationships with $f$-divergences for probability distributions. To further extend our approach to structured objects such as concept hierarchies and ontologies, we introduce information-theoretic metrics on directed acyclic graphs drawn according to a fixed probability distribution. We conduct empirical investigation to demonstrate intuitive interpretation of the new metrics and their effectiveness on real-valued, high-dimensional, and structured data. Extensive comparative evaluation demonstrates that the new metrics outperformed multiple similarity and dissimilarity functions traditionally used in data mining, including the Minkowski family, the fractional $L^p$ family, two $f$-divergences, cosine distance, and two correlation coefficients. Finally, we argue that the new class of metrics is particularly appropriate for rapid processing of high-dimensional and structured data in distance-based learning.