We examined geographic variation within the Ashy Darter, Etheostoma cinereum, of the mitochondrially enconded cytochrome b gene (cyt b) and nuclear recombination activation gene 1 (RAG1) as well as pigmentation, 6 meristic variables, and 20 morphometric variables for patterns indicative of speciation within the complex. Four geographically disjunct entities were identified by at least one of th...

Abstract: This paper proposes a radar target detection algorithm based on information geometry. In particular, the correlation of sample data is modeled as a Hermitian positive-definite (HPD) matrix. Moreover, a class of total Jensen–Bregman divergences, including the total Jensen square loss, the total Jensen log-determinant divergence, and the total Jensen von Neumann divergence, are proposed...

In this section we show how the refined upper bound on the regret of the EXP algorithm proved using the potential function approach (KL divergence) also gives us a better bound for the expert game setup with bandit feedback. Last lecture we showed how in the case of expert prediction with bandit feedback using the Exp3 algorithm, the regret is upper bounded by T 2/3n1/3 using a rough upper boun...

We address the problem of learning a symmetric positive definite matrix. The central issue is to design parameter updates that preserve positive definiteness. Our updates are motivated with the von Neumann divergence. Rather than treating the most general case, we focus on two key applications that exemplify our methods: On-line learning with a simple square loss and finding a symmetric positiv...

We introduce a class of discrete divergences on sets (equivalently binary vectors) that we call the submodular-Bregman divergences. We consider two kinds, defined either from tight modular upper or tight modular lower bounds of a submodular function. We show that the properties of these divergences are analogous to the (standard continuous) Bregman divergence. We demonstrate how they generalize...

Background: Speciation can involve variation in the dimensionality of population divergence (defined as variation in the number of independent ecological variables, phenotypic traits, or genes differing between populations). Recent work indicates that reproductive isolation between populations is multidimensional, but that this multidimensionality has an upper limit. A remaining question is how...

The deep sea is the largest ecosystem on Earth. Recent exploration has revealed that it supports a highly diverse and endemic benthic invertebrate fauna, yet the evolutionary processes that generate this remarkable species richness are virtually unknown. Environmental heterogeneity, topographic complexity, and morphological divergence all tend to decrease with depth, suggesting that the potenti...

Fairness-aware learning is a novel framework for classification tasks. Like regular empirical risk minimization (ERM), it aims to learn a classifier with a low error rate, and at the same time, for the predictions of the classifier to be independent of sensitive features, such as gender, religion, race, and ethnicity. Existing methods can achieve low dependencies on given samples, but this is n...