In this paper, we consider an infinite dimensional exponential family P of probability densities, which are parametrized by functions in a reproducing kernel Hilbert space H, and show it to be quite rich in the sense that a broad class of densities on R can be approximated arbitrarily well in Kullback-Leibler (KL) divergence by elements in P. Motivated by this approximation property, the paper ...

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...

The use of molecular sequence data has increased interest in trying to date evolutionary events, with researchers wanting both an estimate of the divergence time and a confidence interval for that estimate. However, two methodological issues have recently been raised with respect to precision of the estimates: (i) the time of the ancestral event is over-estimated; and (ii) the confidence interv...

This short paper presents a recently reported dynamic data-driven method, Symbolic Dynamic Filtering (SDF), for real-time estimation of the state-of-health (SOH) and state-of-charge (SOC) in lead-acid batteries, as an alternative to model-based analysis techniques. In particular, SOC estimation relies on a k-NN regression algorithm while SOH estimation is obtained from the divergence between ex...

Approximating a divergence between two probability distributions from their samples is a fundamental challenge in statistics, information theory, and machine learning. A divergence approximator can be used for various purposes such as two-sample homogeneity testing, change-point detection, and class-balance estimation. Furthermore, an approximator of a divergence between the joint distribution ...

Inferring the history of isolation and gene flow during species divergence is a central question in evolutionary biology. The European river lamprey (Lampetra fluviatilis) and brook lamprey (L. planeri) show a low reproductive isolation but have highly distinct life histories, the former being parasitic-anadromous and the latter non-parasitic and freshwater resident. Here we used microsatellite...

The mixing distribution is also sometimes called the mixing weights. There are a number of statistical estimation / unsupervised learning tasks associated with mixture models. Three such tasks are as follows (assuming an iid sample from some m? ∈M is given): 1. Density estimation: Here we assume that each distribution in M has a density. The task is to pick m̂ ∈ M such that m̂ is close to m? unde...

Central among the questions explored in biology are those that seek to understand the timing and rates of evolutionary processes. Accurate estimates of species divergence times are vital to understanding historical biogeography, estimating diversification rates, and identifying the causes of variation in rates of molecular evolution. This tutorial will provide a general overview of divergence t...

Species divergence is typically thought to occur in the absence of gene flow, but many empirical studies are discovering that gene flow may be more pervasive during species formation. Although many examples of divergence with gene flow have been identified, few clades have been investigated in a comparative manner, and fewer have been studied using genome-wide sequence data. We contrast species...

— Divergence-time estimation based on molecular phylogenies and the fossil record has provided insights into fundamental questions of evolutionary biology. In 1 . CC-BY 4.0 International license peer-reviewed) is the author/funder. It is made available under a The copyright holder for this preprint (which was not . http://dx.doi.org/10.1101/038455 doi: bioRxiv preprint first posted online Feb. ...