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We present a method of dimensional reduction for the general Markov model of sequence evolution on a phylogenetic tree. We show that taking certain linear combinations of the associated random variables (site pattern counts) reduces the…
We provide a static data structure for distance estimation which supports {\it adaptive} queries. Concretely, given a dataset $X = \{x_i\}_{i = 1}^n$ of $n$ points in $\mathbb{R}^d$ and $0 < p \leq 2$, we construct a randomized data…
Inferences about the evolution of continuous traits based on reconstruction of ancestral states has often been considered more error-prone than analysis of independent contrasts. Here we show that both methods in fact yield identical…
There are few, if any, algorithms in statistical phylogenetics which are used more heavily than Felsenstein's 1973 pruning method for computing the likelihood of a tree. We present LvD, (Likelihood via Decomposition), an alternative to…
The quartet distance is a measure of similarity used to compare two unrooted phylogenetic trees on the same set of $n$ leaves, defined as the number of subsets of four leaves related by a different topology in both trees. After a series of…
The reconstruction of the history of evolutionary genome-wide events among a set of related organisms is of great biological interest. A simplified model that captures only content modifying operations was introduced recently. It allows the…
In an extant population, how much information do extant individuals provide on the pedigree of their ancestors? Recent work by Kim, Mossel, Ramnarayan and Turner (2020) studied this question under a number of simplifying assumptions,…
Statistically consistent estimation of phylogenetic trees or gene trees is possible if pairwise sequence dissimilarities can be converted to a set of distances that are proportional to the true evolutionary distances. Susko et al. (2004)…
Phylogenetic inference can potentially result in a more accurate tree using data from multiple loci. However, if the loci are incongruent--due to events such as incomplete lineage sorting or horizontal gene transfer--it can be misleading to…
The ancestral sequence reconstruction problem is the inference, back in time, of the properties of common sequence ancestors from measured properties of contemporary populations. Standard algorithms for this problem assume independent…
Crystal structure prediction (CSP) for inorganic materials is one of the central and most challenging problems in materials science and computational chemistry. This problem can be formulated as a global optimization problem in which global…
Stochastic gradient descent method and its variants constitute the core optimization algorithms that achieve good convergence rates for solving machine learning problems. These rates are obtained especially when these algorithms are…
One reason why classical phylogenetic reconstruction methods fail to correctly infer the underlying topology is because they assume oversimplified models. In this paper we propose a topology reconstruction method consistent with the most…
The availability of data sets with large numbers of variables is rapidly increasing. The effective application of Bayesian variable selection methods for regression with these data sets has proved difficult since available Markov chain…
Two mechanisms have recently been proposed that can significantly speed up finding distant improving solutions via mutation, namely using a random mutation rate drawn from a heavy-tailed distribution ("fast mutation", Doerr et al. (2017))…
The algebraic properties of flattenings and subflattenings provide direct methods for identifying edges in the true phylogeny -- and by extension the complete tree -- using pattern counts from a sequence alignment. The relatively small…
Phylogenetics uses alignments of molecular sequence data to learn about evolutionary trees relating species. Along branches, sequence evolution is modelled using a continuous-time Markov process characterised by an instantaneous rate…
Shuffling strategies for stochastic gradient descent (SGD), including incremental gradient, shuffle-once, and random reshuffling, are supported by rigorous convergence analyses for arbitrary within-epoch permutations. In particular, random…
A classical result, fundamental to evolutionary biology, states that an edge-weighted tree $T$ with leaf set $X$, positive edge weights, and no vertices of degree 2 can be uniquely reconstructed from the set of leaf-to-leaf distances…
We provide simple and fast polynomial time approximation schemes (PTASs) for several variants of the max-sum diversification problem which, in its most basic form, is as follows: Given n points p_1,...,p_n in R^d and an integer k, select k…