Related papers: Shrinkage Effect in Ancestral Maximum Likelihood
The marginal likelihood of a model is a key quantity for assessing the evidence provided by the data in support of a model. The marginal likelihood is the normalizing constant for the posterior density, obtained by integrating the product…
Affinity Maturation (AM) is the process through which the immune system is able to develop potent antibodies against new pathogens it encounters, and is at the base of the efficacy of vaccines. At its core AM is analogous to a Darwinian…
Maximum likelihood estimators are used extensively to estimate unknown parameters of stochastic trait evolution models on phylogenetic trees. Although the MLE has been proven to converge to the true value in the independent-sample case, we…
Anomaly estimation, or the problem of finding a subset of a dataset that differs from the rest of the dataset, is a classic problem in machine learning and data mining. In both theoretical work and in applications, the anomaly is assumed to…
The main goal of machine learning (ML) is to study and improve mathematical models which can be trained with data provided by the environment to infer the future and to make decisions without necessarily having complete knowledge of all…
Ensemble randomized maximum likelihood (EnRML) is an iterative (stochastic) ensemble smoother, used for large and nonlinear inverse problems, such as history matching and data assimilation. Its current formulation is overly complicated and…
A striking result of [Acharya et al. 2017] showed that to estimate symmetric properties of discrete distributions, plugging in the distribution that maximizes the likelihood of observed multiset of frequencies, also known as the profile…
The Multiple Sequence Alignment (MSA) is a computational abstraction that represents a partial summary either of indel history, or of structural similarity. Taking the former view (indel history), it is possible to use formal automata…
Mixture distributions with dynamic weights are an efficient way of modeling loss data characterized by heavy tails. However, maximum likelihood estimation of this family of models is difficult, mostly because of the need to evaluate…
Structured Latent Attribute Models (SLAMs) are a family of discrete latent variable models widely used in education, psychology, and epidemiology to model multivariate categorical data. A SLAM assumes that multiple discrete latent…
With advances in sequencing technologies, there are now massive amounts of genomic data from across all life, leading to the possibility that a robust Tree of Life can be constructed. However, "gene tree heterogeneity", which is when…
This paper studies a Markov chain for phylogenetic reconstruction which uses a popular transition between tree topologies known as subtree pruning-and-regrafting (SPR). We analyze the Markov chain in the simpler setting that the generating…
Applying a method to reconstruct a phylogenetic tree from random data provides a way to detect whether that method has an inherent bias towards certain tree `shapes'. For maximum parsimony, applied to a sequence of random 2-state data, each…
We propose an efficient algorithm for approximate computation of the profile maximum likelihood (PML), a variant of maximum likelihood maximizing the probability of observing a sufficient statistic rather than the empirical sample. The PML…
In linear regression, the least squares (LS) estimator has certain optimality properties if the errors are normally distributed. This assumption is often violated in practice, partly caused by data outliers. Robust estimators can cope with…
CRISPR technology has enabled large-scale cell lineage tracing for complex multicellular organisms by mutating synthetic genomic barcodes during organismal development. However, these sophisticated biological tools currently use ad-hoc and…
The structure of an evolving network contains information about its past. Extracting this information efficiently, however, is, in general, a difficult challenge. We formulate a fast and efficient method to estimate the most likely history…
We consider phylogeny estimation under a two-state model of sequence evolution by site substitution on a tree. In the asymptotic regime where the sequence lengths tend to infinity, we show that for any fixed $k$ no statistically consistent…
A fundamental characteristic of natural language is the high rate at which speakers produce novel expressions. Because of this novelty, a heavy-tail of rare events accounts for a significant amount of the total probability mass of…
We describe an "embarrassingly parallel" method for Bayesian phylogenetic inference, annealed Sequential Monte Carlo, based on recent advances in the Sequential Monte Carlo literature such as adaptive determination of annealing parameters.…