Related papers: Importance Sampling Approximation of Sequence Evol…
Inferring the sequence of states from observations is one of the most fundamental problems in Hidden Markov Models. In statistical physics language, this problem is equivalent to computing the marginals of a one-dimensional model with a…
In modern data analysis, random sampling is an efficient and widely-used strategy to overcome the computational difficulties brought by large sample size. In previous studies, researchers conducted random sampling which is according to the…
Inferring dependencies between complex biological traits while accounting for evolutionary relationships between specimens is of great scientific interest yet remains infeasible when trait and specimen counts grow large. The…
With a view to connecting random mutation on the molecular level to punctuated equilibrium behavior on the phenotype level, we propose a new model for biological evolution, which incorporates random mutation and natural selection. In this…
Understanding the evolution of binary traits, which affects the birth and survival of species and also the rate of molecular evolution, remains challenging. A typical example is the evolution of mating systems in plant species. In this…
Stochastic processes defined on integer valued state spaces are popular within the physical and biological sciences. These models are necessary for capturing the dynamics of small systems where the individual nature of the populations…
This paper presents a detailed theoretical analysis of the three stochastic approximation proximal gradient algorithms proposed in our companion paper [49] to set regularization parameters by marginal maximum likelihood estimation. We prove…
We propose an adaptive importance sampling scheme for Gaussian approximations of intractable posteriors. Optimization-based approximations like variational inference can be too inaccurate while existing Monte Carlo methods can be too slow.…
Identifying and characterizing mutational paths is an important issue in evolutionary biology and in bioengineering. We here introduce a generic description of mutational paths in terms of the goodness of sequences and of the mutational…
Background: Several sources of noise obfuscate the identification of single nucleotide variation (SNV) in next generation sequencing data. For instance, errors may be introduced during library construction and sequencing steps. In addition,…
Gene gain-loss-duplication models are commonly based on continuous-time birth-death processes. Employed in a phylogenetic context, such models have been increasingly popular in studies of gene content evolution across multiple genomes.…
A simplified model for the growth of a population is studied in which random effects arise because reproducing individuals have a certain probability of surviving until the next breeding season and hence contributing to the next generation.…
We develop algorithms with low regret for learning episodic Markov decision processes based on kernel approximation techniques. The algorithms are based on both the Upper Confidence Bound (UCB) as well as Posterior or Thompson Sampling…
We present a theory and accompanying importance sampling method for computing rate constants in spatially inhomogenious systems. Using the relationship between rate constants and path space partition functions, we illustrate that the…
Temporal point processes are powerful generative models for event sequences that capture complex dependencies in time-series data. They are commonly specified using autoregressive models that learn the distribution of the next event from…
The ancestral maximum-likelihood and phylogeography problems are two fundamental problems involving evolutionary studies. The ancestral maximum-likelihood problem involves identifying a rooted tree alongside internal node sequences that…
We study oracle complexity of gradient based methods for stochastic approximation problems. Though in many settings optimal algorithms and tight lower bounds are known for such problems, these optimal algorithms do not achieve the best…
Traditional methods for unsupervised learning of finite mixture models require to evaluate the likelihood of all components of the mixture. This becomes computationally prohibitive when the number of components is large, as it is, for…
Improving Importance Sampling estimators for rare event probabilities requires sharp approximations of conditional densities. This is achieved for events E_{n}:=(f(X_{1})+...+f(X_{n}))\inA_{n} where the summands are i.i.d. and E_{n} is a…
Random geometric graphs defined on Euclidean subspaces, also called Gilbert graphs, are widely used to model spatially embedded networks across various domains. In such graphs, nodes are located at random in Euclidean space, and any two…