An alternative marginal likelihood estimator for phylogenetic models

Bayesian phylogenetic methods are generating noticeable enthusiasm in the field of molecular systematics. Many phylogenetic models are often at stake and different approaches are used to compare them within a Bayesian framework. The Bayes factor, defined as the ratio of the marginal likelihoods of two competing models, plays a key role in Bayesian model selection. We focus on an alternative estimator of the marginal likelihood whose computation is still a challenging problem. Several computational solutions have been proposed none of which can be considered outperforming the others simultaneously in terms of simplicity of implementation, computational burden and precision of the estimates. Practitioners and researchers, often led by available software, have privileged so far the simplicity of the harmonic mean estimator (HM) and the arithmetic mean estimator (AM). However it is known that the resulting estimates of the Bayesian evidence in favor of one model are biased and often inaccurate up to having an infinite variance so that the reliability of the corresponding conclusions is doubtful. Our new implementation of the generalized harmonic mean (GHM) idea recycles MCMC simulations from the posterior, shares the computational simplicity of the original HM estimator, but, unlike it, overcomes the infinite variance issue. The alternative estimator is applied to simulated phylogenetic data and produces fully satisfactory results outperforming those simple estimators currently provided by most of the publicly available software

Maximum a Posteriori Estimation by Search in Probabilistic Programs

We introduce an approximate search algorithm for fast maximum a posteriori probability estimation in probabilistic programs, which we call Bayesian ascent Monte Carlo (BaMC). Probabilistic programs represent probabilistic models with varying number of mutually dependent finite, countable, and continuous random variables. BaMC is an anytime MAP search algorithm applicable to any combination of random variables and dependencies. We compare BaMC to other MAP estimation algorithms and show that BaMC is faster and more robust on a range of probabilistic models.Comment: To appear in proceedings of SOCS1

Multibody Multipole Methods

A three-body potential function can account for interactions among triples of particles which are uncaptured by pairwise interaction functions such as Coulombic or Lennard-Jones potentials. Likewise, a multibody potential of order $n$ can account for interactions among $n$-tuples of particles uncaptured by interaction functions of lower orders. To date, the computation of multibody potential functions for a large number of particles has not been possible due to its $O(N^n)$ scaling cost. In this paper we describe a fast tree-code for efficiently approximating multibody potentials that can be factorized as products of functions of pairwise distances. For the first time, we show how to derive a Barnes-Hut type algorithm for handling interactions among more than two particles. Our algorithm uses two approximation schemes: 1) a deterministic series expansion-based method; 2) a Monte Carlo-based approximation based on the central limit theorem. Our approach guarantees a user-specified bound on the absolute or relative error in the computed potential with an asymptotic probability guarantee. We provide speedup results on a three-body dispersion potential, the Axilrod-Teller potential.Comment: To appear in Journal of Computational Physic

Beyond the One Step Greedy Approach in Reinforcement Learning

The famous Policy Iteration algorithm alternates between policy improvement and policy evaluation. Implementations of this algorithm with several variants of the latter evaluation stage, e.g, $n$-step and trace-based returns, have been analyzed in previous works. However, the case of multiple-step lookahead policy improvement, despite the recent increase in empirical evidence of its strength, has to our knowledge not been carefully analyzed yet. In this work, we introduce the first such analysis. Namely, we formulate variants of multiple-step policy improvement, derive new algorithms using these definitions and prove their convergence. Moreover, we show that recent prominent Reinforcement Learning algorithms are, in fact, instances of our framework. We thus shed light on their empirical success and give a recipe for deriving new algorithms for future study.Comment: ICML 201