Błażej Miasojedow

An Adaptive Parallel Tempering Algorithm

Parallel tempering is a generic Markov chain Monte Carlo sampling method which allows good mixing with multimodal target distributions, where conventional Metropolis-Hastings algorithms often fail. The mixing properties of the sampler depend strongly on the choice of tuning parameters, such as the temperature schedule and the proposal distribution used for local exploration. We propose an adaptive algorithm with fixed number of temperatures which tunes both the temperature schedule and the parameters of the random-walk Metropolis kernel automatically. We prove the convergence of the adaptation and a strong law of large numbers for the algorithm under general conditions. We also prove as a side result the geometric ergodicity of the parallel tempering algorithm. We illustrate the performance of our method with examples. Our empirical findings indicate that the algorithm can cope well with different kinds of scenarios without prior tuning. Supplementary materials including the proofs and the Matlab implementation are available online.

Nonasymptotic bounds on the estimation error of MCMC algorithms

We address the problem of upper bounding the mean square error of MCMC estimators. Our analysis is non-asymptotic. We first establish a general result valid for essentially all ergodic Markov chains encountered in Bayesian computation and a possibly unbounded target function f: The bound is sharp in the sense that the leading term is exactly �2 as(P; f)=n, where �2 nas(P; f) is the CLT asymptotic variance. Next, we proceed to specific assumptions and give explicit computable bounds for geometrically and polynomially ergodic Markov chains. As a corollary we provide results on confidence estimation.

Predicting the outcomes of organic reactions via machine learning: are current descriptors sufficient?

As machine learning/artificial intelligence algorithms are defeating chess masters and, most recently, GO champions, there is interest – and hope – that they will prove equally useful in assisting chemists in predicting outcomes of organic reactions. This paper demonstrates, however, that the applicability of machine learning to the problems of chemical reactivity over diverse types of chemistries remains limited – in particular, with the currently available chemical descriptors, fundamental mathematical theorems impose upper bounds on the accuracy with which raction yields and times can be predicted. Improving the performance of machine-learning methods calls for the development of fundamentally new chemical descriptors.

Nonasymptotic bounds on the mean square error for MCMC estimates via renewal techniques

The Nummellin’s split chain construction allows to decompose a Markov nchain Monte Carlo (MCMC) trajectory into i.i.d. excursions. Regenerative MCMC nalgorithms based on this technique use a random number of samples. They have nbeen proposed as a promising alternative to usual fixed length simulation [25, 33, n14]. In this note we derive nonasymptotic bounds on the mean square error (MSE) nof regenerative MCMC estimates via techniques of renewal theory and sequential nstatistics. These results are applied to costruct confidence intervals. We then focus non two cases of particular interest: chains satisfying the Doeblin condition and a geometric ndrift condition. Available explicit nonasymptotic results are compared for ndifferent schemes of MCMC simulation.

Optimization of Mutation Pressure in Relation to Properties of Protein-Coding Sequences in Bacterial Genomes

Most mutations are deleterious and require energetically costly repairs. Therefore, it seems that any minimization of mutation rate is beneficial. On the other hand, mutations generate genetic diversity indispensable for evolution and adaptation of organisms to changing environmental conditions. Thus, it is expected that a spontaneous mutational pressure should be an optimal compromise between these two extremes. In order to study the optimization of the pressure, we compared mutational transition probability matrices from bacterial genomes with artificial matrices fulfilling the same general features as the real ones, e.g., the stationary distribution and the speed of convergence to the stationarity. The artificial matrices were optimized on real protein-coding sequences based on Evolutionary Strategies approach to minimize or maximize the probability of non-synonymous substitutions and costs of amino acid replacements depending on their physicochemical properties. The results show that the empirical matrices have a tendency to minimize the effects of mutations rather than maximize their costs on the amino acid level. They were also similar to the optimized artificial matrices in the nucleotide substitution pattern, especially the high transitions/transversions ratio. We observed no substantial differences between the effects of mutational matrices on protein-coding sequences in genomes under study in respect of differently replicated DNA strands, mutational cost types and properties of the referenced artificial matrices. The findings indicate that the empirical mutational matrices are rather adapted to minimize mutational costs in the studied organisms in comparison to other matrices with similar mathematical constraints.

The Wasserstein Distance as a Dissimilarity Measure for Mass Spectra with Application to Spectral Deconvolution

We propose a new approach for the comparison of mass spectra using a metric known in the computer science under the name of Earth Movers Distance and in mathematics as the Wasserstein distance. We argue that this approach allows for natural and robust solutions to various problems in the analysis of mass spectra. In particular, we show an application to the problem of deconvolution, in which we infer proportions of several overlapping isotopic envelopes of similar compounds. Combined with the previously proposed generator of isotopic envelopes, IsoSpec, our approach works for a wide range of masses and charges in the presence of several types of measurement inaccuracies. To reduce the computational complexity of the solution, we derive an effective implementation of the Interior Point Method as the optimization procedure. The software for mass spectral comparison and deconvolution based on Wasserstein distance is available at https://github.com/mciach/wassersteinms.

Estimation of Rates of Reactions Triggered by Electron Transfer in Top-Down Mass Spectrometry

Electron transfer dissociation (ETD) is a versatile technique used in mass spectrometry for the high-throughput characterization of proteins. It consists of several competing reactions triggered by the transfer of an electron from its anion source to the sample cations. One can retrieve relative quantities of the products from mass spectra.

Geometric ergodicity of Rao and Teh’s algorithm for Markov jump processes and CTBNs

Rao and Teh (2013) introduced an efficient MCMC algorithm for sampling from the posterior distribution of a hidden Markov jump process. The algorithm is based on the idea of sampling virtual jumps. In the present paper we show that the Markov chain generated by Rao and Tehs algorithm is geometrically ergodic. To this end we establish a geometric drift condition towards a small set.

Adaptive Monte Carlo Maximum Likelihood

We consider Monte Carlo approximations to the maximum likelihood estimator in models with intractable norming constants. This paper deals with adaptive Monte Carlo algorithms, which adjust control parameters in the course of simulation. We examine asymptotics of adaptive importance sampling and a new algorithm, which uses resampling and MCMC. This algorithm is designed to reduce problems with degeneracy of importance weights. Our analysis is based on martingale limit theorems. We also describe how adaptive maximization algorithms of Newton-Raphson type can be combined with the resampling techniques. The paper includes results of a small scale simulation study in which we compare the performance of adaptive and non-adaptive Monte Carlo maximum likelihood algorithms.

Bayesian inference for age-structured population model of infectious disease with application to varicella in Poland.

The dynamics of the infectious disease transmission are often best understood by taking into account the structure of population with respect to specific features, for example age or immunity level. The practical utility of such models depends on the appropriate calibration with the observed data. Here, we discuss the Bayesian approach to data assimilation in the case of a two-state age-structured model. Such models are frequently used to explore the disease dynamics (i.e. force of infection) based on prevalence data collected at several time points. We demonstrate that, in the case when the explicit solution to the model equation is known, accounting for the data collection process in the Bayesian framework allows us to obtain an unbiased posterior distribution for the parameters determining the force of infection. We further show analytically and through numerical tests that the posterior distribution of these parameters is stable with respect to a cohort approximation (Escalator Boxcar Train) of the solution. Finally, we apply the technique to calibrate the model based on observed sero-prevalence of varicella in Poland.