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A hidden Markov modeling approach for identifying tumor subclones in next-generation sequencing studies

BIOSTATISTICS 2022年第1期23卷 69-82页

作者： Choo-Wosoba, Hyoyoung Albert, Paul S. Zhu, Bin NCI Biostat Branch Div Canc Epidemiol & Genet 9609 Med Ctr Dr Rockville MD 20850 USA

Allele-specific copy number alteration (ASCNA) analysis is for identifying copy number abnormalities in tumor cells. Unlike normal cells, tumor cells are heterogeneous as a combination of dominant and minor subclones with distinct copy number profiles. Estimating the clonal proportion and identifying mainclone and subclone genotypes across the genome are important for understanding tumor progression. Several ASCNA tools have recently been developed, but they have been limited to the identification of subclone regions, and not the genotype of subclones. In this article, we propose subHMM, a hidden Markov model-based approach that estimates both subclone region and region-specific subclone genotype and clonal proportion. We specify a hidden state variable representing the conglomeration of clonal genotype and subclone status. We propose a two-step algorithm for parameter estimation, where in the first step, a standard hidden Markov model with this conglomerated state variable is fit. Then, in the second step, region-specific estimates of the clonal proportions are obtained by maximizing region-specific pseudo-likelihoods. We apply subHMM to study renal cell carcinoma datasets in The Cancer Genome Atlas. In addition, we conduct simulation studies that show the good performance of the proposed approach. The R source code is available online at https://***/tools/analysis/subhmm. Expectation-Maximization algorithm;forward-backward algorithm;Somatic copy number alteration;Tumor subclones.

关键词： E-M algorithm forward-backward algorithm Somatic copy number alteration Tumor subclones

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A sequential smoothing algorithm with linear computational cost

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BIOMETRIKA 2010年第2期97卷 447-464页

作者： Fearnhead, Paul Wyncoll, David Tawn, Jonathan Univ Lancaster Dept Math & Stat Lancaster LA1 4YF England

In this paper we propose a new particle smoother that has a computational complexity of O(N), where N is the number of particles. This compares favourably with the O(N-2) computational cost of most smoothers. The new method also overcomes some degeneracy problems in existing algorithms. Through simulation studies we show that substantial gains in efficiency are obtained for practical amounts of computational cost. It is shown both through these simulation studies, and by the analysis of an athletics dataset, that our new method also substantially outperforms the simple filter-smoother, the only other smoother with computational cost that is O(N).

关键词： Extreme value theory forward-backward algorithm Particle filtering Particle smoothing Two-filter formula

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A HIDDEN MARKOV MODEL APPROACH TO CHARACTERIZING THE PHOTO-SWITCHING BEHAVIOR OF FLUOROPHORES

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ANNALS OF APPLIED STATISTICS 2019年第3期13卷 1397-1429页

作者： Patel, Lekha Gustafsson, Nils Lin, Yu Ober, Raimund Henriques, Ricardo Cohen, Edward Imperial Coll London Dept Math London SW7 2AZ England UCL MRC Lab Mol Cell Biol London WC1E 6BT England European Mol Biol Lab Cell Biol & Biophys D-69117 Heidelberg Germany Texas A&M College Stn TX USA Univ Southampton Ctr Canc Immunol Fac Med Southampton Hants England Francis Crick Inst London NW1 1AT England Texas A&M Univ Dept Biomed Engn College Stn TX 77843 USA

Fluorescing molecules (fluorophores) that stochastically switch between photon-emitting and dark states underpin some of the most celebrated advancements in super-resolution microscopy. While this stochastic behavior has been heavily exploited, full characterization of the underlying models can potentially drive forward further imaging methodologies. Under the assumption that fluorophores move between fluorescing and dark states as continuous time Markov processes, the goal is to use a sequence of images to select a model and estimate the transition rates. We use a hidden Markov model to relate the observed discrete time signal to the hidden continuous time process. With imaging involving several repeat exposures of the fluorophore, we show the observed signal depends on both the current and past states of the hidden process, producing emission probabilities that depend on the transition rate parameters to be estimated. To tackle this unusual coupling of the transition and emission probabilities, we conceive transmission (transition-emission) matrices that capture all dependencies of the model. We provide a scheme of computing these matrices and adapt the forward-backward algorithm to compute a likelihood which is readily optimized to provide rate estimates. When confronted with several model proposals, combining this procedure with the Bayesian Information Criterion provides accurate model selection.

关键词： Hidden Markov models Markov processes rate estimation forward-backward algorithm super-resolution microscopy

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The generalized viscosity explicit rules for solving variational inclusion problems in Banach spaces

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OPTIMIZATION 2021年第12期70卷 2607-2633页

作者： Cholamjiak, Prasit Pholasa, Nattawut Suantai, Suthep Sunthrayuth, Pongsakorn Univ Phayao Sch Sci Phayao Thailand Chiang Mai Univ Fac Sci Dept Math Res Ctr Math & Appl Math Chiang Mai Thailand Rajamangala Univ Technol Thanyaburi RMUTT Fac Sci & Technol Dept Math & Comp Sci Thanyaburi Pathumthani Thailand

In this paper, we propose a generalized viscosity explicit method for finding zeros of the sum of two accretive operators in the framework of Banach spaces. The strong convergence theorem of such method is proved under some suitable assumption on the parameters. As applications, we apply our main result to the variational inequality problem, the convex minimization problem and the split feasibility problem. The numerical experiments to illustrate the behaviour of the proposed method including compare it with other methods are also presented.

关键词： m-accretive operator forward-backward algorithm Banach space strong convergence

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Fast convex optimization via inertial dynamics with Hessian driven damping

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JOURNAL OF DIFFERENTIAL EQUATIONS 2016年第10期261卷 5734-5783页

作者： Attouch, Hedy Peypouquet, Juan Redont, Patrick Univ Montpellier 2 UMR CNRS 5149 Inst Montpellierain Alexander Grothendieck Pl Eugene Bataillon F-34095 Montpellier 5 France Univ Tecn Federico Santa Maria Av Espana 1680 Valparaiso Chile

We first study the fast minimization properties of the trajectories of the second-order evolution equation (x) double over dot (t) + alpha/t (x) over dot(t) + beta del(2)Phi(x(t))(x) double over dot(t) + del Phi(x(t)) = 0, where Phi : H -> R is a smooth convex function acting on a real Hilbert space H, and alpha, beta are positive parameters. This inertial system combines an isotropic viscous damping which vanishes asymptotically, and a geometrical Hessian driven damping, which makes it naturally related to Newton's and Levenberg-Marquardt methods. For alpha >= 3, and beta > 0, along any trajectory, fast convergence of the values Phi(x(t)) - min(H) Phi = O (t(-2)) is obtained, together with rapid convergence of the gradients del Phi(x(t)) to zero. For alpha > 3, just assuming that argmin Phi not equal empty set, we show that any trajectory converges weakly to a minimizer of Phi, and that Phi(x(t)) - min(H) Phi = o(t(-2)). Strong convergence is established in various practical situations. In particular, for the strongly convex case, we obtain an even faster speed of convergence which can be arbitrarily fast depending on the choice of alpha. More precisely, we have Phi (x(t)) - min(H) Phi = O(t(-2/3 alpha)). Then, we extend the results to the case of a general proper lower-semicontinuous convex function Phi : H -> R boolean OR {+infinity}. This is based on the crucial property that-the inertial dynamics with Hessian driven damping can be equivalently written as a first-order system in time and space, allowing to extend it by simply replacing the gradient with the subdifferential. By explicit-implicit time discretization, this opens a gate to new - possibly more rapid - inertial algorithms, expanding the field of FISTA methods for convex structured optimization problems. (C) 2016 Elsevier Inc. All rights reserved.

关键词： Convex optimisation Fast convergent methods Gradient flows Inertial dynamics Hessian-driven damping forward-backward algorithm

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A Dynamical System Associated with the Fixed Points Set of a Nonexpansive Operator

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JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS 2017年第1期29卷 155-168页

作者： Bot, Radu Ioan Csetnek, Ernoe Robert Univ Vienna Fac Math Oskar Morgenstern Pl 1 A-1090 Vienna Austria

We study the existence and uniqueness of (locally) absolutely continuous trajectories of a dynamical system governed by a nonexpansive operator. The weak convergence of the orbits to a fixed point of the operator is investigated by relying on Lyapunov analysis. We show also an order of convergence of for the fixed point residual of the trajectory of the dynamical system. We apply the results to dynamical systems associated with the problem of finding the zeros of the sum of a maximally monotone operator and a cocoercive one. Several dynamical systems from the literature turn out to be particular instances of this general approach.

关键词： Dynamical systems Lyapunov analysis Krasnosel'skii-Mann algorithm Monotone inclusions forward-backward algorithm

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Selection of Variables for Cluster Analysis and Classification Rules

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JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION 2008年第483期103卷 1294-1303页

作者： Fraiman, Ricardo Justel, Ana Svarc, Marcela Univ San Andres Buenos Aires DF Argentina Univ Republica Ctr Matemat Montevideo Uruguay Univ Autonoma Madrid Madrid Spain

In this article we introduce two procedures for variable selection in cluster analysis and classification rules. One is mainly aimed at detecting the ''noisy'' noninformative variables, while the other also deals with multicolinearity and general dependence. Both methods are designed to be used after a ''satisfactory'' grouping procedure has been carried out. A forward-backward algorithm is proposed to make such procedures feasible in large datasets. A small simulation is performed and some real data examples are analyzed.

关键词： Finding relevant variables forward-backward algorithm Pattern recognition

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Computational methods for complex stochastic systems: a review of some alternatives to MCMC

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STATISTICS AND COMPUTING 2008年第2期18卷 151-171页

作者： Fearnhead, Paul Univ Lancaster Dept Math & Stat Lancaster LA1 4YF England

We consider analysis of complex stochastic models based upon partial information. MCMC and reversible jump MCMC are often the methods of choice for such problems, but in some situations they can be difficult to implement;and suffer from problems such as poor mixing, and the difficulty of diagnosing convergence. Here we review three alternatives to MCMC methods: importance sampling, the forward-backward algorithm, and sequential Monte Carlo (SMC). We discuss how to design good proposal densities for importance sampling, show some of the range of models for which the forward-backward algorithm can be applied, and show how resampling ideas from SMC can be used to improve the efficiency of the other two methods. We demonstrate these methods on a range of examples, including estimating the transition density of a diffusion and of a discrete-state continuous-time Markov chain;inferring structure in population genetics;and segmenting genetic divergence data.

关键词： diffusions forward-backward algorithm importance sampling missing data particle filter population genetics

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Generalized viscosity implicit rules for solving quasi-inclusion problems of accretive operators in Banach spaces

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OPTIMIZATION 2017年第7期66卷 1105-1117页

作者： Chang, Shih-sen Wen, Ching-Feng Yao, Jen-Chih China Med Univ Ctr Gen Educ Taichung Taiwan Kaohsiung Med Univ Ctr Fundamental Sci Kaohsiung Taiwan Kaohsiung Med Univ Res Ctr Nonlinear Anal & Optimizat Kaohsiung Taiwan Kaohsiung Med Univ Hosp Dept Med Res Kaohsiung Taiwan

The generalized viscosity implicit rules for solving quasi-inclusion problems of accretive operators in Banach spaces are established. The strong convergence theorems of the rules to a solution of quasi-inclusion problems of accretive operators are proved under certain assumptions imposed on the sequences of parameters. The results presented in this paper extend and improve the main results of Refs. (Moudafi, J Math Anal Appl. 2000;241:46-55;Xu et al., Fixed Point Theory Appl. 2015;2015:41;Lopez et al., Abstr Appl Anal. 2012;2012;Cholamjiak, Numer Algor. DOI:10.1007/s11075-015-0030-6.). Moreover, some applications to monotone variational inequalities, convex minimization problem and convexly constrained linear inverse problem are presented.

关键词： The generalized viscosity implicit rules accretive operator maximal monotone operator Banach space splitting method forward-backward algorithm

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Filtering recursions for calculating likelihoods for queues based on inter-departure time data

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STATISTICS AND COMPUTING 2004年第3期14卷 261-266页

作者： Fearnhead, P Univ Lancaster Dept Math & Stat Lancaster LA1 4YF England

We consider inference for queues based on inter-departure time data. Calculating the likelihood for such models is difficult, as the likelihood involves summing up over the (exponentially-large) space of realisations of the arrival process. We demonstrate how a likelihood recursion can be used to calculate this likelihood efficiently for the specific cases of M/G/1 and Er/G/1 queues. We compare the sampling properties of the mles to the sampling properties of estimators, based on indirect inference, which have previously been suggested for this problem.

关键词： Er/G/1 queues forward-backward algorithm indirect inference likelihood recursions M/G/1 queues missing data

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