The Epigenetic Pacemaker: modeling epigenetic states under an evolutionary framework

Abstract Summary Epigenetic rates of change, much as evolutionary mutation rate along a lineage, vary during lifetime. Accurate estimation of the epigenetic state has vast medical and biological implications. To account for these non-linear epigenetic changes with age, we recently developed a formalism inspired by the Pacemaker model of evolution that accounts for varying rates of mutations with time. Here, we present a python implementation of the Epigenetic Pacemaker (EPM), a conditional expectation maximization algorithm that estimates epigenetic landscapes and the state of individuals and may be used to study non-linear epigenetic aging. Availability and Implementation The EPM is available at https://pypi.org/project/EpigeneticPacemaker/ under the MIT license. The EPM is compatible with python version 3.6 and above.

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Gauss process state-space model optimization algorithm with expectation maximization

International Journal of Distributed Sensor Networks ◽

10.1177/1550147719862217 ◽

2019 ◽

Vol 15 (7) ◽

pp. 155014771986221

Author(s):

Hongqiang Liu ◽

Haiyan Yang ◽

Tao Zhang ◽

Bo Pan

Keyword(s):

State Space ◽

Optimization Algorithm ◽

Expectation Maximization ◽

Conditional Expectation ◽

State Space Model ◽

Expectation Maximization Algorithm ◽

Model Optimization ◽

Laboratory Environment ◽

Space Model ◽

Gauss Process

A Gauss process state-space model trained in a laboratory cannot accurately simulate a nonlinear system in a non-laboratory environment. To solve this problem, a novel Gauss process state-space model optimization algorithm is proposed by combining the expectation–maximization algorithm with the Gauss process Rauch–Tung–Striebel smoother algorithm, that is, the EM-GP-RTSS algorithm. First, a theoretical formulation of the Gauss process state-space model is proposed, which is not found in previous references. Second, a Gauss process state-space model optimization framework with the expectation–maximization algorithm is proposed. In the expectation–maximization algorithm, the unknown system state is considered as the lost data, and the maximization of measurement likelihood function is transformed into that of a conditional expectation function. Then, the Gauss process–assumed density filter algorithm and the Gauss process Rauch–Tung–Striebel smoother algorithm are proposed with the Gauss process state-space model defined in this article, in order to calculate the smoothed distribution in the conditional expectation function. Finally, the Monte Carlo numerical integral method is used to obtain the approximate expression of the conditional expectation function. The simulation results demonstrate that the Gauss process state-space model optimized by the EM-GP-RTSS can simulate the system in the non-laboratory environment better than the Gauss process state-space model trained in the laboratory, and can reach or exceed the estimation accuracy of the traditional state-space model.

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An epigenetic pacemaker is detected via a fast conditional expectation maximization algorithm

Epigenomics ◽

10.2217/epi-2017-0130 ◽

2018 ◽

Vol 10 (6) ◽

pp. 695-706 ◽

Cited By ~ 5

Author(s):

Sagi Snir ◽

Matteo Pellegrini

Keyword(s):

Expectation Maximization ◽

Conditional Expectation ◽

Expectation Maximization Algorithm

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A stochastic estimation procedure for intermittently-observed semi-Markov multistate models with back transitions

Statistical Methods in Medical Research ◽

10.1177/0962280217736342 ◽

2017 ◽

Vol 28 (3) ◽

pp. 770-787

Author(s):

Hilary Aralis ◽

Ron Brookmeyer

Keyword(s):

Expectation Maximization ◽

Likelihood Function ◽

Expectation Maximization Algorithm ◽

Estimation Procedure ◽

Elderly Subjects ◽

Accurate Estimation ◽

Parameter Estimates ◽

Multistate Models ◽

Observation Process ◽

Wide Range

Multistate models provide an important method for analyzing a wide range of life history processes including disease progression and patient recovery following medical intervention. Panel data consisting of the states occupied by an individual at a series of discrete time points are often used to estimate transition intensities of the underlying continuous-time process. When transition intensities depend on the time elapsed in the current state and back transitions between states are possible, this intermittent observation process presents difficulties in estimation due to intractability of the likelihood function. In this manuscript, we present an iterative stochastic expectation-maximization algorithm that relies on a simulation-based approximation to the likelihood function and implement this algorithm using rejection sampling. In a simulation study, we demonstrate the feasibility and performance of the proposed procedure. We then demonstrate application of the algorithm to a study of dementia, the Nun Study, consisting of intermittently-observed elderly subjects in one of four possible states corresponding to intact cognition, impaired cognition, dementia, and death. We show that the proposed stochastic expectation-maximization algorithm substantially reduces bias in model parameter estimates compared to an alternative approach used in the literature, minimal path estimation. We conclude that in estimating intermittently observed semi-Markov models, the proposed approach is a computationally feasible and accurate estimation procedure that leads to substantial improvements in back transition estimates.

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Human Epigenetic Aging is Logarithmic with Time across the Entire LifeSpan

10.1101/401992 ◽

2018 ◽

Cited By ~ 2

Author(s):

Sagi Snir ◽

Matteo Pellegrini

Keyword(s):

Methylation Status ◽

Real Data ◽

Chronological Age ◽

Epigenetic Changes ◽

Critical Question ◽

Epigenetic Aging ◽

Epigenetic Age ◽

Non Linear ◽

Development And Aging

AbstractIt is well established that organisms undergo epigenetic changes both during development and aging. Developmental changes have been extensively studied to characterize the differentiation of stem cells into diverse lineages. Epigenetic changes during aging have been characterized by multiple epigenetic clocks, that allow the prediction of chronological age based on methylation status. Despite their accuracy and utility, epigenetic age biomarkers leave many questions about epigenetic aging unanswered. Specifically, they do not permit the unbiased characterization of non-linear epigenetic aging trends across entire life spans, a critical question underlying this field of research. Here we a provide an integrated framework to address this question. Our model, inspired from evolutionary models, is able to account for acceleration/deceleration in epigenetic changes by fitting an individuals model age, the epigenetic age, which is related to chronological age in a non-linear fashion. We have devised a two stage procedure leveraging these model ages to infer aging trends over the entire lifespan of a population. Application of this procedure to real data measured across broad age ranges, from before birth to old age, and from two tissue types, suggests a universal logarithmic trend characterizes epigenetic aging across entire lifespans. This observation may have important implications for the development and application of future, more accurate, aging biomarkers.

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A Generalized Dynamic Factor Model for Panel Data: Estimation with a Two-Cycle Conditional Expectation-Maximization Algorithm

SSRN Electronic Journal ◽

10.2139/ssrn.2201608 ◽

2013 ◽

Author(s):

Nikolaos Zirogiannis ◽

Yorghos Tripodis

Keyword(s):

Panel Data ◽

Expectation Maximization ◽

Conditional Expectation ◽

Factor Model ◽

Expectation Maximization Algorithm ◽

Dynamic Factor ◽

Dynamic Factor Model ◽

Panel Data Estimation ◽

Data Estimation

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A Harmonic Impedance Estimation Method Based on the Cauchy Mixed Model

Mathematical Problems in Engineering ◽

10.1155/2020/1580475 ◽

2020 ◽

Vol 2020 ◽

pp. 1-13 ◽

Cited By ~ 1

Author(s):

Zhirong Tang ◽

Huaqiang Li ◽

Fangwei Xu ◽

Qin Shu ◽

Yue Jiang

Keyword(s):

Expectation Maximization ◽

Mixed Model ◽

Expectation Maximization Algorithm ◽

Data Distribution ◽

Estimation Method ◽

Measured Data ◽

Estimation Methods ◽

Accurate Estimation ◽

Point Of Common Coupling ◽

Common Coupling

In this paper, a new method without any tradition assumption to estimate the utility harmonic impedance of a point of common coupling (PCC) is proposed. But, the existing estimation methods usually are built on some assumptions, such as, the background harmonic is stable and small, the harmonic impedance of the customer side is much larger than that of utility side, and the harmonic sources of both sides are independent. However these assumptions are unpractical to modern power grid, which causes very wrong estimation. The proposed method first uses a Cauchy Mixed Model (CMM) to express the Norton equivalent circuit of the PCC because we find that the CMM can right fit the statistical distribution of the measured harmonic data for any PCC, by testing and verifying massive measured harmonic data. Also, the parameters of the CMM are determined by the expectation maximization algorithm (EM), and then the utility harmonic impedance is estimated by means of the CMM’s parameters. Compared to the existing methods, the main advantages of our method are as follows: it can obtain the accurate estimation results, but it is no longer dependent of any assumption and is only related to the measured data distribution. Finally, the effectiveness of the proposed method is verified by simulation and field cases.

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