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arXiv 2022年

作者： Majumdar, Koyel Silva, Romina Perry, Antoinette Sabrina Watson, Ronald William Rau, Andrea Jaffrezic, Florence Murphy, Thomas Brendan Gormley, Isobel Claire School of Mathematics and Statistics University College Dublin Ireland School of Medicine University College Dublin Ireland Conway Institute of Biomedical and Biomolecular Research University College Dublin Ireland School of Biology and Environmental Science University College Dublin Ireland INRAE UMR1313 AgroParisTech GABI Université Paris-Saclay France

Identifying differentially methylated cytosine-guanine dinucleotide (CpG) sites between benign and tumour samples can assist in understanding disease. However, differential analysis of bounded DNA methylation data often requires data transformation, reducing biological interpretability. To address this, a family of beta mixture models (BMMs) is proposed that (i) objectively infers methylation state thresholds and (ii) identifies differentially methylated CpG sites (DMCs) given untransformed, beta-valued methylation data. The BMMs achieve this through model-based clustering of CpG sites and by employing parameter constraints, facilitating application to different study settings. Inference proceeds via an expectation-maximisation algorithm, with an approximate maximization step providing tractability and computational feasibility. Performance of the BMMs is assessed through thorough simulation studies, and the BMMs are used for differential analyses of DNA methylation data from a prostate cancer study. Intuitive and biologically interpretable methylation state thresholds are inferred and DMCs are identified, including those related to genes such as GSTP1, RASSF1 and RARB, known for their role in prostate cancer development. Gene ontology analysis of the DMCs revealed significant enrichment in cancer-related pathways, demonstrating the utility of BMMs to reveal biologically relevant insights. An R package betaclust facilitates widespread use of BMMs. © 2022, CC BY.

关键词： expectation maximization algorithm

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A Large Confirmatory Dynamic Factor Model for Stock Market Returns in Different Time Zones

arXiv

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arXiv 2022年

作者： Linton, Oliver B. Tang, Haihan Wu, Jianbin Faculty of Economics University of Cambridge Austin Robinson Building Sidgwick Avenue CambridgeCB3 9DD United Kingdom International School of Finance Fudan University 220 Handan Road Yangpu District Shanghai200433 China School of Business Nanjing University 22 Hankou Road Gulou District Nanjing210093 China

We propose a confirmatory dynamic factor model for a large number of stocks whose returns are observed daily across multiple time zones. The model has a global factor and a continental factor that both drive the individual stock return series. We propose two estimators of the model: a quasi-maximum likelihood estimator (QML-just-identified), and an improved estimator based on an expectation maximization (EM) algorithm (QML-all-res). Our estimators are consistent and asymptotically normal under the large approximate factor model setting. In particular, the asymptotic distributions of QML-all-res are the same as those of the infeasible OLS estimators that treat factors as known and utilize all the restrictions on the parameters of the model. We apply the model to MSCI equity indices of 42 developed and emerging markets, and find that most markets are more integrated when the CBOE Volatility Index (VIX) is high. © 2022, CC BY-NC-ND.

关键词： expectation maximization algorithm

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Addressing maximization Bias in Reinforcement Learning with Two-Sample Testing

arXiv

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arXiv 2022年

作者： Waltz, Martin Okhrin, Ostap Technische Universität Dresden Dresden01062 Germany Leipzig Dresden Germany

Value-based reinforcement-learning algorithms have shown strong results in games, robotics, and other real-world applications. Overestimation bias is a known threat to those algorithms and can sometimes lead to dramatic performance decreases or even complete algorithmic failure. We frame the bias problem statistically and consider it an instance of estimating the maximum expected value (MEV) of a set of random variables. We propose the T-Estimator (TE) based on two-sample testing for the mean, that flexibly interpolates between over- and underestimation by adjusting the significance level of the underlying hypothesis tests. We also introduce a generalization, termed K-Estimator (KE), that obeys the same bias and variance bounds as the TE and relies on a nearly arbitrary kernel function. We introduce modifications of Q-Learning and the Bootstrapped Deep Q-Network (BDQN) using the TE and the KE, and prove convergence in the tabular setting. Furthermore, we propose an adaptive variant of the TE-based BDQN that dynamically adjusts the significance level to minimize the absolute estimation bias. All proposed estimators and algorithms are thoroughly tested and validated on diverse tasks and environments, illustrating the bias control and performance potential of the TE and KE. © 2022, CC BY.

关键词： expectation maximization algorithm

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Policy Choice in Time Series by Empirical Welfare maximization

arXiv

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arXiv 2022年

作者： Kitagawa, Toru Wang, Weining Xu, Mengshan Department of Economics Brown University United States Department of Economics University College London United Kingdom Faculty of economics and business University of Groningen Netherlands Department of Economics University of Mannheim Germany

This paper develops a novel method for policy choice in a dynamic setting where the available data is a multi-variate time series. Building on the statistical treatment choice framework, we propose Time-series Empirical Welfare maximization (T-EWM) methods to estimate an optimal policy rule by maximizing an empirical welfare criterion constructed using nonparametric potential outcome time series. We characterize conditions under which T-EWM consistently learns a policy choice that is optimal in terms of conditional welfare given the time-series history. We derive a nonasymptotic upper bound for conditional welfare regret. To illustrate the implementation and uses of T-EWM, we perform simulation studies and apply the method to estimate optimal restriction rules against Covid-19. © 2022, CC BY.

关键词： expectation maximization algorithm

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Statistical channel model for underwater wireless optical communication system under a wide range of air bubble populations

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OPTICAL ENGINEERING 2021年第3期60卷 036111-036111页

作者： Singh, Mandeep Singh, Maninder Lal Singh, Gurpreet Gill, Harpuneet Singh Guru Nanak Dev Univ Dept Elect Technol Amritsar Punjab India

The performance of the underwater wireless optical communication (UWOC) system is severely affected by the presence of air bubbles in the water. Therefore, an experimental setup is designed to investigate the effect of different sized air bubbles on the laser beam propagating through the UWOC system. A wide range of air bubbles has been generated in the water tank by varying the diameter of the holes in a copper tube and by varying the air flow rates. When an optical beam propagates through the underwater environment in the presence of air bubbles, the received optical beam undergoes severe intensity fluctuations. The distribution of these intensity fluctuations conveys very useful information to predict the behavior of the underwater channel. The distributions of these intensity fluctuations have been modeled using a Gaussian mixture model (GMM), which is the sum of Gaussian functions. The parameters of the proposed GMM model are estimated by expectation maximization algorithm to obtain maximum likelihood estimation. The goodness of fit is also performed by considering a confidence interval of (95%) to estimate the feasibility of the proposed GMM model, which provides excellent results. The proposed GMM model excellently fits the experimental data for all the considered cases. In addition, based on this proposed model and experimental observations, the performance of the UWOC system is evaluated in terms of signal-to-noise ratio, outage probability, bit error rate, maximum Q-factor, etc. The results show an exact match between the experimental and proposed theoretical results that are modeled using GMM model and hence signifies the precision of the proposed model. (C) 2021 Society of Photo-Optical Instrumentation Engineers (SPIE)

关键词： underwater wireless optical communication channel modeling Gaussian mixture model expectation maximization algorithm signal-to-noise ratio outage probability

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Remaining useful life re-prediction methodology based on Wiener process: Subsea Christmas tree system as a case study

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COMPUTERS & INDUSTRIAL ENGINEERING 2021年 151卷 106983-106983页

作者： Cai, Baoping Fan, Hongyan Shao, Xiaoyan Liu, Yonghong Liu, Guijie Liu, Zengkai Ji, Renjie China Univ Petr Natl Engn Lab Offshore Geophys & Explorat Equipme Qingdao 266580 Shandong Peoples R China China Univ Petr Coll Mech & Elect Engn Qingdao 266580 Shandong Peoples R China Ocean Univ China Dept Mech & Elect Engn Qingdao 266100 Shandong Peoples R China

With the continuous improvement of the complexity and comprehensive level of the system, its reliability becomes more and more important. The remaining useful life (RUL) estimation method using the degradation model with random effect to describe the degradation process of the system has been widely used such as Wiener process. However, the conventional Wiener-process-based degradation model only considers the current monitoring data but not the historical degradation data, which leads to the inaccuracy of RUL prediction. Furthermore, in engineering, there will always be data missing caused by sensor networks, long life cycle properties of system and so on, leading to unsatisfactory results. This paper contributed a RUL re-prediction method based on Wiener process combining the current monitoring status and historical degradation data of the system. In the initial prediction process, the Wiener process is used to describe the degradation process of the system, the drift coefficient and diffusion coefficient are estimated by expectation maximization algorithm (EM algorithm), and the dynamic Bayesian networks (DBNs) model for system performance degradation is established to solve the uncertainty caused by missing data. In the re-prediction process, n groups of performance degradation monitoring data and historical predicted data are combined to calculate the basic degradation in each stage of Wiener process, and the DBNs are used for modeling. The RUL value is obtained by the time difference between the detection point and the predicted fault point, it is determined by the failure threshold finally. A case of subsea Christmas tree system is adopted to demonstrate the proposed approach.

关键词： Remaining useful life Wiener process Dynamic Bayesian networks expectation maximization algorithm Subsea Christmas tree system

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Application of Hidden Markov Models in Stock Trading 6

Application of Hidden Markov Models in Stock Trading

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6th International Conference on Advanced Computing and Communication Systems (ICACCS)

作者： Chandrika, P., V Visalakshmi, K. Srinivasan, K. Sakthi Vellore Inst Technol VITBS Vellore Tamil Nadu India

ISBN: (纸本)9781728151977;9781728151960

The stock market index forecasting is quite a popular topic in the present economy. There are many micro and macro-economic factors which influence the stock prices. With the emergence of machine learning techniques, algorithmic trading became most popular in forecasting the stock prices. There are many traditional machine learning techniques like ARMA, ARIMA which are used to forecast the stock market index. However these techniques consider trends and patterns involved in the data. Since the stock market data is a time series and irregular in nature there will be some noise involved. The present research paper studies the forecasting of stock market index by applying Hidden Markov models which considers the hidden states within the stock market index and traditional ARIMA model. 11MM considers the posterior probabilities on different hidden states using expectation maximization algorithm. The data considered for the study includes 5 different stock market index Dow Jones, NIFTY 50, 5 & P 500, New York Stock Index (NYSE) and KOSPL The data includes daily prices of Low, High, Close, Open, Volume for a period of 5 years that is 2014-2019 which accounts to approximately 1380 data points. In 11MM model the closing price of the index is considered for determining the transition states and posterior probabilities at 2, 3, 4 and 5 hidden states. Akaike Information Criteria (AIC) and Bayesian information Criterion (BIC) are used to determine the states from HMM. The research paper studies the direction of the market the closing price of the stock index considering HMM. The paper is divided into 5 parts which include Part 1: Introduction, Part 2: Past study, Part 3: Machine Learning algorithms, Part4: Data Analysis using HMM and Part 5: Results and Conclusion.

关键词： Stock Market Index Hidden Markov Modth Posterior probabilities expectation maximization algorithm Akaike Information Criterion Bayesian Information Criterion

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THE NOISY expectation-maximization algorithm

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FLUCTUATION AND NOISE LETTERS 2013年第3期12卷 1350012-1350012页

作者： Osoba, Osonde Mitaim, Sanya Kosko, Bart Univ So Calif Inst Signal & Image Proc Dept Elect Engn Los Angeles CA 90089 USA Thammasat Univ Dept Elect & Comp Engn Fac Engn Pathum Thani 12120 Thailand

We present a noise-injected version of the expectation-maximization (EM) algorithm: the noisy expectation-maximization (NEM) algorithm. The NEM algorithm uses noise to speed up the convergence of the EM algorithm. The NEM theorem shows that additive noise speeds up the average convergence of the EM algorithm to a local maximum of the likelihood surface if a positivity condition holds. Corollary results give special cases when noise improves the EM algorithm. We demonstrate these noise benefits on EM algorithms for three data models: the Gaussian mixture model (GMM), the Cauchy mixture model (CMM), and the censored log-convex gamma model. The NEM positivity condition simplifies to a quadratic inequality in the GMM and CMM cases. A final theorem shows that the noise benefit for independent identically distributed additive noise decreases with sample size in mixture models. This theorem implies that the noise benefit is most pronounced if the data is sparse.

关键词： Noise benefit stochastic resonance expectation maximization algorithm maximum likelihood Gaussian mixture model sparse data

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3D variability analysis: Resolving continuous flexibility and discrete heterogeneity from single particle cryo-EM

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JOURNAL OF STRUCTURAL BIOLOGY 2021年第2期213卷 107702-107702页

作者： Punjani, Ali Fleet, David J. Univ Toronto Dept Comp Sci Toronto ON M5S 3G4 Canada Vector Inst 710661 Univ Ave Toronto ON M5G 1M1 Canada Struct Biotechnol Inc 129-100 Coll Ave Toronto ON M5G 1L5 Canada

Single particle cryo-EM excels in determining static structures of protein molecules, but existing 3D reconstruction methods have been ineffective in modelling flexible proteins. We introduce 3D variability analysis (3DVA), an algorithm that fits a linear subspace model of conformational change to cryo-EM data at high resolution. 3DVA enables the resolution and visualization of detailed molecular motions of both large and small proteins, revealing new biological insight from single particle cryo-EM data. Experimental results demonstrate the ability of 3DVA to resolve multiple flexible motions of a-helices in the sub-50 kDa transmembrane domain of a GPCR complex, bending modes of a sodium ion channel, five types of symmetric and symmetry-breaking flexibility in a proteasome, large motions in a spliceosome complex, and discrete conformational states of a ribosome assembly. 3DVA is implemented in the cryoSPARC software package.

关键词： Single particle analysis Electron microscopy Principle component analysis Continuous heterogeneity Image processing expectation maximization algorithm

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Dynamic Discrete-Continuous Choice Models: Identification and Conditional Choice Probability Estimation

arXiv

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arXiv 2025年

作者： Bruneel-Zupanc, Christophe Department of Economics KU Leuven Belgium

This paper develops a general framework for dynamic models in which individuals simultaneously make both discrete and continuous choices. The framework incorporates a wide range of unobserved heterogeneity. I show that such models are nonparametrically identified. Based on constructive identification arguments, I build a novel two-step estimation method in the lineage of Hotz and Miller (1993) and Arcidiacono and Miller (2011) but extended to simultaneous discrete-continuous choice. In the first step, I recover the (type-dependent) optimal choices with an expectation-maximization algorithm and instrumental variable quantile regression. In the second step, I estimate the primitives of the model taking the estimated optimal choices as given. The method is especially attractive for complex dynamic models because it significantly reduces the computational burden associated with their estimation compared to alternative full solution methods. © 2025, CC BY.

关键词： expectation maximization algorithm

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