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Scalable spatiotemporal regression model based on Moran's eigenvectors

INTERNATIONAL JOURNAL OF GEOGRAPHICAL INFORMATION SCIENCE 2023年第1期37卷 162-188页

作者： Nishi, Hayato Asami, Yasushi Baba, Hiroki Shimizu, Chihiro Hitotsubashi Univ Ctr Promot Social Data Sci Educ & Res Tokyo Japan Univ Tokyo Dept Urban Engn Tokyo Japan Kyoto Univ Ctr Southeast Asian Studies Hakubi Ctr Adv Res Kyoto Japan

We propose a scalable regression model with spatially and temporally varying coefficients based on Moran's eigenvectors and efficient computation algorithms. Regression models that consider spatiotemporal non-stationarity are important because many real-world datasets, such as housing prices, are tied to geographical and temporal locations. Although geographically weighted regression (GWR) and its variants are widely used to model spatially varying coefficients, they cannot handle large datasets. We employ an alternative modelling method of spatially varying coefficients based on Moran's eigenvectors and extend it to handle large spatiotemporal datasets. Additionally, we introduce a scalable learning algorithm that exploits the model structures based on the Kalman filter and the expectation-maximisation algorithm. Our scalable algorithm is efficient even for large datasets that cannot be handled by GWR. To evaluate the performance of the proposed model, we applied it to a housing market dataset collected in Tokyo, Japan. The results show that the predictive performance of the proposed model is comparable to that of GWR while increasing the computational speed. Moreover, larger datasets can accelerate the algorithm convergence.

关键词： Eigenvector spatial filtering spatiotemporal modelling state-space model expectation-maximisation algorithm spatially varying coefficients

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The subclass approach for mutational spectrum analysis: Application of the SEM algorithm

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JOURNAL OF THEORETICAL BIOLOGY 1998年第4期192卷 475-487页

作者： Glazko, GB Milanesi, L Rogozin, IB Russian Acad Sci Inst Cytol & Genet Novosibirsk 630090 Russia CNR Ist Tecnol Biomed Avanzate I-20090 Segrate Milano Italy

Analysis and comparison of mutational spectra represents an important problem in molecular biology. To analyse a mutational spectra we apply an algorithm based on the SEM subclass approach (Simulation, expectation, Maximization). The algorithm tries to classify the mutational sites according to different mutation probabilities, and each site should belong to one class. Each class is approximated by binomial distribution and thus any real mutational spectrum is regarded as a mixture of binomial distributions. The separation process runs iteratively. Each iteration includes the simulation, maximization and estimation procedures. To evaluate the quality of the classification results, the X-2 test is used. The algorithm has been checked on random spectra with preset parameters and on real mutational spectra. As has been shown, 17 out of 19 analysed real mutational spectra can be divided into two or more classes of sites, of which one contains hotspots of mutation. For the G:C --> A:T mutational spectra induced by Sn1 alkylating mutagens (11 spectral the classification accuracy was 0.95. To test different site volumes, each Sn1-induced spectrum was divided into the G --> A and C --> T spectra. The classification accuracy for these spectra was 0.96. From the analysis of classification errors it is possible to suggest that at least part of them cannot be ascribed to the faults of the algorithm but are caused by some special features of the mutagenesis itself. The results of the real data are in good relation with existing knowledge. The approach we present is an attempt to formalize the concept of a "mutational hotspot". The program implementing the SEM algorithm is available on the Web server (http://***/webmutation).

关键词： Dna-sequence data Escherichia-coli Laci gene Em algorithm Somatic hypermutagenesis Immunoglobulin genes Environmental carcinogens Maximum-likelihood Base substitution Mutagenesis Spectra Immunoglobulin Gene Scanning Electron Microscope expectation-maximisation algorithm maximum likelihood algorithms Binomial Distribution Environmental Carcinogens Mutagenesis nucleic acid base substitution

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Acceleration of the EM algorithm

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Systems and Computers in Japan 2000年第2期31卷 10-18页

作者： Ikeda, Shiro PRESTO Japan Sci. and Technol. Corporation Wako 351-0198 Japan

The EM algorithm is used for many applications, including the Boltzmann machine, stochastic Perceptron, and HMM. This algorithm gives an iterating procedure for calculating the MLE of stochastic models which have hidden random variables. It is simple, but the convergence is slow. We also have the "Fisher scoring method." Its convergence is faster, but the calculation load is heavy. We show that by using the EM algorithm recursively, we can connect these two methods and accelerate the EM algorithm. Also, Louis, Meng, and Rubin showed they can accelerate the EM algorithm, but our algorithm is simpler. We present some numerical simulations using our algorithm. © 2000 Scripta Technica.

关键词： EM algorithm Fisher scoring method maximum likelihood estimate Scoring Methods acceleration expectation-maximisation algorithm maximum likelihood estimation Hidden Markov models calculated loads

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xREI: a phylo-grammar visualization webserver

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NUCLEIC ACIDS RESEARCH 2008年第Web Server issue期36卷 W65-W69页

作者： Barquist, Lars Holmes, Ian Univ Calif Berkeley Dept Bioengn Berkeley CA 94720 USA

Phylo-grammars, probabilistic models combining Markov chain substitution models with stochastic grammars, are powerful models for annotating structured features in multiple sequence alignments and analyzing the evolution of those features. In the past, these methods have been cumbersome to implement and modify. xrate provides means for the rapid development of phylo-grammars (using a simple file format) and automated parameterization of those grammars from training data (via the expectation Maximization algorithm). xREI (pron. 'X-ray') is an intuitive, flexible AJAX (Asynchronous Javascript And XML) web interface to xrate providing grammar visualization tools as well as access to xrate's training and annotation functionality. It is hoped that this application will serve as a valuable tool to those developing phylo-grammars, and as a means for the exploration and dissemination of such models. xREI is available at http://***/xrei/.

关键词： Exploration Sequence Alignment Visualization Probabilistic Model Online resources Dissemination syntax expectation-maximisation algorithm file format

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Total variation norm for three-dimensional iterative reconstruction in limited view angle tomography

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PHYSICS IN MEDICINE AND BIOLOGY 2001年第3期46卷 853-866页

作者： Persson, M Bone, D Elmqvist, H Karolinska Inst Dept Med Engn S-14186 Huddinge Sweden

An iterative Bayesian reconstruction algorithm for limited view angle tomography, or ectomography, based on the three-dimensional total variation (TV) norm has been developed. The TV norm has been described ill the literature as a method for reducing noise in two-dimensional images while preserving edges, without introducing ringing or edge artefacts. It has also been proposed as a 2D regularization function in Bayesian reconstruction, implemented in an expectation maximization algorithm (TV-EM). The TV-EM was developed for 2D single photon emission computed tomography imaging, and the algorithm is capable of smoothing noise while maintaining edges without introducing artefacts. The TV norm was extended from 2D to 3D and incorporated into an ordered subsets expectation maximization algorithm for limited view angle geometry. The algorithm, called TV3D-EM, was evaluated using a modelled point spread function and digital phantoms. Reconstructed images were compared with those reconstructed with the 2D filtered backprojection algorithm currently used in ectomography. Results show a substantial reduction in artefacts related to the limited view angle geometry, and noise levels were also improved. Perhaps most important, depth resolution was improved by at least 45%. In conclusion, the proposed algorithm has been shown to improve the perceived image quality.

关键词： Image Processing Computer-Assisted Phantoms Imaging Tomography Emission-Computed 图像处理计算机辅助体模显象术体层摄影术发射型计算机 look angles (electronics) Imaging Paranormal phenomena Image processing Imaging Phantom expectation-maximisation algorithm depth resolution computer-assisted two dimentional images Television Tomography Image quality Artifacts

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Posterior Weighted Reinforcement Learning with State Uncertainty

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NEURAL COMPUTATION 2010年第5期22卷 1149-1179页

作者： Larsen, Tobias Leslie, David S. Collins, Edmund J. Bogacz, Rafal Univ Bristol Dept Comp Sci Bristol BS8 1UB Avon England Univ Bristol Dept Math Bristol BS8 1TW Avon England

Reinforcement learning models generally assume that a stimulus is presented that allows a learner to unambiguously identify the state of nature, and the reward received is drawn from a distribution that depends on that state. However, in any natural environment, the stimulus is noisy. When there is state uncertainty, it is no longer immediately obvious how to perform reinforcement learning, since the observed reward cannot be unambiguously allocated to a state of the environment. This letter addresses the problem of incorporating state uncertainty in reinforcement learning models. We show that simply ignoring the uncertainty and allocating the reward to the most likely state of the environment results in incorrect value estimates. Furthermore, using only the information that is available before observing the reward also results in incorrect estimates. We therefore introduce a new technique, posterior weighted reinforcement learning, in which the estimates of state probabilities are updated according to the observed rewards ( e. g., if a learner observes a reward usually associated with a particular state, this state becomes more likely). We show analytically that this modified algorithm can converge to correct reward estimates and confirm this with numerical experiments. The algorithm is shown to be a variant of the expectation-maximization algorithm, allowing rigorous convergence analyses to be carried out. A possible neural implementation of the algorithm in the cortico-basal-ganglia-thalamic network is presented, and experimental predictions of our model are discussed.

关键词： simply ignoring reinforcement learning longer immediately learning (artificial intelligence) state of the environment Reward expectation-maximisation algorithm Learning Uncertainty

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A comparison of imputation techniques for internal preference mapping, using Monte Carlo simulation

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FOOD QUALITY AND PREFERENCE 1995年第4期6卷 281-297页

作者： Hedderley, D Wakeling, I Institute of Food Research Earley Gate Whiteknights Road Reading RG6 6BZ UK

The usual algorithm for internal preference mapping requires a complete set of observations, meaning the technique cannot be used to analyse trials based on incomplete block designs. A simulation study was carried out to compare techniques for imputing missing values under various conditions. Sets of simulated preference data with different characteristics were constructed. Monte Carlo simulation was used to create missing observations in these sets;the imputation techniques were applied to the data;and the results of preference mapping based on the imputed data compared to those from the complete data set. Convergence problems were found with two techniques. Analysis of variance revealed that effects on performance were dominated by the proportion of data missing, the level of noise in the data, and the size of the data set. Differences in performance among the three convergent imputation techniques were small;mean substitution is recommended, as it performed as well as more complex iterative techniques. The results were broadly confirmed by a similar study on a genuine set of preference data.

关键词： preference mapping missing values imputation simulation expectation-maximisation algorithm row-column substitution algorithm MISTRESS algorithm PRINQUAL procedure mean substitution

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Bessel regression and bbreg package to analyse bounded data

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AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS 2021年第4期63卷 685-706页

作者： Barreto-Souza, Wagner Mayrink, Vinicius D. Simas, Alexandre B. King Abdullah Univ Sci & Technol Stat Program Thuwal 239556900 Makkah Saudi Arabia Univ Fed Minas Gerais Dept Estat Belo Horizonte MG Brazil Univ Fed Paraiba Dept Matemat Joao Pessoa Paraiba Brazil

Beta regression has been extensively used by statisticians and practitioners to model bounded continuous data without a strong competitor having the same main features. A class of normalised inverse-Gaussian (N-IG) process was introduced in the literature and has been explored in the Bayesian context as a powerful alternative to the Dirichlet process. Until this moment, no attention has been paid to the univariate N-IG distribution in the classical inference. In this paper, we propose the bessel regression based on the univariate N-IG distribution, which is an alternative to the beta model. The estimation of the parameters is done through an expectation-maximisation (EM) algorithm and the paper discusses how to perform inference. A useful and practical discrimination procedure is proposed for model selection between bessel and beta regressions. A new R package called bbreg is developed for fitting both bessel and beta regression models based on the EM-algorithm and further providing graphical tools for model adequacy and model selection as well. Proper documentation for this package is available. The performances of the models are evaluated under misspecification in a simulation study. An empirical illustration is explored to confront results from bessel and beta regressions by using the new R package bbreg.

关键词： beta regression expectation-maximisation algorithm normalised inverse-Gaussian distribution misspecification model selection

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Analysis of change in the presence of informative censoring: application to a longitudinal clinical trial of progressive renal disease

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STATISTICS IN MEDICINE 2001年第7期20卷 989-1007页

作者： Schluchter, MD Greene, T Beck, GJ Case Western Reserve Univ Rainbow Babies & Childrens Hosp Dept Pediat Div Clin Epidemiol & Biostat Cleveland OH 44106 USA Cleveland Clin Fdn Dept Biostat & Epidemiol Cleveland OH 44195 USA

The rate of change in a continuous variable, measured serially over time, is often used as an outcome in longitudinal studies or clinical trials. When patients terminate the study before the scheduled end of the study, there is a potential for bias in estimation of rate of change using standard methods which ignore the missing data mechanism. These methods include the use of unweighted generalized estimating equations methods and likelihood-based methods assuming an ignorable missing data mechanism. We present a model for analysis of informatively censored data, based on an extension of the two-stage linear random effects model, where each subject's random intercept and slope are allowed to be associated with an underlying time to event. The joint distribution of the continuous responses and the time-to-event variable are then estimated via maximum likelihood using the EM algorithm, and using the bootstrap to calculate standard errors. We illustrate this methodology and compare it to simpler approaches and usual maximum likelihood using data from a multi-centre study of the effects of diet and blood pressure control on progression of renal disease, the Modification of Diet in Renal Disease (MDRD) Study. Sensitivity analyses and simulations are used to evaluate the performance of this methodology in the context of the MDRD data, under various scenarios where the drop-out mechanism is ignorable as well as non-ignorable. Copyright (C) 2001 John Wiley & Sons, Ltd.

关键词： algorithms Analysis of Variance Data Interpretation Statistical Dietary Proteins 算法方差分析数据说明统计膳食蛋白质类肾功能衰竭慢性磷 Kidney Diseases event variable maximum likelihood expectation-maximisation algorithm algorithms Analysis of Variance Data interpretation Representation of data Dietary Proteins Clinical Trial change rate missing data

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Case-parent triads: Estimating single- and double-dose effects of fetal and maternal disease gene haplotypes

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ANNALS OF HUMAN GENETICS 2006年第3期70卷 382-396页

作者： Gjessing, HK Lie, RT Norwegian Inst Publ Hlth Div Epidemiol N-0403 Oslo Norway Univ Bergen Dept Publ Hlth & Primary Hlth Care Sect Epidemiol & Med Stat N-5020 Bergen Norway

Case-parent triad data are considered a robust basis for studying association between variants of a gene and a disease. Methods evaluating statistical significance of association, like the TDT-test and its extensions, are frequently used. When there are prior hypotheses of a causal effect of the gene under study, however, methods measuring penetrance of alleles or haplotypes as relative risks will be more informative. Log-linear models have been proposed as a flexible tool for such relative risk estimation. We demonstrate an extension of the log-linear model to a natural framework for also estimating effects of multiple alleles or haplotypes, incorporating both single- and double-dose effects. The model also incorporates effects of single- and double-dose maternal haplotypes on a fetus during pregnancy. Unknown phase of haplotypes as well as missing parents are accounted for by the EM algorithm. A number of numerical improvements to maximum likelihood estimation are also implemented to facilitate a larger number of haplotypes. Software for these analyses, HAPLIN, is publicly available through our web site. As an illustration we have re-analyzed data on the MSX1 homeobox-gene on chromosome 4 to show how haplotypes may influence the risk of oral clefts.

关键词： Risk estimation Chromosomes, Human, Pair 4 Relative Risk Fetus linear models expectation-maximisation algorithm Haplotypes maternal disease Penetrance maximum likelihood estimation multiple allele

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