On the inappropriateness of an EM algorithm based procedure for blinded sample size re-estimation by T. Friede and M. Kieser, Statistics in Medicine 2002; 21:165-176.
Explore the source record for details and available documents.
Algorithms↗
SEARCH · Search PubMed
Results for “EM algorithm”
Search indexed PubMed citations on genomics, clinical trials, systematic reviews and public health. Explore titles, authors and supplied subject terms, then open the PubMed record.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
Estimation of gametic frequencies from F2 populations using the EM algorithm and its application in the analysis of crossover interference in rice.
The gametes produced in meiosis provide information on the frequency of recombination and also on the interdependence of recombination events, i.e. interference. Using F(2) individuals, it is not possible in all cases to derive the gametes, which have fused, and which provide the information about interference unequivocally when three or more segregating markers are considered simultaneously. Therefore, a method was developed to estimate the gametic frequencies using a maximum likelihood approach together with the expectation maximisation algorithm. This estimation procedure was applied to F(2) mapping data from rice (Oryza sativa L.) to carry out a genome-wide analysis of crossover interference. The distribution of the coefficient of coincidence in dependence on the recombination fraction revealed for all chromosomes increasing positive interference with decreasing interval size. For some chromosomes this mutual inhibition of recombination was not so strong in small intervals. The centromere had a significant effect on interference. The positive interference found in the chromosome arms were reduced significantly when the intervals considered spanned the centromere. Two chromosomes even demonstrated independent recombination and slightly negative interference for small intervals including the centromere. Different marker densities had no effect on the results. In general, interference depended on the frequency of recombination events in relation to the physical length. The strength of the centromere effect on interference seemed to depend on the strength of recombination suppression around the centromere.
Centromere↗
Using the EM algorithm to weight data sets of unknown precision when modelling fish stocks.
Stocks of commercial fish are often modelled using sampling data of various types, of unknown precision, and from various sources assumed independent. We want each set to contribute to estimates of the parameters in relation to its precision and goodness of fit with the model. Iterative re-weighting of the sets is proposed for linear models until the weight of each set is found to be proportional to (relative weighting) or equal to (absolute weighting) the set-specific residual invariances resulting from a generalised least squares fit. Formulae for the residual variances are put forward involving fractional allocation of degrees of freedom depending on the numbers of independent observations in each set, the numbers of sets contributing to the estimate of each parameter, and the number of weights estimated. To illustrate the procedure, numbers of the 1984 year-class of North Sea cod (a) landed commercially each year, and (b) caught per unit of trawling time by an annual groundfish survey are modelled as a function of age to estimate total mortality, Z, relative catching power of the two fishing methods, and relative precision of the two sets of observations as indices of stock abundance. It was found that the survey abundance indices displayed residual variance about 29 times higher than that of the annual landings.
Algorithms↗
Evaluation of an EMS algorithm system. American College of Emergency Physicians Algorithm Review Subcommitte.
The American College of Emergency Physicians algorithm project was a pilot study designed to identify a method for evaluating algorithms by peer review and field test. The intent of the pilot project was to make recommendations which would permit a more extensive evaluation of the logic, usefulness, and safety of various algorithms. The project yielded a report which summarized the research design and suggests possible revisions to the phases of peer review, algorithm assignment, and field test. It is anticipated that the report will be used by the National Center for Health Services Research in developing a method to carefully assess the various algorithms developed to date prior to their widespread use. Presented here is the executive summary of the report.
Decision Making↗
An EM algorithm for obtaining maximum likelihood estimates in the multi-phenotype variance components linkage model.
In recent years variance components models have been developed for localising genes that contribute to human quantitative variation. In typical applications one assumes a multivariate normal model for phenotypes and estimates model parameters by maximum likelihood. For the joint analysis of several correlated phenotypes, however, finding the maximum likelihood estimates for an appropriate multivariate normal model can be a difficult computational task due to complex constraints among the model parameters. We propose an algorithm for computing maximum likelihood estimates in a multi-phenotype variance components linkage model that readily accommodates these parameter constraints. Data simulated for Genetic Analysis Workshop 10 are used to demonstrate the potential increase in power to detect linkage that can be obtained if correlated phenotypes are analysed jointly rather than individually.
Algorithms↗
An EM algorithm for mapping quantitative resistance loci.
Many disease resistance traits in plants have a polygenic background and the disease phenotypes are modified by environmental factors. As a consequence, the phenotypic values usually show a quantitative variation. The phenotypes of such disease traits, however, are often measured in discrete but ordered categories. These traits are called ordinal traits. In terms of disease resistance, they are called quantitative resistance traits, as opposed to qualitative resistance traits, and are controlled by the quantitative resistance loci (QRL). Classical quantitative trait locus mapping methods are not optimal for ordinal trait analysis because the assumption of normal distribution is violated. Methods for mapping binary trait loci are not suitable either because there are more than two categories in ordinal traits. We developed a maximum likelihood method to map these QRL. The method is implemented via a multicycle expectation-conditional-maximization (ECM) algorithm under the threshold model, where we can estimate both the QRL effects and the thresholds that link the disease liability and the categorical phenotype. The method is verified in simulated data under various combinations of the parameters. An SAS program is available to implement the multicycle ECM algorithm. The program can be downloaded from our website at www.statgen.ucr.edu.
Algorithms↗
HAPLO: a program using the EM algorithm to estimate the frequencies of multi-site haplotypes.
Explore the source record for details and available documents.
Algorithms↗
Adaptive snakes using the EM algorithm.
Deformable models (e.g., snakes) perform poorly in many image analysis problems. The contour model is attracted by edge points detected in the image. However, many edge points do not belong to the object contour, preventing the active contour from converging toward the object boundary. A new algorithm is proposed in this paper to overcome this difficulty. The algorithm is based on two key ideas. First, edge points are associated in strokes. Second, each stroke is classified as valid (inlier) or invalid (outlier) and a confidence degree is associated to each stroke. The expectation maximization algorithm is used to update the confidence degrees and to estimate the object contour. It is shown that this is equivalent to the use of an adaptive potential function which varies during the optimization process. Valid strokes receive high confidence degrees while confidence degrees of invalid strokes tend to zero during the optimization process. Experimental results are presented to illustrate the performance of the proposed algorithm in the presence of clutter, showing a remarkable robustness.
Algorithms↗
A Markov model for blind image separation by a mean-field EM algorithm.
This paper deals with blind separation of images from noisy linear mixtures with unknown coefficients, formulated as a Bayesian estimation problem. This is a flexible framework, where any kind of prior knowledge about the source images and the mixing matrix can be accounted for. In particular, we describe local correlation within the individual images through the use of Markov random field (MRF) image models. These are naturally suited to express the joint pdf of the sources in a factorized form, so that the statistical independence requirements of most independent component analysis approaches to blind source separation are retained. Our model also includes edge variables to preserve intensity discontinuities. MRF models have been proved to be very efficient in many visual reconstruction problems, such as blind image restoration, and allow separation and edge detection to be performed simultaneously. We propose an expectation-maximization algorithm with the mean field approximation to derive a procedure for estimating the mixing matrix, the sources, and their edge maps. We tested this procedure on both synthetic and real images, in the fully blind case (i.e., no prior information on mixing is exploited) and found that a source model accounting for local autocorrelation is able to increase robustness against noise, even space variant. Furthermore, when the model closely fits the source characteristics, independence is no longer a strict requirement, and cross-correlated sources can be separated, as well.
Algorithms↗
The impact of the EM algorithm on medical statistics.
Explore the source record for details and available documents.
Acquired Immunodeficiency Syndrome↗
Alternative implementations of Monte Carlo EM algorithms for likelihood inferences.
Two methods of computing Monte Carlo estimators of variance components using restricted maximum likelihood via the expectation-maximisation algorithm are reviewed. A third approach is suggested and the performance of the methods is compared using simulated data.
Algorithms↗
The EM algorithm for the mover-stayer model.
Explore the source record for details and available documents.
Algorithms↗
Haplotype analysis of VDR gene polymorphisms: a meta-analysis.
INTRODUCTION: Although many studies have addressed the relationship between multiple individual polymorphisms in the vitamin D receptor (VDR) gene and bone health, few have analyzed this data in terms of haplotypes. We performed a meta-analysis of studies with data on the BsmI, ApaI, and TaqI polymorphisms in order to (a) estimate haplotype frequencies, (b) determine linkage disequilibrium (LD), and (c) estimate the magnitude of the association between haplotypes and osteoporosis/bone mineral density (BMD). METHODS: Haplotypes were inferred using the expectation-maximization algorithm (EM); log-linear models were used to determine association with osteoporosis; and regression analysis with variance components was used to determine association with BMD. RESULTS: Our results indicate that the most common haplotype for the VDR gene, regardless of ethnicity, is baT, followed by BAt and bAT in Caucasians, and bAT and BaT in Asians. This indicates strong LD between the BsmI and TaqI polymorphisms. We demonstrate a gain in power when considering the haplotypes rather than the individual polymorphisms separately, i.e., although BsmI, ApaI, and TaqI were not significantly associated with osteoporosis on their own, the haplotypes Bat and BAt were significantly associated, with an OR of approximately 4. CONCLUSION: We have applied haplotype analysis to the VDR polymorphisms and bone measures. We also highlight a number of methodologic issues, including linkage disequilibrium, the robustness of the EM algorithm in this context, and the potential for exploring effect modification.
Bone Density↗
CARTHAGENE: constructing and joining maximum likelihood genetic maps.
Genetic mapping is an important step in the study of any organism. An accurate genetic map is extremely valuable for locating genes or more generally either qualitative or quantitative trait loci (QTL). This paper presents a new approach to two important problems in genetic mapping: automatically ordering markers to obtain a multipoint maximum likelihood map and building a multipoint maximum likelihood map using pooled data from several crosses. The approach is embodied in an hybrid algorithm that mixes the statistical optimization algorithm EM with local search techniques which have been developed in the artificial intelligence and operations research communities. An efficient implementation of the EM algorithm provides maximum likelihood recombination fractions, while the local search techniques look for orders that maximize this maximum likelihood. The specificity of the approach lies in the neighborhood structure used in the local search algorithms which has been inspired by an analogy between the marker ordering problem and the famous traveling salesman problem. The approach has been used to build joined maps for the wasp Trichogramma brassicae and on random pooled data sets. In both cases, it compares quite favorably with existing softwares as far as maximum likelihood is considered as a significant criteria.
Algorithms↗
A three-state disease model with interval-censored data: estimation and applications to AIDS and cancer.
In presence of interval-censored data, we propose a general three-state disease model with covariates. Such data can arise, for example, in epidemiologic studies of infectious disease where both the times of infection and disease onset are not directly observed, or in cancer studies where the time of disease metastasis is known up to a specified interval. The proposed model allows the distributions of the transition times between states to depend on covariates and the time in the previous state. An estimation procedure for the underlying distributions and the model coefficients is suggested with the EM algorithm. The EMS algorithm (Smoothed EM algorithm) is also considered to obtain smooth estimates of the distributions. The proposed method is illustrated with data from an AIDS study and a study of patients with malignant melanoma.
Acquired Immunodeficiency Syndrome↗
Partially supervised learning using an EM-boosting algorithm.
Training data in a supervised learning problem consist of the class label and its potential predictors for a set of observations. Constructing effective classifiers from training data is the goal of supervised learning. In biomedical sciences and other scientific applications, class labels may be subject to errors. We consider a setting where there are two classes but observations with labels corresponding to one of the classes may in fact be mislabeled. The application concerns the use of protein mass-spectrometry data to discriminate between serum samples from cancer and noncancer patients. The patients in the training set are classified on the basis of tissue biopsy. Although biopsy is 100% specific in the sense that a tissue that shows itself to have malignant cells is certainly cancer, it is less than 100% sensitive. Reference gold standards that are subject to this special type of misclassification due to imperfect diagnosis certainty arise in many fields. We consider the development of a supervised learning algorithm under these conditions and refer to it as partially supervised learning. Boosting is a supervised learning algorithm geared toward high-dimensional predictor data, such as those generated in protein mass-spectrometry. We propose a modification of the boosting algorithm for partially supervised learning. The proposal is to view the true class membership of the samples that are labeled with the error-prone class label as missing data, and apply an algorithm related to the EM algorithm for minimization of a loss function. To assess the usefulness of the proposed method, we artificially mislabeled a subset of samples and applied the original and EM-modified boosting (EM-Boost) algorithms for comparison. Notable improvements in misclassification rates are observed with EM-Boost.
Algorithms↗
EM reconstruction algorithms for emission and transmission tomography.
Two proposed likelihood models for emission and transmission image reconstruction accurately incorporate the Poisson nature of photon counting noise and a number of other relevant physical features. As in most algebraic schemes, the region to be reconstructed is divided into small pixels. For each pixel a concentration or attenuation coefficient must be estimated. In the maximum likelihood approach these parameters are estimated by maximizing the likelihood (probability of the observations). EM algorithms are iterative techniques for finding maximum likelihood estimates. In this paper we discuss the general principles behind all EM algorithms and derive in detail the specific algorithms for emission and transmission tomography. The virtues of the EM algorithms include (a) accurate incorporation of a good physical model, (b) automatic inclusion of non-negativity constraints on all parameters, (c) an excellent measure of the quality of a reconstruction, and (d) global convergence to a single vector of parameter estimates. We discuss the specification of necessary physical features such as source and detector geometries. Actual reconstructions are deferred to a later time.
Fourier Analysis↗
Bayesian Gaussian process classification with the EM-EP algorithm.
Gaussian process classifiers (GPCs) are Bayesian probabilistic kernel classifiers. In GPCs, the probability of belonging to a certain class at an input location is monotonically related to the value of some latent function at that location. Starting from a Gaussian process prior over this latent function, data are used to infer both the posterior over the latent function and the values of hyperparameters to determine various aspects of the function. Recently, the expectation propagation (EP) approach has been proposed to infer the posterior over the latent function. Based on this work, we present an approximate EM algorithm, the EM-EP algorithm, to learn both the latent function and the hyperparameters. This algorithm is found to converge in practice and provides an efficient Bayesian framework for learning hyperparameters of the kernel. A multiclass extension of the EM-EP algorithm for GPCs is also derived. In the experimental results, the EM-EP algorithms are as good or better than other methods for GPCs or Support Vector Machines (SVMs) with cross-validation.
Algorithms↗