PubMed Health⌕ Search

SEARCH · PubMed Health

Results for “EM algorithm”

Explore indexed PubMed citations for clinical trials, systematic reviews and public health research. Read source abstracts and follow each citation to its original PubMed record.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 19 recordsLinked to original sources
PubMed1989

Trials, tribulations, and triumphs of the EM algorithm in pedigree analysis.

The EM algorithm is an iterative method for finding maximum-likelihood estimates. Its advantages often include numerical stability, simplicity of computer implementation, and natural incorporation of parameter constraints. However, the EM algorithm must be tailored to each specific problem. Smith (1957) and Ott (1977, 1979) have accomplished this for a variety of problems in human pedigree analysis. The present paper clarifies their theory by presenting it from a modern perspective. Five practical numerical examples are also given in an attempt to assess the value of the EM algorithm in realistic genetic modelling. These examples deal with racial admixture, linkage homogeneity, classical segregation analysis, a Mendelian latent trait model for schizophrenia, and a heterozygote detection assay for Ataxia-telangiectasia. Comparison with a quasi-Newton method of optimization reveals that the EM algorithm generally converges more slowly, but also more stably.

Algorithms↗
PubMedDate not supplied

Application of the EM algorithm to radiographic images.

The expectation maximization (EM) algorithm has received considerable attention in the area of positron emitted tomography (PET) as a restoration and reconstruction technique. In this paper, the restoration capabilities of the EM algorithm when applied to radiographic images is investigated. This application does not involve reconstruction. The performance of the EM algorithm is quantitatively evaluated using a "perceived" signal-to-noise ratio (SNR) as the image quality metric. This perceived SNR is based on statistical decision theory and includes both the observer's visual response function and a noise component internal to the eye-brain system. For a variety of processing parameters, the relative SNR (ratio of the processed SNR to the original SNR) is calculated and used as a metric to compare quantitatively the effects of the EM algorithm with two other image enhancement techniques: global contrast enhancement (windowing) and unsharp mask filtering. The results suggest that the EM algorithm's performance is superior when compared to unsharp mask filtering and global contrast enhancement for radiographic images which contain objects smaller than 4 mm.

Algorithms↗
PubMed1988

Fitting mixture models to grouped and truncated data via the EM algorithm.

The fitting of finite mixture models via the EM algorithm is considered for data which are available only in grouped form and which may also be truncated. A practical example is presented where a mixture of two doubly truncated log-normal distributions is adopted to model the distribution of the volume of red blood cells in cows during recovery from anemia.

Algorithms↗
PubMed1988

An alternative two stage method via the EM-algorithm for the estimation of population pharmacokinetic parameters.

There has been a considerable increase in popularity of the NONMEM method as a technique for estimating population pharmacokinetic parameters. The authors present another approach to population pharmacokinetic analysis, the alternative two stage method (ATS). ATS uses the EM-algorithm for maximizing the likelihood of variance components. The performance of ATS was compared with the NONMEM method on a microcomputer. Simulation studies showed that the precision and accuracy of estimates obtained with ATS were comparable to the NONMEM method, however, the computation time, dependences on initial estimates and convergence properties were somewhat different. ATS could be a valuable alternative to the NONMEM method for estimating population pharmacokinetic parameters in some cases.

Algorithms↗
PubMed1990

On the estimation of the age at onset distribution in Huntington's chorea using the EM algorithm.

Huntington's chorea is a late onset disease of the nervous system whose mode of inheritance conforms to the autosomal dominant model. The present paper shows how the problem of estimating the distribution of age at onset of the disease can be dealt with as an incomplete data problem via the EM algorithm, both in the parametric and non-parametric setting. In this way it is possible to take into account not only the heterozygotes in the population under study who are manifestly affected, but also those who are apparently unaffected. The estimation of the distribution of age at onset of the disease is required for estimating the posterior probability of heterozygosity of the individual at risk using Bayes' theorem. The proposed approach was applied to data derived from a survey carried out on the population of Latium, Italy.

Adolescent↗
PubMed1988

The EM algorithm for maximum likelihood estimation in the mover-stayer model.

The discrete-time mover-stayer model (Blumen, Kogan, and McCarthy, 1955, The Industrial Mobility of Labor as a Probability Process, Ithaca, New York: Cornell University Press) is a useful model for studying changes over time in heterogeneous populations. Using the EM algorithm, we present an alternative method for obtaining maximum likelihood estimates of the parameters of the mover-stayer model, and consider an extension of the basic model to the problem of incomplete follow-up in panel studies. The models and the methods are illustrated with data from a community-based survey of changes in mental health status over a 1-year period.

Algorithms↗
PubMed1990

An expectation maximization (EM) algorithm for the identification and characterization of common sites in unaligned biopolymer sequences.

Statistical methodology for the identification and characterization of protein binding sites in a set of unaligned DNA fragments is presented. Each sequence must contain at least one common site. No alignment of the sites is required. Instead, the uncertainty in the location of the sites is handled by employing the missing information principle to develop an "expectation maximization" (EM) algorithm. This approach allows for the simultaneous identification of the sites and characterization of the binding motifs. The reliability of the algorithm increases with the number of fragments, but the computations increase only linearly. The method is illustrated with an example, using known cyclic adenosine monophosphate receptor protein (CRP) binding sites. The final motif is utilized in a search for undiscovered CRP binding sites.

Algorithms↗
PubMed1977

Counting methods (EM algorithm) in human pedigree analysis: linkage and segregation analysis.

The likelihood of human pedigree data can be written in such a form as to allow the computation of derivatives. This is done for various parameters in linkage and segregation analysis. The equations for the maximum likelihood estimates are represented in a particularly appealing form which allows iterative solutions. This process is an extension to pedigress of Smith's (1957) counting methods. All these procedures belong to a general class of MLE methods for incomplete data called EM algorithms (Dempster et al. 1976).

Gene Frequency↗
PubMed1992

Semiparametric estimation of random effects using the Cox model based on the EM algorithm.

Consider a survival experiment where individuals within a certain subset of the population share a common, unobservable, random frailty. Such a frailty could be an unobservable genetic or early environmental effect if individuals were in sibling groups or an environmental effect if individuals were grouped by households. Suppose that if the frailty, omega, is known, the Cox proportional hazards model for the observable covariates is valid with the consequence of the random effect being a multiplicative factor on the hazard rate. Assuming tht the random frailties follow a gamma distribution, estimates of the fixed and random effects are obtained by using an EM algorithm based on a profile likelihood construction. The method developed is applied to the Framingham Heart Study to examine the risks of smoking and cholesterol levels, adjusting for potential random effects.

Adult↗
PubMed1989

Statistical evaluation of cell kinetic data from DNA flow cytometry (FCM) by the EM algorithm.

Flow cytometric DNA measurements yield the amount of DNA for each of a large number of cells. A DNA histogram normally consists of a mixture of one or more constellations of G0/G1-, S-, G2/M-phase cells, together with internal standards, debris, background noise, and one or more populations of clumped cells. We have modelled typical DNA histograms as a mixed distribution with Gaussian densities for the G0/G1 and G2/M phases, an S-phase density, assumed to be uniform between the G0/G1 and G2/M peaks, observed with a Gaussian error, and with Gaussian densities for standards of chicken and trout red blood cells. The debris is modelled as a truncated exponential distribution, and we also have included a uniform background noise distribution over the whole observation interval. We have explored a new approach for maximum-likelihood analyses of complex DNA histograms by the application of the EM algorithm. This algorithm was used for four observed DNA histograms of varying complexity. Our results show that the algorithm works very well, and it converges to reasonable values for all parameters. In simulations from the estimated models, we have investigated bias, variance, and correlations of the estimates.

Algorithms↗
PubMed1989

Correction of nonuniform attenuation in cardiac SPECT imaging.

Correction for photon attenuation in cardiac SPECT imaging using a measured attenuation distribution with an iterative expectation maximization (EM) algorithm and an iterative Chang algorithm were compared with the conventional filtered backprojection and an iterative EM algorithm without attenuation correction. The attenuation distribution was determined from a transmission computed tomography study that was obtained using an external collimated sheet source. The attenuation of the emitting photons was modeled in the EM algorithm by an attenuated projector-backprojector that used the estimated attenuation distribution to calculate attenuation factors for each pixel along each projection and backprojection ray. Results from a heart-lung phantom study and a 201Tl patient study demonstrated that the iterative EM algorithm with attenuation correction provided improved image quality in terms of reduced streak artifacts and noise, and more accurate quantitative information in terms of improved radioactivity distribution uniformity where uniformity existed, and better anatomic object definition.

Algorithms↗
PubMed1991

Counting algorithms for linkage: correction to Morton and Collins.

In a recent paper, Morton & Collins (1990) claimed: (1) that the Lander-Green algorithm for genetic linkage analysis is not the EM algorithm for finding the maximum likelihood map; and (2) that a proposed alternative algorithm does have these properties. Here, we show that these assertions are both incorrect: the Lander-Green algorithm is an EM algorithm, while the Morton-Collins algorithm is not. We note that Morton and Collins concur with these conclusions.

Algorithms↗
PubMed1992

Computer-assisted analysis of mixtures (C.A.MAM): statistical algorithms.

This paper presents various algorithmic approaches for computing the maximum likelihood estimator of the mixing distribution of a one-parameter family of densities and provides a unifying computer-oriented concept for the statistical analysis of unobserved heterogeneity (i.e., observations stemming from different subpopulations) in a univariate sample. The case with unknown number of population subgroups as well as the case with known number of population subgroups, with emphasis on the first, is considered in the computer package C.A.MAN (Computer Assisted Mixture Analysis). It includes an algorithmic menu with choices of the EM algorithm, the vertex exchange algorithm, a combination of both, as well as the vertex direction method. To ensure reliable convergence, a step-length menu is provided for the three latter methods, each achieving monotonicity for the direction of choice. C.A.MAN has the option to work with restricted support size-that is, the case when the number of components is known a priori. In the latter case, the EM algorithm is used. Applications of mixture modelling in medical problems are discussed.

Algorithms↗
PubMed1992

Three-dimensional SPECT reconstruction of combined cone beam and parallel beam data.

Single photon emission computed tomography (SPECT) using cone beam (CB) collimation exhibits increased sensitivity compared with acquisition geometries using parallel (P) hole collimation. However, CB collimation has a smaller field-of-view which may result in truncated projections and image artifacts. A primary objective of this work is to investigate maximum likelihood-expectation maximization (ML-EM) methods to reconstruct simultaneously acquired parallel and cone beam (P&CB) SPECT data. Simultaneous P&CB acquisition can be performed with commercially available triple camera systems by using two cone-beam collimators and a single parallel-hole collimator. The loss in overall sensitivity (relative to the use of three CB collimators) is about 15 to 20%. We have developed three methods to combine P&CB data using modified ML-EM algorithms. The first method consists of using both data sets to reconstruct a single intermediate image after each iteration using the ML-EM algorithm. The other two iterative algorithms combine intermediate parallel beam (PB) and CB source estimates to enhance image quality. For these methods, a PB estimate and a CB estimate are obtained for the first iteration. The second method consists of summing the PB and CB estimates for each subsequent iteration to obtain new PB and CB estimates. The third method is similar to the second method, with the exception that the new PB estimate simply is set equal to the PB estimate after each iteration. The combined source estimate is used in each subsequent iteration step of the EM algorithm. These algorithms are evaluated using projection data simulated using a Monte Carlo SPECT model. The P&CB SPECT images demonstrate marked improvement as compared with the CB-only reconstruction, particularly when the projections are truncated.

Algorithms↗
PubMed1989

Probits of mixtures.

The tolerances of individuals (insects, parasites) in a population have a frequency or probability distribution called a tolerance distribution. Many tolerance distributions in bioassay studies can be the result of a rather heterogeneous population of individuals and can often be modelled as a mixture of a number of standard unimodal distributions. A probit analysis can be generalized to the case where the tolerance distribution is a mixture of location and scale parameter distributions. In this article, the existence and determination of the maximum likelihood estimates are investigated. An expectation-maximization (EM) algorithm for probits of mixtures is developed and it is shown that by application of the EM algorithm, the problem of probits of mixtures can be separated into a series of probits of individual component tolerance distributions.

Algorithms↗
PubMed2026

ADAMIXTURE: adaptive first-order optimization for biobank-scale genetic clustering.

MOTIVATION: Estimating genetic clusters from sequencing data is a fundamental task in population and medical genetics, enabling demographic inference and adjustment for population structure in association studies. ADMIXTURE, a widely used model-based clustering method, employs an accelerated Expectation-Maximization (EM) algorithm to infer population parameters; however, its computational demands scale poorly, limiting its usefulness for modern biobank-sized datasets. While recent EM acceleration strategies employing second-order quasi-Newton schemes preserve accuracy, they remain computationally intensive. Conversely, EM-free approaches that prioritize speed often compromise solution quality. RESULTS: We introduce ADAMIXTURE, a novel optimization framework that integrates the EM algorithm with Adaptive Moment Estimation (Adam). Unlike traditional acceleration methods, ADAMIXTURE utilizes first-order gradients with adaptive learning rates derived from raw and squared moments to approximate curvature information, bypassing the computational overhead of Hessian approximations. This approach surpasses the convergence efficiency of second-order methods while maintaining the low computational complexity of first-order updates. Across simulated and large-scale empirical datasets, ADAMIXTURE demonstrates substantial reductions in wall-clock runtime and enhanced scalability compared to state-of-the-art methods, while maintaining comparable or improved inference accuracy. Its GPU implementation runs in under 2 h on half a million samples and variants, a two order of magnitude speedup over current state-of-the-art. AVAILABILITY AND IMPLEMENTATION: Source code is available at: https://github.com/AI-sandbox/ADAMIXTURE.

Clustering Algorithms↗