Frailty-Augmented Logistic-Weighted Lomax Mixture regression for survival analysis

Using incremental general regression neural network for learning mixture models from incomplete data

Most of the current QTL mapping methods are developed for the backcross and F2 populations. The inter-crossed F3 population is also popular and has been well devised in genetic study. As the F3 population can provide more recombinants than the backcross and F2 populations, it can facilitate the detection of closely linked QTL. In this paper, we propose a statistical model to estimate the effects and positions of QTL for the F3 population by considering the differences in the genome structure between the F3 and F2 populations. As the genotypes of QTL are usually unknown, the statistical model is a finite mixture model. By treating the mixture model as an incomplete data problem, the EM algorithm is implemented to obtain the maximum likelihood estimates of the parameters. Simulations were used to illustrate the performance of the proposed method and evaluate the relative efficiency in the F3 population (as comparing to that of the F2 population) in QTL mapping under several factors, such as sample size, genetic distance between QTL (and markers), the proportion of trait variance contributed by QTL (i.e. heritability). It is found that the QTL mapping by using the F3 population is more powerful and precise in separating closely linked QTL and in estimating the parameters as compare to the use of the F2 population, especially for small sample size, close genetic distance and low heritability. The paper can help outline a strategy of detecting tightly linked QTL for the advanced intercross populations to improve the resolution of genetic architecture of quantitative traits.

In statistical classification, such mixture models allow a formal approach to unsupervised clustering. Fitting mixture distributions can be handled by a wide variety of techniques. A standard method to fit finite mixture models to observed data is the Expectation-Maximization (EM) algorithm which is an iterative procedure which converges to a (local) maximum of the marginal a posteriori probability function. In this paper we provide a review on the Gaussian classification for polarimetric images. In this review work, the analysis of multi-look polarimetric covariance matrix data uses an automated statistical clustering method based upon the expectation maximization (EM) algorithm for finite mixture modeling, using the complex Wishart probability density function. This classification technique is compared to that obtained with the most known standard H/ decomposition combined to the Wishart distribution which gives 8 fixed classes identified from the H/ space, in opposite to the EM-Wishart classifiaction which automatically determines the number of statistically distinct clusters in finite mixture modeling in an image using the Goodness-of-fit (GoF) and more than eight classes can be identified. Both approaches conducted on the polarimetric images show very convincing clustering results.

The expectation-maximization (EM) algorithm is a popular approach for parameter estimation of finite mixture model (FMM). A drawback of this approach is that the number of components of the finite mixture model is not known in advance, nevertheless, it is a key issue for EM algorithms. In this paper, a penalized minimum matching distance-guided EM algorithm is discussed. Under the framework of Greedy EM, a fast and accurate algorithm for estimating the number of components of the Gaussian mixture model (GMM) is proposed. The performance of this algorithm is validated via simulative experiments of univariate and bivariate Gaussian mixture models.

Many diseases show dichotomous phenotypic variation but do not follow a simple Mendelian pattern of inheritance. Variances of these binary diseases are presumably controlled by multiple loci and environmental variants. A least-squares method has been developed for mapping such complex disease loci by treating the binary phenotypes (0 and 1) as if they were continuous. However, the least-squares method is not recommended because of its ad hoc nature. Maximum Likelihood (ML) and Bayesian methods have also been developed for binary disease mapping by incorporating the discrete nature of the phenotypic distribution. In the ML analysis, the likelihood function is usually maximized using some complicated maximization algorithms (e.g. the Newton-Raphson or the simplex algorithm). Under the threshold model of binary disease, we develop an Expectation Maximization (EM) algorithm to solve for the maximum likelihood estimates (MLEs). The new EM algorithm is developed by treating both the unobserved genotype and the disease liability as missing values. As a result, the EM iteration equations have the same form as the normal equation system in linear regression. The EM algorithm is further modified to take into account sexual dimorphism in the linkage maps. Applying the EM-implemented ML method to a four-way-cross mouse family, we detected two regions on the fourth chromosome that have evidence of QTLs controlling the segregation of fibrosarcoma, a form of connective tissue cancer. The two QTLs explain 50-60% of the variance in the disease liability. We also applied a Bayesian method previously developed (modified to take into account sex-specific maps) to this data set and detected one additional QTL on chromosome 13 that explains another 26% of the variance of the disease liability. All the QTLs detected primarily show dominance effects.

Using general regression with local tuning for learning mixture models from incomplete data sets

In the statistical modeling framework, the form of the income distribution can be approaching based on certain statistical distributions. The use of the finite mixture model is relatively flexible in the modeling of the income distribution that has a multimodal pattern. The multimodal pattern can be indicated as the existence of different cluster on the data. The different clusters which can reflect the economic homogeneity of income are represented by the mixture components of the finite mixture model. In this paper, the finite mixture model is implemented for modeling the distribution of household income per capita in Indonesia based on The Fifth Wave of the Indonesia Family Life Survey (IFLS5) 2014-2015. The mixture components of the finite mixture model have been build based on the heavy-tailed statistical distributions, i.e., gamma, lognormal, and Weibull distributions. The estimation of the fitting finite mixture model was conducted using the maximum-likelihood estimation method through the expectation-maximization (EM) algorithm. The suitable finite mixture models were verified with the bootstrap likelihood ratio statistics test, Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC). Based on the results, the distribution of household income per capita in Indonesia can be modeled by the four components-lognormal mixture model.

Monte Carlo based thermal radiative transfer (TRT) codes provide a flexible framework for large-scale high-energy-density simulations. Compared to their deterministic counterparts, Monte Carlo methods are easier to implement in complex geometries and higher dimensions. However, the probabilistic nature of the Monte Carlo approach and the complexity of the underlying TRT equations describing nonlinear interactions between radiation and matter imply that Monte Carlo radiation transport codes involve massive amounts of particle data and have enormous memory footprints. This study is focused on building a statistical learning framework that can be employed to `compress' IMC data into a few probability density functions characterized by a relatively small number of distribution parameters. In order to learn complex distributions describing Monte Carlo data, we employ the Expectation Maximization (EM) method and finite mixture models adapted to learn particle distributions in the energy and angular domains targeting Implicit Monte Carlo (IMC) simulations in 1-d. Specifically, we couple EM iteration to the weighted hyper-Erlang finite mixture model in order to learn parameters of the photon distributions. We couple the EM iteration to the von Mises (Circular Normal) finite mixture model in order to learn angular distributions. The learning approach proposed in this study promises accurate resampling and significant memory savings at checkpointing and restarts of the IMC and other Monte Carlo radiation transport codes.

Process task duration data often exhibit multiple peaks, indicating differences in, for example, customer ages and preferences, resource capabilities or the day/hour of a week. This heterogeneous data, which captures diverse customer patterns, should be represented using different models, resulting in an overall mixture model. This paper introduces gamma mixture models to represent various customer patterns in task duration data, with a focus on automating the fitting process. The approach involves a two-stage procedure: first, divide-and-conquer using peak-, equidistance- and cluster-based techniques to partition data, and automatically fit gamma distributions to each subset. The second stage then improves the fitted mixture model by directly searching the log-likelihood surface. The method is compared with the expectation–maximization (EM) algorithm and an open tool (HyperStar), using both artificially generated datasets and a publicly available hospital billing dataset, demonstrating its effectiveness and time efficiency in modelling heterogeneous process duration data. Furthermore, a case study on process conformance checking is conducted using the hospital billing dataset, highlighting a potential application area for the method in process mining.

Recently, the expectation maximisation (EM) algorithm has been applied to a lot of problems of estimating parameters and learning and there are some theoretical analyses, however, prediction error is not mentioned yet. We are trying to evaluate the learning error when a machine learns with the EM algorithm and the probability distribution of the estimated parameters is mentioned here as the first step for the learning curve.

Left Ventricular Diastolic Dysfunction (LVDD) is a decompensatory change in the relaxation properties of the heart, the risk for which increases with age. Currently, physicians use a decision-tree-like algorithm to distinguish between discrete LVDD levels. This approach, based on cut-off thresholds, can potentially lead to information loss and possibly to misdiagnosis. This paper aims to explore an alternative diagnostic method to determine LVDD risk level, taking into account a wide variety of attributes available in patient records, without pre-setting cut-off thresholds. Using a large dataset derived from the Baltimore Longitude Study of Aging (BLSA), and adjusting the data for age and gender, we employ the Chi Square test and the information gain criterion to identify attributes that correlate well with the physician-assigned grades; such attributes are referred to as distinguishing attributes. We then apply the expectation maximization (EM) algorithm, as well as the K-Means, in order to cluster records that are represented using distinguishing attributes. While clusters resulting from the K-Means are not stable, three stable and tightly-formed clusters, which are obtained from the EM algorithm, roughly correspond to the physician-assigned categories. Based on the results from the EM algorithm, we can compute a patient's probability to have low, high or no risk for LVDD, and use this probability as a basis for defining a risk score to determine the patient's LVDD severity.

Objective: Data being missed is an unavoidable problem in cohort studies. This paper compares the imputation effect of eight common missing data imputation methods involved in cutting longitudinal data through simulation study to provide a valuable reference for the treatment of missing data in longitudinal studies. Methods: The simulation study is based on R language software and generates missing longitudinal data by the Monte Carlo method. By comparing the average absolute deviation, average relative deviation, and TypeⅠerror from the regression analysis of different imputation methods, the imputation effect of varying imputation methods on missing longitudinal data and the influence on subsequent multivariate analysis are evaluated. Results: The mean imputation, k nearest neighbor (KNN), regression imputation, and random forest all have a similar imputation effect, which is also steady. However, the hot deck is inferior to the above imputation methods. K-means clustering and expectation maximization (EM) algorithm are among the worst and unstable. Mean imputation, EM algorithm, random forest, KNN, and regression imputation can control TypeⅠerror. Still, multiple imputations, hot deck, and K-means clustering cannot effectively manage the TypeⅠerror. Conclusions: For missing data in longitudinal studies, mean imputation, KNN, regression imputation, and random forest can be used as better imputation methods under the mechanism of missing at random. When the missing ratio is not too large, multiple imputations and hot deck can also perform well, but K-means clustering and EM algorithm are not recommended.

Methodology for PET system modeling using image-space techniques in the expectation maximization (EM) algorithm is presented. The approach, applicable to both list-mode data and projection data, is of particular significance to EM algorithm implementations which otherwise only use basic system models (such as those which calculate the system matrix elements on the fly). A basic version of the proposed technique can be implemented using image-space convolution, in order to include resolution effects into the system matrix, so that the EM algorithm gradually recovers the modeled resolution with each update. The improved system modeling (achieved by inclusion of two convolutions per iteration) results in both enhanced resolution and lower noise, and there is often no need for regularization-other than to limit the number of iterations. Tests have been performed with simulated list-mode data and also with measured projection data from a GE Advance PET scanner, for both [/sup 18/F]-FDG and [/sup 124/I]-NaI. The method demonstrates improved image quality in all cases when compared to the conventional FBP and EM methods presently used for clinical data (which do not include resolution modeling). The benefits of this approach for /sup 124/I (which has a low positron yield and a large positron range, usually resulting in noisier and poorer resolution images) are particularly noticeable.

In this work, an expectation maximization (EM) algorithm is derived for maximum likelihood estimation of the autocorrelation function of a linear distortion channel as well as the level of additive noise, under the assumption that the source signal comes from a mixture of Gaussian sources. To facilitate parameter initialization in the EM algorithm, a correlation-matching based estimation algorithm is developed for the channel autocorrelation function. The proposed EM algorithm was evaluated on speech-derived simulated data of multiple autoregressive Gaussian sources and real speech of isolated digits under signal-to-noise ratios (SNRs) of 20 dB down to 0 dB. The algorithm is shown to produce convergent estimation results as well as estimates of signal statistics that lead to significantly improved classification accuracy under additive and convolutive noise conditions.

We are interested in an estimate of the usual residents in the Netherlands. Capture-recapture estimation with three registers enables us to estimate the size of the total population, of which the usual residents are a part. However, usual residence cannot be used as a covariate because it is not available in one of the registers. We approach this as a missing data problem. There are different methods available to handle missing data. In this manuscript we use Expectation Maximization (EM) algorithm and Predictive Mean Matching (PMM). The EM algorithm is often used in categorical data analysis, but PMM has the advantage of flexibility in the choice for a specific part of the observed data used for the imputation of the missing data. Four scenarios have been identified where the missing data are completed via either the EM algorithm or PMM imputation, resulting in different population size estimates for usual residence. It was found that the different scenarios lead to different population size estimates. Even small changes in the completed data lead to different population size estimates. In this study PMM imputation performs best according flexibility and it is theoretically better motivated.