Parameters Of Mixture Model Research Articles

A methodological framework for characterizing fish swimming and escapement behaviors in trawls.

Knowledge about fish behavior is crucial to be able to influence the capture process and catch species composition. The rapid expansion of the use of underwater cameras has facilitated unprecedented opportunities for studying the behavior of species interacting with fishing gears in their natural environment. This technological advance would greatly benefit from the parallel development of dedicated methodologies accounting for right-censored observations and variable observation periods between individuals related to instrumental, environmental and behavioral events. In this paper we proposed a methodological framework, based on a parametric Weibull mixture model, to describe the process of escapement attempts through time, test effects of covariates and estimate the probability that a fish will attempt to escape. We additionally proposed to better examine the escapement process at the individual level with regard to the temporal dynamics of escapement over time. Our approach was used to analyze gadoids swimming and escapement behaviors collected using a video set up in front of a selective device known to improve selectivity on gadoids in the extension of a bottom trawl. Comparison of the fit of models indicates that i) the instantaneous rate of escape attempts is constant over time and that the escapement process can be modelled using an exponential law; ii) the mean time before attempting to escape increases with the increasing number of attempts; iii) more than 80% of the gadoids attempted to escape through the selective device; and iv) the estimated probability of success was around 15%. Effects of covariates on the probability of success were investigated using binomial regression but none of them were significant. The data set collected is insufficient to make general statements, and further observations are required to properly investigate the effect of intrinsic and extrinsic factors governing gadoids behavior in trawls. This methodology could be used to better characterize the underlying behavioral process of fish in other parts of a bottom trawl or in relation to other fishing gears.

ON4 Heterogeneity in Survival with Immuno-Oncologic Therapy and Its Implications for Survival Extrapolations: A Case Study in Untreated Metastatic Melanoma

Short clinical trial follow-up periods at the time of submission and heterogeneity in outcomes often introduce uncertainty in the health technology assessment of immuno-oncologic (IO) therapies. To address this, some agencies prefer to use conservative methods for survival extrapolation. To evaluate the predictive accuracy of various survival extrapolation methods using data from CheckMate 067, a phase III trial of nivolumab plus ipilimumab (NIVO+IPI) vs either monotherapy in untreated metastatic melanoma. Six different extrapolation models were independently fitted to overall survival (OS) data for the three arms of CheckMate 067 using successive database locks (DBL) at: 28, 40, 52 and 60 months. NICE DSU TSD 14 informed model selection. 60-month follow-up from CheckMate 067, as well as external data for ipilimumab, were used to evaluate the predictive accuracy of the survival models. Extrapolated 20-year mean survival times (20-YR MST) were also compared with a 5% discount rate applied. For the 28-month DBL, standard parametric models, piecewise models and splines underestimated 60-month survival (range -3.8% to -11.7% across methods/arms). Mixture cure models (MCM), parametric mixture models (PMM) and response-based landmark models (RBLM) provided more accurate estimates (range -3.2% to +2.0% across methods/arms). MCM, PMM and RBLM produced closer estimates of 7-year and 10-year OS when compared to the external data for ipilimumab than other methods. 20-YR MSTs were higher for MCM, PMM and RBLM (NIVO+IPI: 6.02-7.02 years) than those for other models (NIVO+IPI: 4.56-5.62 years). Estimates of 20-YR MST for MCM, PMM and RBLM were more consistent across the successive database locks than with other methods. MCM, PMM and RBLM provided accurate and consistent estimates of OS across a range of follow-up periods. Extrapolation models that fail to account for heterogeneity in survival may result in biased assessments of the survival benefit of IO therapies for melanoma.

NM1 A Comparison on Different Network-Meta Analysis (NMA) Models Using Randomized Clinical Trials (RCTS) in Transplant-Ineligible (TIE) NEWLY Diagnosed Multiple Myeloma (NDMM)

An NMA survival extrapolation decision-framework based on clinical plausibility is proposed. It suggests mixture-cure models in case cure is clinically realistic. In case of no cure, parametric mixture (PM) models are proposed for subgroups with long-term survival, and piecewise (PW), splines (S) and fractional polynomial (FP) models are suggested for subsets with fluctuating hazards. Otherwise, standard parametric approaches are proposed. Following the framework, a parametric NMA (PNMA) would be most clinically plausible in TIE NDMM since cure, and subgroups with long-term survival and fluctuating hazards are not anticipated. It was aimed to compare estimated survival using different NMA methods. The network of evidence included n=5 RCTs on n=3 treatments (MP, MPT-T, MPR-R) in TIE NDMM. Published Kaplan-Meiers were used to extract individual-patient data. The proportional-hazard assumption was violated, and thus a PNMA was conducted. The PNMA has been compared to PW, S, PM, and FP models. Mixture- and non-mixture cure models were excluded since cure was not clinically realistic. Only the Weibull distribution was used to extrapolate survival. The overall model fit was assessed using the leave-one-out-information-criteria (LOOIC). The PNMA demonstrated lowest LOOIC [6588.62], compared to the other models (second-lowest: FP [6588.89]). PNMA and FP models predicted survival of respectively 4.47 and 4.67 years for MP, 5.50 and 5.50 years for MPT-T, and 4.70 and 4.45 years for MPR-R. Incremental survival of MP against MPT-T and MPR-R was 1.04 and 0.23 years for PNMA and 0.83 and 0.22 years for FP. Incremental survival between PNMA and FP was 0.20 and 0.45 years for MP versus MPT-T and MPR-R, respectively. The framework demonstrates to work. Estimated survival varied per model, which impacts health economic outcomes such as the incremental cost-effectiveness ratio (ICER), relevant for medical decision-making. Conducting NMA methods should be tailored to the data and take clinical plausibility into account.

EX1 How to Select the Appropriate Survival Extrapolation Method? a Proposed Framework

For HTA, apart from standard parametric models (SPMs), other extrapolation approaches are applied such as piecewise, splines, mixture cure and non-mixture cure, parametric-mixture, and fractional polynomial models. The objective is to validate a survival extrapolation decision framework suggesting cure models for curative therapies, parametric-mixture models in case of a subgroup of long-term survivors, piecewise, splines and fractional polynomials in case of fluctuating hazards, and SPMs for other data. All survival extrapolation approaches were fitted on immature data of three trials; in melanoma the framework recommends a cure model as cure seems clinically plausible, in breast cancer (BC) a parametric-mixture as a subgroup of long-term survivors is expected, and in multiple myeloma (MM) an SPM as no cure, long-term survivors or fluctuating hazards are expected. The statistical fit of the models was assessed using LOOIC. The extrapolation on immature data was compared to mature trial data in terms of ΔMean-Absolute-Deviation (ΔMAD) in months for all arms in the trial. Lower LOOIC and ΔMAD imply better predictions. Restricted mean survival time (RMST) of the mature data was determined to assess the relative size of ΔMAD. The best fitting approach on the melanoma dataset (RMST: 67.88 months) was the log-logistic parametric-mixture (LOOIC=2,870, ΔMAD=19.59). The best fitting cure model was the lognormal (LOOIC=3,249, ΔMAD=10.89). On the BC dataset (RMST: 123.42 months), the lognormal parametric-mixture fitted best (LOOIC=1,782, ΔMAD=9.86) and had one of the lowest ΔMAD. On the MM dataset (RMST: 92.55 months), the Weibull parametric-mixture fitted best (LOOIC=1,944, ΔMAD=11.24), and the best fitting SPM was the exponential (LOOIC=1,988, ΔMAD=7.21). This study shows that the model recommended by the framework generally leads to better long-term extrapolations compared to the statistically best fitting model. Therefore, additional to historical data and long-term comparative effectiveness expectations, this framework can be used for model selection.

Strain monitoring based bridge reliability assessment using parametric Bayesian mixture model

Bridge condition assessment by use of structural health monitoring (SHM) data has been recognized as a promising approach towards the condition-based preventive maintenance. In-service bridges are normally subjected to multiple types of loads such as highway traffic, railway traffic, wind and thermal effect, resulting in heterogeneous and multimodal data structure of strain/stress responses. This study aims to develop an SHM-based bridge reliability assessment procedure in terms of parametric Bayesian mixture modelling. The parametric mixture model admits representation of multimodal structural responses, while the Bayesian paradigm enables both aleatory and epistemic uncertainties to be accounted for in modelling. By defining appropriate priors for the mixture parameters that are viewed as random variables to interpret the model uncertainty, an analytical form of the full conditional posteriors is derived. A Markov chain Monte Carlo (MCMC) algorithm in conjunction with Bayes factor is explored to determine the optimal model order and estimate the joint posterior of the mixture parameters. In full compliance with the Bayesian framework, a conditional reliability index is elicited with the parametric Bayesian mixture model by using the first-order reliability method. The estimated value of the reliability index, which serves as a quantitative measure of health condition for the in-service bridge, can be successively updated with the accumulation of monitoring data. The proposed method is exemplified by using one-year strain monitoring data acquired from the instrumented Tsing Ma Suspension Bridge, in which the evolution of the estimated reliability index is obtained.

Mixture of Birnbaum-Saunders Distributions: Identifiability, Estimation and Testing Homogeneity with Randomly Censored Data

Random censoring is frequently utilized to analyze lifetime data in life-testing and reliability experiments. However, no published work discussed parameter estimation and testing homogeneity under random censoring for the mixture of Birnbaum-Saunders (BS) distributions, which is a useful model for describing reliability data. In this paper, first the proof of the identifiability of a finite mixture of BS distributions with g components is developed using Laplace transform of BS distributions. Then based on random censoring, parameter estimation and testing homogeneity are discussed. An EM algorithm is proposed to obtain the maximum likelihood (ML) estimates of the mixture model parameters and an EM test is implemented to test for homogeneity in the mixture of BS distributions. A Monte Carlo simulation study is conducted to evaluate the performance of the ML estimates through the bias and mean squared error. Additionally, the performance of the EM test is investigated through its size and power which are calculated by Monte Carlo simulation. Finally, an example of aircraft Windshield data is used to illustrate the estimation and testing procedures.

Bayesian mixture models for cytometry data analysis

AbstractBayesian mixture models are increasingly used for model‐based clustering and the follow‐up analysis on the clusters identified. As such, they are of particular interest for analyzing cytometry data where unsupervised clustering and association studies are often part of the scientific questions. Cytometry data are large quantitative data measured in a multidimensional space that typically ranges from a few dimensions to several dozens, and which keeps increasing due to innovative high‐throughput biotechonologies. We present several recent parametric and nonparametric Bayesian mixture modeling approaches, and describe advantages and limitations of these models under different research context for cytometry data analysis. We also acknowledge current computational challenges associated with the use of Bayesian mixture models for analyzing cytometry data, and we draw attention to recent developments in advanced numerical algorithms for estimating large Bayesian mixture models, which we believe have the potential to make Bayesian mixture model more applicable to new types of single‐cell data with higher dimensions.This article is categorized under: Statistical Learning and Exploratory Methods of the Data Sciences > Knowledge Discovery Statistical Learning and Exploratory Methods of the Data Sciences > Modeling Methods Statistical and Graphical Methods of Data Analysis > Bayesian Methods and Theory

Implications of COVID-19 for HIV Research: data sources, indicators and longitudinal analyses.

Implications of COVID-19 for HIV Research: data sources, indicators and longitudinal analyses.

Low light image denoising solution with contrast enhancement in curvelet domain using Gaussian mixture adaptation model

Images captured under low light are noisy and consist of unidentifiable features. Low light noise problem occurs in imaging devices because of smaller sensor size or insufficient exposure. Low light image denoising is an exacting task in many image processing applications. This paper proposes a patch-based image denoising method for low light images in the curvelet domain with contrast enhancement. Curvelet transform is a directional transform and it gives the best sparse representation for images with edges. Here the Expectation–Maximization (EM) algorithm, based on the Gaussian mixture adaptation method is performed in the curvelet domain for denoising. EM Algorithm helps in computing the Gaussian mixture model (GMM) parameters from the patches which are used in maximum a posteriori estimation to update them. GMM parameters and patches are updated periodically until a satisfactory result is achieved. Simulation is performed on standard test data set, and then extended to natural low light noisy images. The results of the proposed technique are then compared using quality metrics such as Peak Signal to Noise Ratio and Structural Similarity Index. It is observed that the use of curvelet transform in denoising process helps to restore the structural information satisfactorily.

Estimating the parameters of twofold Weibull mixture model in right-censored reliability data by using genetic algorithm

In this article, a new method was practiced to form a model by using twofold Weibull mixture distribution in right-censored reliability data. The method depends on estimating the parameters of right-censored twofold Weibull mixture distribution in a most appropriate way to the data by using genetic algorithm techniques. The best model was tried to be found by using MSE, MAE and MAPE metrics, respectively, as fitness function in the method. To test the model, failure data of aircraft planes’ windshield, which is often used in the literature, was used and the results were compared with other methods in the literature. Furthermore, the performance of the method was compared for the sample sizes, censorship ratios and mixture proportions by conducting Monte Carlo simulation study.

Beyond HC: More sensitive tests for rare/weak alternatives

Higher criticism (HC) is a popular method for large-scale inference problems based on identifying unusually high proportions of small $p$-values. It has been shown to enjoy a lower-order optimality property in a simple normal location mixture model which is shared by the ‘tailor-made’ parametric generalised likelihood ratio test (GLRT) for the same model; however, HC has also been shown to perform well outside this ‘narrow’ model. We develop a higher-order framework for analysing the power of these and similar procedures, which reveals the perhaps unsurprising fact that the GLRT enjoys an edge in power over HC for the normal location mixture model. We also identify a similar parametric mixture model to which HC is similarly ‘tailor-made’ and show that the situation is (at least partly) reversed there. We also show that in the normal location mixture model a procedure based on the empirical moment-generating function enjoys the same local power properties as the GLRT and may be recommended as an easy to implement (and interpret), complementary procedure to HC. Some other practical advice regarding the implementation of these procedures is provided. Finally, we provide some simulation results to help interpret our theoretical findings.

Income modeling with the Weibull mixtures

In this paper, we introduce six Weibull based mixture distributions to model income data. Several statistical properties of these models are derived and their closed forms are presented. The mixture model parameters are estimated using the maximum likelihood method and their performances are assessed with respect to average income per tax unit data for ten countries using information based criteria approaches as well as graphical observations. In addition, we provide application of these models to two popular inequality measures, the Gini and Bonferroni indexes as well as the common generalized entropy index. Analytic expressions of the poverty measures are given for head-count ratio and poverty-gap ratio. All the mixture models show good fit to the data with close proximity to empirical Gini and Bonferroni indexes in almost all ten countries where the income data sets are studied.

Identifiability of nonparametric mixture models and Bayes optimal clustering

Motivated by problems in data clustering, we establish general conditions under which families of nonparametric mixture models are identifiable by introducing a novel framework involving clustering overfitted parametric (i.e., misspecified) mixture models. These identifiability conditions generalize existing conditions in the literature and are flexible enough to include, for example, mixtures of infinite Gaussian mixtures. In contrast to the recent literature, we allow for general nonparametric mixture components and instead impose regularity assumptions on the underlying mixing measure. As our primary application we apply these results to partition-based clustering, generalizing the notion of a Bayes optimal partition from classical parametric model-based clustering to nonparametric settings. Furthermore, this framework is constructive, so that it yields a practical algorithm for learning identified mixtures, which is illustrated through several examples on real data. The key conceptual device in the analysis is the convex, metric geometry of probability measures on metric spaces and its connection to the Wasserstein convergence of mixing measures. The result is a flexible framework for nonparametric clustering with formal consistency guarantees.

Optimizing the Estimation of a Histogram-Bin Width—Application to the Multivariate Mixture-Model Estimation

A maximum-likelihood estimation of a multivariate mixture model’s parameters is a difficult problem. One approach is to combine the REBMIX and EM algorithms. However, the REBMIX algorithm requires the use of histogram estimation, which is the most rudimentary approach to an empirical density estimation and has many drawbacks. Nevertheless, because of its simplicity, it is still one of the most commonly used techniques. The main problem is to estimate the optimum histogram-bin width, which is usually set by the number of non-overlapping, regularly spaced bins. For univariate problems it is usually denoted by an integer value; i.e., the number of bins. However, for multivariate problems, in order to obtain a histogram estimation, a regular grid must be formed. Thus, to obtain the optimum histogram estimation, an integer-optimization problem must be solved. The aim is therefore the estimation of optimum histogram binning, alone and in application to the mixture model parameter estimation with the REBMIX&EM strategy. As an estimator, the Knuth rule was used. For the optimization algorithm, a derivative based on the coordinate-descent optimization was composed. These proposals yielded promising results. The optimization algorithm was efficient and the results were accurate. When applied to the multivariate, Gaussian-mixture-model parameter estimation, the results were competitive. All the improvements were implemented in the rebmix R package.

Simultaneous dimension reduction and clustering via the NMF-EM algorithm

Mixture models are among the most popular tools for clustering. However, when the dimension and the number of clusters is large, the estimation of the clusters become challenging, as well as their interpretation. Restriction on the parameters can be used to reduce the dimension. An example is given by mixture of factor analyzers for Gaussian mixtures. The extension of MFA to non-Gaussian mixtures is not straightforward. We propose a new constraint for parameters in non-Gaussian mixture model: the $K$ components parameters are combinations of elements from a small dictionary, say $H$ elements, with $H \ll K$. Including a nonnegative matrix factorization (NMF) in the EM algorithm allows us to simultaneously estimate the dictionary and the parameters of the mixture. We propose the acronym NMF-EM for this algorithm, implemented in the R package {\tt nmfem}. This original approach is motivated by passengers clustering from ticketing data: we apply NMF-EM to data from two Transdev public transport networks. In this case, the words are easily interpreted as typical slots in a timetable.

The Deep Neural Network and Content Transcription-based Speech Recognition Algorithm in Keyword Detection

Objective: It is hoped that the DNN-Hidden Markov Model (HMM) acoustic model and the long-short-term memory neural network-Hidden Markov (LSTM-HMM) acoustic model can be used to improve the accuracy rate of speech recognition in keyword detection. Method: First, the principles of speech recognition and related algorithms are introduced. Then, a DNN algorithm is applied to the speech recognition system, and a keyword detection system is established based on the DNN-HMM acoustic model. As for the experimental comparison, the proposed DNN model is used for acoustic modeling, and the effect of the DNN algorithm on the performance of the recognition system is analyzed experimentally. Results: The size of the training parameters of the proposed LSTM model is 436570, the size of the training parameters of the deep neural network (DNN) is 698100, and the size of the training parameters of the Gaussian mixture model (GMM) is 1226700. The accuracy of speech recognition based on the LSTM-HMM model and DNN-HMM model is 965% and 91.6%, respectively, which is significantly higher than 78.5% of the traditional speech recognition model (GMM-HMM). Conclusion: The speech recognition technology based on LSTM-HMM and DNN-HMM models has higher accuracy and is more suitable for speech keyword detection.

Grasp prediction and evaluation of multi-fingered dexterous hands using deep learning

Learning from human skills has become one of the popular inspirations in grasp prediction and evaluation, but lack of effective methods on groups of grasp points for multi-fingered dexterous hands yields an open challenge. When facing an object, humans firstly predict a variety of options for grasps, which can be concerned as a complex multi-valued problem. After prediction, humans evaluate grasps and then choose the optimal one. Inspired by human skills, we propose Grasp Prediction Networks (GPNs) based on Convolutional Neural Networks (CNNs) and Mixture Density Networks (MDNs). The proposed GPNs map from a depth image to a set of parameters for Gaussian Mixture Model (GMM), from which candidate groups of grasp points can be sampled for prediction. Besides, we also propose Grasp Evaluation Networks (GENs) to evaluate candidate groups and then choose the optimal group of grasp points. The proposed GENs consider force-closure metric as grasp quality for evaluation. Different from other related work, our method (1) utilizes a probabilistic model to predict multiple groups of grasp points from a monocular depth image and (2) evaluates grasp quality with force-closure metric given a monocular depth image and a group of grasp points. Furthermore, we built a grasp dataset which consists of depth images, groups of grasp points and each group’s grasp quality. Herein, three different experiments were designed to validate our approach. The first one was a comparative experiment and revealed that GPNs show equivalent performance as GraspIt! in terms of high-quality grasp planning. The second one was also a comparative experiment, which validated that GENs can evaluate grasps as precisely as GraspIt!. Moreover, the last one was an actual experiment implemented on Shadow Hand Lite, and experimental results indicated that our approach achieved finely grasp of novel objects.

Clone granular soils with mixed particle morphological characteristics by integrating spherical harmonics with Gaussian mixture model, expectation–maximization, and Dirichlet process

Computers have been taught to clone granular soil particles for discrete element method simulations to alleviate difficulties of using three-dimensional imaging techniques for scanning a large number of particles. In this process, computers analyze a few scanned particles to extract morphological characteristics of the target soil, which are used to clone as many particles as necessary. However, many natural granular soils contain a wide range of particle shapes mixing more than one type of morphological characteristics, causing difficulties in cloning. This research aims to address this challenge by integrating spherical harmonics with Gaussian mixture model, expectation–maximization, and Dirichlet process. Spherical harmonics coefficients are used to characterize morphological information of the granular soil. Gaussian mixture model is used to fit a function to the mixed morphological characteristics. The expectation–maximization and Dirichlet process are used to estimate the fitting parameters in Gaussian mixture model. Then, Gaussian mixture model is used to generate new spherical harmonics coefficients and then generate new particles. The effectiveness and accuracy of the proposed methodology are verified using a Griffin sand. Although this approach is developed for granular soils, the proposed technique can also be used to clone other particulate materials.

Gaussian Mixture Model Based Classification Revisited: Application to the Bearing Fault Classification

Condition monitoring and fault detection are nowadays popular topic. Different loads, enviroments etc. affect the components and systems differently and can induce the fault and faulty behaviour. Most of the approaches for the fault detection rely on the use of the good classification method. Gaussian mixture model based classification are stable and versatile methods which can be applied to a wide range of classification tasks. The main task is the estimation of the parameters in the Gaussian mixture model. Those can be estimated with various techniques. Therefore, the Gaussian mixture model based classification have different variants which can vary in performance. To test the performance of the Gaussian mixture model based classification variants and general usefulness of the Gaussian mixture model based classification for the fault detection, we have opted to use the bearing fault classification problem. Additionally, comparisons with other widely used non-parametric classification methods are made, such as support vector machines and neural networks. The performance of each classification method is evaluated by multiple repeated k-fold cross validation. From the results obtained, Gaussian mixture model based classification methods are shown to be competitive and efficient methods and usable in the field of fault detection and condition monitoring.

Estimating and Controlling Overlap in Gaussian Mixtures for Clustering Methods Evaluation

The ad hoc nature of the clustering methods makes simulated data paramount in assessing the performance of clustering methods. Real datasets could be used in the evaluation of clustering methods with the major drawback of missing the assessment of many test scenarios. In this paper, we propose a formal quantification of component overlap. This quantification is derived from a set of theorems which allow us to derive an automatic method for artificial data generation. We also derive a method to estimate parameters of existing models and to evaluate the results of other approaches. Automatic estimation of the overlap rate can also be used as an unsupervised learning approach in data mining to determine the parameters of mixture models from actual observations.