Mixture Regression Research Articles

Modelling Healthcare Demand Count Data with Excessive Zeros and Overdispersion

ABSTRACT In healthcare economics count datasets often exhibit excessive zeros or right-skewed tails. When covariates are available, such datasets are typically modelled using the zero-inflated (ZI) or finite mixture (FM) regression models. However, neither model performs adequately when the dataset has both excessive zeros and a long tail, which is often the case in practice. In this paper we combine these two models to create a more flexible, versatile class of ZIFM models. With this model we perform a comprehensive analysis on the number of visits to a physician’s office using the US healthcare demand dataset that has been used in numerous healthcare studies in the literature. After comparing to other existing models which have been reported to perform well on this dataset, we find that the ZIFM model substantially outperforms alternative models. In addition, the model offers a new interpretation that is in contrast to previous empirical findings regarding the factors associated with the demand for the physicians, which can shed a fresh light on the healthcare utilisation policies.

Human-robot skill transmission for mobile robot via learning by demonstration.

This paper proposed a skill transmission technique for the mobile robot via learning by demonstration. When the material is transported to the designated location, the robot can show the human-like capabilities: autonomous tracking target. In this case, a skill transmission framework is designed, which the Kinect sensor is utilized to distinguish human activity recognition to create a planned path. Moreover, the dynamic movement primitive method is implemented to represent the teaching data, and the Gaussian mixture regression is utilized to encode the learning trajectory. Furthermore, in order to realize the accurate position control of trajectory tracking, a model predictive tracking control is investigated, where the recurrent neural network is used to eliminate the uncertain interaction. Finally, some experimental tasks using the mobile robot (BIT-6NAZA) are carried out to demonstrate the effectiveness of the developed techniques in real-world scenarios.

Learning Grasp Configuration Through Object-Specific Hand Primitives for Posture Planning of Anthropomorphic Hands.

The proposal of postural synergy theory has provided a new approach to solve the problem of controlling anthropomorphic hands with multiple degrees of freedom. However, generating the grasp configuration for new tasks in this context remains challenging. This study proposes a method to learn grasp configuration according to the shape of the object by using postural synergy theory. By referring to past research, an experimental paradigm is first designed that enables the grasping of 50 typical objects in grasping and operational tasks. The angles of the finger joints of 10 subjects were then recorded when performing these tasks. Following this, four hand primitives were extracted by using principal component analysis, and a low-dimensional synergy subspace was established. The problem of planning the trajectories of the joints was thus transformed into that of determining the synergy input for trajectory planning in low-dimensional space. The average synergy inputs for the trajectories of each task were obtained through the Gaussian mixture regression, and several Gaussian processes were trained to infer the inputs trajectories of a given shape descriptor for similar tasks. Finally, the feasibility of the proposed method was verified by simulations involving the generation of grasp configurations for a prosthetic hand control. The error in the reconstructed posture was compared with those obtained by using postural synergies in past work. The results show that the proposed method can realize movements similar to those of the human hand during grasping actions, and its range of use can be extended from simple grasping tasks to complex operational tasks.

Mapping the PHQ-8 to EQ-5D, HUI3 and SF6D in patients with depression

BackgroundThere is limited evidence of mapping clinical instruments to a generic preference-based instrument in Asian patient populations. The current study aims to map the eight-item Patient Health Questionnaire depression scale (PHQ-8) onto the EuroQol Five-Dimension (EQ-5D), the Health Utilities Index Mark 3 (HUI3) and the Short Form Six-Dimension (SF-6D) which helps to inform future cost-utility analyses of treatments for depression.MethodsA total of 249 participants who had completed PHQ-8, EQ-5D, SF-6D and HUI3 questionnaires were included in the analyses. A beta regression mixture model was used to map the utility scores as a function of PHQ-8 total scores, PHQ-squared, age and gender. The predictive accuracy of the models was examined using mean absolute error and root mean square error.ResultsThe results were compared against two common regression methods including Ordinary Least Square (OLS) and Tobit regression models. The mean age of the sample was 36.2 years (SD = 11.1). The mean EQ-5D-3L, EQ-5D-5L, HUI3 and SF-6D utility scores were 0.615, 0.709, 0.461 and 0.607, respectively. The EQ-5D-3L, EQ-5D-5L and SF-6D utility scores were best predicted by the beta mixture regression model consisting of PHQ-8 total sores, PHQ-squared, and covariates including age and gender. The HUI3 was best predicted by the OLS regression model.ConclusionsThe current study provides important evidence to clinicians and researchers about the mapping algorithms that can be used in economic evaluation among patients with depression.

A Gaussian mixture regression model based adaptive filter for non-Gaussian noise without a priori statistic

In many engineering systems, the distribution of measurement noise is unknown and non-Gaussian, such as skewed, multimodal, time-varying distributions and we can not obtain these prior statistics in advance. How to achieve state estimation via this kind of non-Gaussian measurement noises without prior statistic information is a challenging problem. In this paper, a novel Gaussian mixture regression model (GMRM) is proposed to model the unknown non-Gaussian measurement likelihood for Bayesian update to achieve nonlinear state estimation. Without any prior assumption or limitation of measurement noises’ statistics and distributions, the GMRM can still describe the measurement likelihood accurately based on a group of parameters which are adjusted by maximizing the evidence lower bound. Based on the optimized GMRM, a new variational Bayesian Gaussian mixture filter is proposed by using the variational Bayesian approach. To eliminate the influence of the initialization of the introduced parameters, a learning scheme is proposed to adaptively optimize their hyper-parameters based on the historical measurements. Finally, simulation examples are employed to illustrate the effectiveness of the filter.

Interpretable Decision-Making for Autonomous Vehicles at Highway On-Ramps With Latent Space Reinforcement Learning

This paper presents a latent space reinforcement learning method for interpretable decision-making of autonomous vehicles at highway on-ramps. This method is based on the latent model and the combination model of the hidden Markov model and Gaussian mixture regression (HMM-GMR). It is difficult for the traditional decision-making method to understand the environment because its input is high-dimensional and lacks an understanding of the task. By utilizing the HMM-GMR model, we can obtain the interpretable state providing semantic information and environment understanding. A framework is proposed to unify representation learning with the deep reinforcement learning (DRL) approach, in which the latent model is used to reduce the dimension of interpretable state by extracting underlying task-relevant information. Experimental results are presented and the results show the right balance between driving safety and efficiency in the challenging scenarios of highway on-ramps merging.

Application of Gaussian Mixture Regression for the Correction of Low Cost PM2.5 Monitoring Data in Accra, Ghana

Low-cost sensors (LCSs) for air quality monitoring have enormous potential to improve air quality data coverage in resource-limited parts of the world such as sub-Saharan Africa. LCSs, however, are affected by environment and source conditions. To establish high-quality data, LCSs must be collocated and calibrated with reference grade PM2.5 monitors. From March 2020, a low-cost PurpleAir PM2.5 monitor was collocated with a Met One Beta Attenuation Monitor 1020 in Accra, Ghana. While previous studies have shown that multiple linear regression (MLR) and random forest regression (RF) can improve accuracy and correlation between PurpleAir and reference data, MLR and RF yielded suboptimal improvement in the Accra collocation (R2 = 0.81 and R2 = 0.81, respectively). We present the first application of Gaussian mixture regression (GMR) to air quality data calibration and demonstrate improvement over traditional methods by increasing the collocated PM2.5 correlation and accuracy to R2 = 0.88 and MAE = 2.2 μg m–3. Gaussian mixture models (GMMs) are a probability density estimator and clustering method from which nonlinear regressions that tolerate missing inputs can be derived. We find that even when given missing inputs, GMR provides better correlation than MLR and RF performed with complete data. GMR also allows us to estimate calibration certainty. When evaluated, 95% confidence intervals agreed with reference PM2.5 data 96% of the time, suggesting that the model accurately assesses its own confidence. Additionally, clustering within the GMM is consistent with climate characteristics, providing confidence that the calibration approach can learn underlying relationships in data.

Research on the Path Planning Algorithm of a Manipulator Based on GMM/GMR-MPRM

Autonomous, flexible, and human–robot collaboration are the key features of the next-generation robot. Such unstructured and dynamic environments bring great challenges in online adaptive path planning. The robots have to avoid dynamic obstacles and follow the original task path as much as possible. A robust and efficient online path planning method is required accordingly. A method based on the Gaussian Mixture Model (GMM), Gaussian Mixture Regression (GMR), and the Probabilistic Roadmap (PRM) is proposed to overcome the above difficulties. During the offline stage, the GMM was used to model teaching data, and it can represent the offline-demonstrated motion and constraints. The optimal solution was encoded in the mean value, while the environmental constraints were encoded in the variance value. The GMR generated a smooth path with variance as the resample space according to the GMM of the teaching data. This representation isolated the old environment model with the novel obstacle. During the online stage, a Modified Probabilistic Roadmap (MPRM) was used to plan the motion locally. Because the GMM provides the distribution of all the feasible motion, the sampling space of the MPRM was generated by the variable density resampling method, and then, the roadmap was constructed according to the Euclidean and Probability Distance (EPD). The Dijkstra algorithm was used to search for the feasible path between the starting point and the target point. Finally, shortcut pruning and B-spline interpolation were used to generate a smooth path. During the simulation experiment, two obstacles were added to the recurrent scene to indicate the difference from the teaching scene, and the GMM/GMR-MPRM algorithm was used for path planning. The result showed that it can still plan a feasible path when the recurrent scene is not the same as the teaching scene. Finally, the effectiveness of the algorithm was verified on the IRB1200 robot experiment platform.

Learning robot anomaly recovery skills from multiple time-driven demonstrations

Robots are prone to making anomalies when performing manipulation tasks in unstructured environments, it is often desirable to rapidly adapt the robotic behavior to avoid environmental changes by learning from experts’ demonstrations. We propose a framework for learning robot anomaly recovery skills from time-driven demonstrations based on a Gaussian process regression with prior mean derived by Gaussian mixture regression, named as mean-prior GPR (MP-GPR), which allows an end-user to adjust the anomalous trajectory intuitively by simultaneously considering the variability of the demonstrations and the adaptation of recovery skills. Evaluations are divided into two phases, a benchmarking dataset with robot reaching, pushing, writing, and pressing tasks are first used to verify the path accuracy and variability, and then a real-time robot bin-picking task for evaluating the adaptation of the framework. Our method has a fair comparison with probabilistic-based methods in the field of robot learning from demonstrations, including Gaussian mixture regression, probabilistic movement primitives, and kernelized movement primitives. The results indicate that our proposed method can efficiently encode the variability from multiple demonstrations and rapidly anomaly recovery skills learning by modulating a learned trajectory to safe via-points.

Nonlinear variational Bayesian Student’s-t mixture regression and inferential sensor application with semisupervised data

Gaussian mixture models have been widely applied to predict those significant but hard-to-measure quality variables in industrial processes. However, outliers that result from disturbances of noise, and incorrect instrument readings, will deteriorate the prediction accuracy of Gaussian mixture models. Student’s-t mixture regression and its variants have been proposed for robust inferential sensor development. Nevertheless, for those Student’s-t mixture regression-based inferential sensors, the functional dependency between the quality and process variables in each component is assumed to be linear. Such configuration in practice might be incapable of adequately modeling the complicated nonlinearity between the quality and process variables. In addition, large amounts of unlabeled samples are easily to be obtained and informative for model performance improvement, however, the computations are significantly increased as well. To get over these issues, this paper proposes a novel semisupervised nonlinear variational Bayesian Student’s-t mixture regression model, in which the nonlinear component model can effectively capture the non-linearity between the quality and process variables. For tackling the low training efficiency issue caused by large number of training samples, the parallel computing strategy is introduced to complete model training. A numerical example and two real industrial processes are supplied to validate the effectiveness of the proposed method.

Ring Gaussian Mixture Modelling and Regression for collaborative robots

Task Parametrised Gaussian Mixture Modelling and Regression (TP-GMM/R) is an eminent algorithm to enable collaborative robots (cobots) to adapt to new environments intuitively by learning robotic paths demonstrated by humans. Task parameters in the TP-GMM/R algorithm, i.e., frames associated with demonstration paths, are considered to have orientations by default. This requirement, however, limits the range of applications that TP-GMM/R can support. To address the issue, in this paper, a novel ring Gaussian (rGaussian) is defined to cater for orientation-less frames, and an improved TP-GMM/R algorithm based on rGaussians is developed to improve the adaptability and robustness of the algorithm. In the improved algorithm, firstly, kernels are incorporated to enable Gaussians encoding points from all demonstrations, and criteria are devised to judge a frame to be oriented or orientation-less. Then, improved Gaussian mixture regression that caters for rGaussians and orientation-less frames is developed to generate regression paths adaptable to complex environments. Finally, a series of case studies are used to benchmark the improved TP-GMM/R algorithm with the conventional TP-GMM/R algorithm under different conditions. Quantitative analyses are conducted in terms of smoothness, efficiency and reachability. Results show that the improved algorithm outperformed the conventional algorithm on all the cases.

Change in Juvenile Offending Versatility Predicted by Individual, Familial, and Environmental Risks

Developmental and life-course criminology elucidate the developmental course and change of antisociality over time, considering that longitudinal trajectories differ. Specific relations between risks and different antisociality outcomes are emphasized. We assume that adolescents have different longitudinal trajectories considering the change of offending over time and that risks contribute variably to offending pathways. The current study is based on a German research project in which adolescents (N = 577) were interviewed in two German cities. Based on self-reported crime data, we utilized the slope values of offending versatility (OV) over time as outcome values in regression mixture models capturing the trends for participants over age and exhibiting two components of offending adolescents. We explored the contribution of different risks to OV, defining specific risk patterns: Acceptance of violence and peer delinquency have significant negative effects on the emergence of OV within the group of adolescents with decreasing OV. Acceptance of violence has a significant negative effect, and corporal punishment has a significant positive effect on the emergence of OV within the group of adolescents with increasing or rather stable OV. The results underline the relevance of the violence-related risk factor corporal punishment for the emergence of OV within the last-mentioned group.

The distribution of common-variant effect sizes.

The genetic effect-size distribution of a disease describes the number of risk variants, the range of their effect sizes and sample sizes that will be required to discover them. Accurate estimation has been a challenge. Here I propose Fourier Mixture Regression (FMR), validating that it accurately estimates real and simulated effect-size distributions. Applied to summary statistics for ten diseases (average [Formula: see text]), FMR estimates that 100,000-1,000,000 cases will be required for genome-wide significant SNPs to explain 50% of SNP heritability. In such large studies, genome-wide significance becomes increasingly conservative, and less stringent thresholds achieve high true positive rates if confounding is controlled. Across traits, polygenicity varies, but the range of their effect sizes is similar. Compared with effect sizes in the top 10% of heritability, including most discovered thus far, those in the bottom 10-50% are orders of magnitude smaller and more numerous, spanning a large fraction of the genome.

Robust estimates of insurance misrepresentation through kernel quantile regression mixtures

AbstractThis paper pertains to a class of nonparametric methods for studying the misrepresentation issue in insurance applications. For this purpose, mixture models based on quantile regression in reproducing kernel Hilbert spaces are employed. Compared with the existing parametric approaches, the proposed framework features a more flexible statistics structure which could alleviate the risk of model misspecification, and is in the meantime more robust to outliers in the data. The proposed framework can not only estimate the prevalence of misrepresentation in the data, but also help identify the most suspicious individuals for the validation purpose. Through embedding state‐of‐the‐art machine learning techniques, we present a novel statistics procedure to efficiently estimate the proposed misrepresentation model in the presence of massive data. The proposed methodology is applied to study the Medical Expenditure Panel Survey data, and a significant degree of misrepresentation activity is found on the self‐reported insurance status.

Effects of Mixing Weights and Predictor Distributions on Regression Mixture Models

ABSTRACT Regression mixture models (RMMs) can be used to specifically test for and model differential effects in heterogeneous populations. Based on the results of the Aim 1 simulation study, enumeration conducted with constrained predictor means appears to be advantageous. Furthermore, researchers should estimate the K and K+1 unconditional models (chosen during initial enumeration), adding the C on X paths, to investigate the potential for model instability as well as the possibility that the models are misspecified because the underlying populations contain predictor variance differences in the subgroups. The Aim 2 simulation study explored the extent to which RMMs are robust to predictor variance differences. Although the coverage rates for the simulation conditions where the predictor variances differed across classes were not the nominal rate, parameter estimates were not biased even in the presence of moderate violations of this assumption.

Generalized Poisson-Poisson Mixture Model for Misreported Counts with an Application to Smoking Data

The assumption that is usually made when modeling count data is that the response variable, which is the count, is correctly reported. Some counts might be over- or under-reported. We derive the Generalized PoissonPoisson mixture regression (GPPMR) model that can handle accurate, underreported and overreported counts. The parameters in the model will be estimated via the maximum likelihood method. We apply the GPPMR model to a real-life data set.

The effects of wind generation and other market determinants on price spikes

Electricity spot prices have shifted in response to increasing renewable energy infrastructure throughout the United States in recent decades. These shifts manifest as changes in the spot price mean and variance. One major factor influencing the variance of spot prices is the prevalence of price spikes. How renewables influence the magnitude and frequency of price spikes is not well understood. This study examines the influence of wind and additional determinants (load, nuclear generation, natural gas prices, as well as the load-to-capacity ratio) on electricity spot prices in the Electric Reliability Council of Texas system using a multiple regression mixture model framework. We focus on the influence of these determinants on the magnitude of spot prices within a low-price regime and a high-price regime, with the latter representative of price spikes. We also examine how system determinants influence the frequency of occurrence of each regime. We show that increases in wind generation drive average spot prices down in both the low and high price regime. However, system shortfalls of wind generation, particularly during times of high load, result in increased price magnitudes in both regimes, as well as more frequent price spike events.

ITARGEX analysis of yeast deletome reveals novel regulators of transcriptional buffering in S phase and protein turnover

Integrating omics data with quantification of biological traits provides unparalleled opportunities for discovery of genetic regulators by in silico inference. However, current approaches to analyze genetic-perturbation screens are limited by their reliance on annotation libraries for prioritization of hits and subsequent targeted experimentation. Here, we present iTARGEX (identification of Trait-Associated Regulatory Genes via mixture regression using EXpectation maximization), an association framework with no requirement of a priori knowledge of gene function. After creating this tool, we used it to test associations between gene expression profiles and two biological traits in single-gene deletion budding yeast mutants, including transcription homeostasis during S phase and global protein turnover. For each trait, we discovered novel regulators without prior functional annotations. The functional effects of the novel candidates were then validated experimentally, providing solid evidence for their roles in the respective traits. Hence, we conclude that iTARGEX can reliably identify novel factors involved in given biological traits. As such, it is capable of converting genome-wide observations into causal gene function predictions. Further application of iTARGEX in other contexts is expected to facilitate the discovery of new regulators and provide observations for novel mechanistic hypotheses regarding different biological traits and phenotypes.

Analysis of Pulmonary Function Test Results By Using Gaussian Mixture Regression Model

Background: FEV1/FVC value is used in the diagnosis of obstructive and restrictive diseases of the lung. It is a parameter reported in the literature that it varies according to lung disease as well as weight, age and gender characteristics. The aim of this study is to investigate the relationship between age, weight, gender and height characteristics and FEV1/FVC value using a heterogeneous population using Gaussian mixture regression method. Material and Methods: GMR was used to separate the data into components and to make a parameter estimation for each component. The analysis performed on this model revealed that the patients were divided into 5 optimal groups and that these groups showed a regular transition from obstructive pattern to restrictive pattern. Results: The mean values of the components for FEV1/FVC were found as 50.071 (3.238), 67.034 (1.725), 82.156 (1.329), 93.592 (1.041), 98.466 (0.303), respectively. The effect of the weight on the components in terms of parameter estimation and standard errors of the components was determined as 0.445 (0.129) **, 0.226 (0.053) **, 0.173 (0.053) **, -0.036 (0.026), -0.040 (0.018) *, respectively. Conclusion: Direct proportional relationship between the patient's weight and the severity of the obstructive pattern, and between the severity of the disease and the age of the patient in both the obstructive and restrictive pattern are expilicitly proved. Furthermore, it has been revealed that data sets containing heterogeneity can be analyzed by dividing them into sub-components using the GMR model.

Risk of adverse events in gastrointestinal endoscopy: Zero-inflated Poisson regression mixture model for count data and multinomial logit model for the type of event.

We analyze the possible predictive variables for Adverse Events (AEs) during sedation for gastrointestinal (GI) endoscopy. We consider 23,788 GI endoscopies under sedation on adults between 2012 and 2019. A Zero-Inflated Poisson Regression Mixture (ZIPRM) model for count data with concomitant variables is applied, accounting for unobserved heterogeneity and evaluating the risks of multi-drug sedation. A multinomial logit model is also estimated to evaluate cardiovascular, respiratory, hemorrhagic, other AEs and stopping the procedure risk factors. In 7.55% of cases, one or more AEs occurred, most frequently cardiovascular (3.26%) or respiratory (2.77%). Our ZIPRM model identifies one population for non-zero counts. The AE-group reveals that age >75 years yields 46% more AEs than age <66 years; Body Mass Index (BMI) ≥27 27% more AEs than BMI <21; emergency 11% more AEs than routine. Any one-point increment in the American Society of Anesthesiologists (ASA) score and the Mallampati score determines respectively a 42% and a 16% increment in AEs; every hour prolonging endoscopy increases AEs by 41%. Regarding sedation with propofol alone (the sedative of choice), adding opioids to propofol increases AEs by 43% and adding benzodiazepines by 51%. Cardiovascular AEs are increased by age, ASA score, smoke, in-hospital, procedure duration, midazolam/fentanyl associated with propofol. Respiratory AEs are increased by BMI, ASA and Mallampati scores, emergency, in-hospital, procedure duration, midazolam/fentanyl associated with propofol. Hemorrhagic AEs are increased by age, in-hospital, procedure duration, midazolam/fentanyl associated with propofol. The risk of suspension of the endoscopic procedure before accomplishment is increased by female gender, ASA and Mallampati scores, and in-hospital, and it is reduced by emergency and procedure duration. Age, BMI, ASA score, Mallampati score, in-hospital, procedure duration, other sedatives with propofol increase the risk for AEs during sedation for GI endoscopy.