Mixture Model Research Articles

The EX-Lindley distribution with applications to renewable energy sources data

This study introduces a novel extension of the X-Lindley model, called the EX-Lindley model. The EX-Lindley model is a mixture model that combines the characteristics of the gamma model with the weighted Lindley model. The EX-Lindley model is analyzed to determine various statistical properties, including ordinary moments, inverse moments, moment generating function, incomplete moments, conditional moments, mean deviation, Lorenz, mean residual life, mean inactivity time, order statistics, and extropy. The maximum likelihood method is employed to estimate model parameters using complete data. Moreover, the simulation study is used to compare and evaluate the attributes of the estimations for this generalized model. Finally, two examples of datasets on renewable energy sources are utilized to show the importance of the new model compared to some well-known statistical models.

Calling for Equity-focused Quantitative Methodology in Discipline-based Education Research: An Introduction to Latent Class Analysis.

Mixture modeling is a latent variable (i.e., a variable that cannot be measured directly) approach to quantitatively represent unobserved subpopulations within an overall population. It includes a range of cross-sectional (such as latent class [LCA] or latent profile analysis) and longitudinal (such as latent transition analysis) analyses and is often referred to as a "person-centered" approach to quantitative data. This research methods paper describes one type of mixture modeling, LCA, and provides examples of how this method can be applied to discipline-based education research in biology and other science, technology, engineering, and math (STEM) disciplines. This paper briefly introduces LCA, explores the affordances LCA provides for equity-focused STEM education research, highlights some of its limitations, and provides suggestions for researchers interested in exploring LCA as a method of analysis. We encourage discipline-based education researchers to consider how statistical analyses may conflict with their equity-minded research agendas while also introducing LCA as a method of leveraging the affordances of quantitative data to pursue research goals aligned with equity, inclusion, access, and justice agendas.

Deep Single Image Defocus Deblurring via Gaussian Kernel Mixture Learning.

This paper proposes an end-to-end deep learning approach for removing defocus blur from a single defocused image. Defocus blur is a common issue in digital photography that poses a challenge due to its spatially-varying and large blurring effect. The proposed approach addresses this challenge by employing a pixel-wise Gaussian kernel mixture (GKM) model to accurately yet compactly parameterize spatially-varying defocus point spread functions (PSFs), which is motivated by the isotropy in defocus PSFs. We further propose a grouped GKM (GGKM) model that decouples the coefficients in GKM, so as to improve the modeling accuracy with an economic manner. Afterward, a deep neural network called GGKMNet is then developed by unrolling a fixed-point iteration process of GGKM-based image deblurring, which avoids the efficiency issues in existing unrolling DNNs. Using a lightweight scale-recurrent architecture with a coarse-to-fine estimation scheme to predict the coefficients in GGKM, the GGKMNet can efficiently recover an all-in-focus image from a defocused one. Such advantages are demonstrated with extensive experiments on five benchmark datasets, where the GGKMNet outperforms existing defocus deblurring methods in restoration quality, as well as showing advantages in terms of model complexity and computational efficiency.

Changes in Skeletal Muscle Mass in the First 3 Months Following Gastrointestinal Cancer Surgery: A Prospective Study.

Surgical resection is the primary treatment for gastrointestinal (GI) cancers, but postoperative skeletal muscle loss (SML) is common and linked to poor prognosis. This study aims to identify patterns of muscle change, examine its association with quality of life (QoL), and explore predictors of SML in the first 3 months. A prospective cohort study was conducted on patients newly diagnosed with GI cancer and undergoing surgery in China between September 2021 and May 2022. Skeletal muscle mass (SMM) and QoL were assessed at admission, 7 days, 1 month, and 3 months post-surgery. Demographic, clinical data, and biomarkers were collected. Missing data were imputed using multiple imputation. Data were analyzed using growth mixture modelling, bivariate analyses, and logistic regression. A total of 483 patients completed baseline assessment. Of the 242 patients with complete muscle assessments, 92% experienced SML. Three distinct patterns of muscle change were identified: 57% had normal preoperative SMM with mild postoperative SML, 16% had low preoperative SMM with moderate SML, and 27% had normal preoperative mass but severe postoperative SML. Moderate/severe SML was associated with more postoperative complications, poorer health, and higher symptom burden. Independent predictors included advanced age, preoperative sarcopenia, advanced cancer stage, and low prognostic nutrition index (PNI ≤ 45). The results did not change when using imputed values. Although SML is prevalent, patterns of muscle change are heterogeneous among patients. Advanced age, preoperative sarcopenia, advanced cancer stage, and cancer-related inflammation are predictors for moderate/severe SML, highlighting the need for early detection and management.

Towards Effective Clustered Federated Learning: A Peer-to-Peer Framework With Adaptive Neighbor Matching

In federated learning (FL), clients may have diverse objectives, and merging all clients' knowledge into one global model will cause negative transfer to local performance. Thus, clustered FL is proposed to group similar clients into clusters and maintain several global models. In the literature, centralized clustered FL algorithms require the assumption of the number of clusters and hence are not effective enough to explore the latent relationships among clients. In this paper, without assuming the number of clusters, we propose a peer-to-peer (P2P) FL algorithm named PANM. In PANM, clients communicate with peers to adaptively form an effective clustered topology. Specifically, we present two novel metrics for measuring client similarity and a two-stage neighbor matching algorithm based Monte Carlo method and Expectation Maximization under the Gaussian Mixture Model assumption. We have conducted theoretical analyses of PANM on the probability of neighbor estimation and the error gap to the clustered optimum. We have also implemented extensive experiments under both synthetic and real-world clustered heterogeneity. Theoretical analysis and empirical experiments show that the proposed algorithm is superior to the P2P FL counterparts, and it achieves better performance than the centralized cluster FL method. PANM is effective even under extremely low communication budgets.

Functional Concurrent Regression Mixture Models Using Spiked Ewens-Pitman Attraction Priors.

Functional concurrent, or varying-coefficient, regression models are a form of functional data analysis methods in which functional covariates and outcomes are collected concurrently. Two active areas of research for this class of models are identifying influential functional covariates and clustering their relations across observations. In various applications, researchers have applied and developed methods to address these objectives separately. However, no approach currently performs both tasks simultaneously. In this paper, we propose a fully Bayesian functional concurrent regression mixture model that simultaneously performs functional variable selection and clustering for subject-specific trajectories. Our approach introduces a novel spiked Ewens-Pitman attraction prior that identifies and clusters subjects' trajectories marginally for each functional covariate while using similarities in subjects' auxiliary covariate patterns to inform clustering allocation. Using simulated data, we evaluate the clustering, variable selection, and parameter estimation performance of our approach and compare its performance with alternative spiked processes. We then apply our method to functional data collected in a novel, smartphone-based smoking cessation intervention study to investigate individual-level dynamic relations between smoking behaviors and potential risk factors.

Design of an effective multiple objects tracking framework for dynamic video scenes

Nowadays, the applications corresponding to video surveillance systems are getting popular due to their wide range of deployment in various places such as schools, roads, and airports. Despite the continuous evolution and increasing deployment of object-tracking features in video surveillance applications, the loopholes still need to be solved due to the limited functionalities of video-tracking systems. The existing video surveillance systems pose high processing overhead due to the larger size of video files. However, the traditional literature report quite sophisticated schemes which might successfully retain higher object detection accuracy from the video scenes but needs more effectiveness regarding computational complexity under limited computing resources. The study thereby identifies the scope of enhancement in traditional object-tracking functions. Further, it introduces a novel, cost-effective tracking model based on Gaussian mixture model (GMM) and Kalman filter (KF) that can accurately identify numerous mobile objects from a dynamic video scene and ensures computing efficiency. The study's outcome shows that the proposed strategic modelling offers better tracking performance for dynamic objects with cost-effective computation compared to the popular baseline approaches.

A latent variable mixture model for composition-on-composition regression with application to chemical recycling

A latent variable mixture model for composition-on-composition regression with application to chemical recycling

Clustering based strategic 3D deployment and trajectory optimization of UAVs with A-star algorithm for enhanced disaster response

A broad spectrum of communication and information technologies is currently being investigated for their potential applications in disaster management. A high level of situational awareness, combined with a prompt and accurate response, is essential for the preservation of life during catastrophe scenarios. This study presents a novel communication strategy employing Unmanned Aerial Vehicles (UAVs) as aerial base stations for providing connectivity to the affected area. The system takes advantage of the flexibility and quick deployment characteristics of UAVs. The main focus is to determine the optimal UAV deployment along with trajectory planning to ensure connectivity in areas where conventional base stations are inaccessible. The proposed system employs two types of UAVs: cluster UAVs which act as stationary base stations and relay UAVs acting as mobile base stations. A three-step strategy is proposed to find the suitable location of cluster UAVs, optimize their height and power, and find the optimal trajectory of the relay UAVs to maximize the percentage of users served. Gaussian Mixture Model (GMM) clustering is employed to determine the optimal horizontal location of cluster UAVs. An optimization problem is framed for finding out the optimal height and power for cluster UAVs. Heuristic-based A-star algorithm is used to find out the trajectory of the relay UAVs which can efficiently minimize the overall path length while avoiding obstacles. The simulation results confirm the effectiveness of the proposed approach and demonstrate the performance enhancement by comparing it with the benchmark schemes.

Tests of covariate effects under finite Gaussian mixture regression models

Mixture of regression model is widely used to cluster subjects from a suspected heterogeneous population due to differential relationships between response and covariates over unobserved subpopulations. In such applications, statistical evidence pertaining to the significance of a hypothesis is important yet missing to substantiate the findings. In this case, one may wish to test hypotheses regarding the effect of a covariate such as its overall significance. If confirmed, a further test of whether its effects are different in different subpopulations might be performed. This paper is motivated by the analysis of Chiroptera dataset, in which, we are interested in knowing how forearm length development of bat species is influenced by precipitation within their habitats and living regions using finite Gaussian mixture regression (GMR) model. Since precipitation may have different effects on the evolutionary development of the forearm across the underlying subpopulations among bat species worldwide, we propose several testing procedures for hypotheses regarding the effect of precipitation on forearm length under finite GMR models. In addition to the real analysis of Chiroptera data, through simulation studies, we examine the performances of these testing procedures on their type I error rate, power, and consequently, the accuracy of clustering analysis.

High-dimensional robust regression under heavy-tailed data: asymptotics and universality

Abstract We investigate the high-dimensional properties of robust regression estimators in the presence of heavy-tailed contamination of both the covariates and response functions. In particular, we provide a sharp asymptotic characterisation of M-estimators trained on a family of elliptical covariate and noise data distributions including cases where second and higher moments do not exist. We show that, despite being consistent, the Huber loss with optimally tuned location parameter δ is suboptimal in the high-dimensional regime in the presence of heavy-tailed noise, highlighting the necessity of further regularisation to achieve optimal performance. This result also uncovers the existence of a transition in δ as a function of the sample complexity and contamination. Moreover, we derive the decay rates for the excess risk of ridge regression. We show that, while it is both optimal and universal for covariate distributions with finite second moment, its decay rate can be considerably faster when the covariates’ second moment does not exist. Finally, we show that our formulas readily generalise to a richer family of models and data distributions, such as generalised linear estimation with arbitrary convex regularisation trained on mixture models.

On the Detection of Population Heterogeneity in Causation Between Two Variables: Finite Mixture Modeling of Data Collected from Twin Pairs.

Causal inference is inherently complex and relies on key assumptions that can be difficult to validate. One strong assumption is population homogeneity, which assumes that the causal direction remains consistent across individuals. However, there may be variation in causal directions across subpopulations, leading to potential heterogeneity. In psychiatry, for example, the co-occurrence of disorders such as depression and substance use disorder can arise from multiple sources, including shared genetic or environmental factors (common causes) or direct causal pathways between the disorders. A patient diagnosed with two disorders might have one recognized as primary and the other as secondary, suggesting the existence of different types of comorbidity. For example, in some individuals, depression might lead to substance use, while in others, substance use could lead to depression. We account for potential heterogeneity in causal direction by integrating the Direction of Causation (DoC) model for twin data with finite mixture modeling, which allows for the calculation of individual-level likelihoods for alternate causal directions. Through simulations, we demonstrate the effectiveness of using the Direction of Causation Twin Mixture (mixDoC) model to detect and model heterogeneity due to varying causal directions.

Emotional regulation and coping strategies predicted trajectories of anxiety across the first year of the COVID-19 pandemic.

Adverse impacts of the COVID-19 pandemic on mental health have been well-documented, but only a few studies have characterized distinct trajectories of anxiety over time. Further, whether specific emotion regulation and coping efforts to manage pandemic distress predict these distinct trajectories remains unexamined. The study characterized anxiety trajectories across the first year of the pandemic and identified emotion regulation and coping strategies that predict these classes of anxiety trajectories. A national sample of 1108 U.S. adults completed online surveys six times in the first year of the pandemic. Five emotion regulation and coping strategies were assessed (substance use, active, behavioral disengagement, positive reappraisal, and catastrophizing). Latent Growth Mixture Modeling (LGGM) analyses were performed to identify anxiety trajectory classes. LGMM revealed five latent classes: Resilience (consistently very low anxiety; 79.9%), Moderate Anxiety (8.8%), Chronic High Anxiety (4.6%), Improving-Worsening Anxiety (3.2%), and Worsening-Improving Anxiety (3.5%). Using substances, disengagement, and catastrophizing to deal with COVID-19 stress consistently predicted trajectories higher in anxiety as did active coping, while positive reappraisal was unrelated to trajectory class membership. These results identify emotion regulation and coping strategies that appeared to exacerbate anxiety during the course of the pandemic.

A Clustering Approach to Detect Imposter Syndrome Among Sri Lankan Undergraduates

Imposter Syndrome is another name for perceived fraudulence, which is characterized by feelings of personal inadequacy and self-doubt that endure despite education, achievement, experience and success. This is not a disease or abnormality, so there is no obvious reason to imposter emotions. Therefore, even if they suffer from imposter syndrome, they are not able to know this. The results of an undergraduate with imposter syndrome may be inappropriate academic choices, the impact on mental health and social isolation. The aim of the present study is to develop a computerized framework based on a data mining strategy to identify the Severity Level of imposter syndrome for Sri Lankan undergraduates. Thus, this research shows whether the person suffers from imposter syndrome as Low or Moderate or High in level. During the model development, a formal questionnaire was developed examining different influencing factors like depression, anxiety, parentification, family expectations, perfectionism, and low trait self-esteem that can affect the imposter syndrome of an undergraduate and was used to collect data from Sri Lankan undergraduates. In this study, five different unsupervised machine learning techniques, namely K-means, K-medoids, Spectral Clustering, Hierarchical Clustering and Gaussian Mixture Model Clustering were used. Clustering was selected as the best approach as it allows to detect patterns and similarities associated with undergraduates linked to imposter syndrome. To calculate the goodness of the clustering algorithms, the Silhouette index and the Calinski-Harabasz index were used. Among these five clustering algorithms, the best result was shown in the three clusters of K-means Hence, the finalized method helps to predict and classify severity levels of imposter syndrome among Sri Lankan Undergraduates into three groups as low, moderate or high. The research found that among 316 data points, 32.28% showed a low level of imposter syndrome, 16.77% displayed a moderate level, and 50.95% exhibited a high level.

Methodological Advances with Penalized Structural Equation Models

Penalized structural equation models (PSEM) is a powerful technique that unlocks a variety of new modeling frameworks. PSEM applications have been established previously for standard SEM and ESEM models. In this note we aim to extend these ideas to more general types of models such as finite mixture models, multilevel models as well as models with more general types of outcomes. Maximum likelihood and weighted least squares estimation methods naturally accommodate a penalty term. In Mplus 8.12 the PSEM methodology is implemented for all models that can be estimated with these two estimators. Therefore we can now easily combine the more general models with the features of PSEM such as EFA, Alignment, and parameter invariance. Some additional basic SEM applications are also included.

Big data processing using hybrid Gaussian mixture model with salp swarm algorithm

The traditional methods used in big data, like cluster creation and query-based data extraction, fail to yield accurate results on massive networks. To address such issues, the proposed approach involves using the Hadoop Distributed File System (HDFS) for data processing, the map-reduce programming paradigm for data processing, and query optimization techniques to quickly and effectively extract accurate outcomes from a variety of options with a high processing capacity. The methodology proposed in this work makes use of Gaussian Mixture Model (GMM) for data clustering and the Salp Swarm Algorithm (SSA) for optimization. The security of preprocessed data stored on networked clusters with interconnections has been ensured by SHA algorithms. Finally, incorporating into consideration the important parameters, evaluation findings for the experimental performance of the model in the indicated methodology are produced. For this work, the estimated range of input file sizes is 60–100 MB. The processing of 100 MB of input files yielded an accuracy of 96% and results for specificity and sensitivity of 90% and 93%, respectively. The outcomes have been compared with well-known methods like fuzzy C-means and K-means approaches, and the results show that the proposed method effectively distributes accurate data processing to cluster nodes with low latency. Moreover, it uses the least amount of memory resources possible when operating on functional CPUs. As a result, the proposed approach outperforms existing techniques.

A calibration method for projecting future extremes via a linear mapping of parameters

AbstractIn order to study potential impacts arising from climate change, future projections of numerical model output often must be calibrated to be comparable to observations. Rather than calibrating the data values themselves, we propose a novel statistical calibration method for extremes that assumes there exists a linear relationship between parameters associated with model output and parameters associated with observations. This approach allows us to capture uncertainty in both parameter estimates and the linear calibration, which we achieve via bootstrap. To focus on extreme behavior, we assume both model output and observations have distributions composed of a mixture model combining a Weibull distribution with a generalized Pareto distribution for the tail. A simulation study shows good coverage rates. We apply the method to project future daily-averaged river runoff at the Purgatoire River in southeastern Colorado.

Two Fuzzy Clustering Algorithms Based on ARMA Model

This study proposes two fuzzy clustering algorithms based on autoregressive moving average (ARMA) model for series data. The first, referred to as Tsallis entropy-regularized fuzzy c-ARMA model (TFCARMA), is created from k-ARMA, a conventional hard clustering algorithm for series data. TFCARMA is motivated by the relationship between the two clustering algorithms for vectorial data: k-means and Tsallis entropy-regularized fuzzy c-means. The second, referred to as q-divergence-based fuzzy c-ARMA model (QFCARMA), is created from ARMA mixtures, a conventional probabilistic clustering algorithm for series data. QFCARMA is motivated by the relationship between the two clustering algorithms for vectorial data: Gaussian mixture model and q-divergence-based fuzzy c-means. Based on numerical experiments using an artificial dataset, we observed the effects of fuzzification parameters in the proposed algorithms and relationship between the proposed and conventional algorithms. Moreover, numerical experiments using seven real datasets compared the clustering accuracy among the proposed and conventional algorithms.

The Trajectory and Influencing Factors of Fear of Childbirth in Third Trimester Primiparas: A Prospective Longitudinal Study.

Maternal fear of childbirth fluctuates throughout pregnancy. However, no studies have investigated the changing characteristics and influencing factors of fear of childbirth. This study aimed to identify the trajectory patterns of fear of childbirth in third-trimester primiparas and to examine the factors influencing these patterns. This study followed the STROBE checklist for observational research. A prospective longitudinal design was employed, using the Intolerance of Uncertainty Scale, Childbirth Self-Efficacy Inventory and Childbirth Attitudes Questionnaire as primary measures. Data were collected from 226 primiparous women at 28-29 weeks, 32-33 weeks, 36-37 weeks and 39-41 weeks of gestation. Growth mixture modelling (GMM) was fitted using Mplus 8.3 software to analyse the trajectory of fear of childbirth. Logistic regression was conducted to identify the factors influencing these trajectories. The results revealed heterogeneity in the trajectory of fear of childbirth, which could be categorised into six groups: a normal group without fear, a group with no initial fear but increased fear later, a group with mild fear that decreased, a group with mild fear that worsened, a mild fear stable group and a moderate fear stable group. Logistic regression showed that intolerance of uncertainty, childbirth self-efficacy and childbirth preference were the primary factors influencing these trajectories (p < 0.05). This study highlights the varying trajectories of fear of childbirth in third-trimester primiparas. Different categories of fear emerge, each following a distinct path of change. Healthcare providers can use this information to create individualised interventions, addressing specific concerns and influencing factors at various stages, to support the psychological well-being of primiparas during the perinatal period. Healthcare providers should be vigilant about primiparas' awareness of and response to childbirth fear. This study shows that the fear of childbirth often begins to increase or decrease between 32 and 33 weeks of gestation. Screening and interventions should thus be initiated during this period, with follow-up mechanisms in place. Providers should also assess primiparas' capacity to cope with childbirth fear, offering targeted guidance and education to reduce uncertainty, enhance childbirth self-efficacy and ultimately alleviate fear. No patient or public contribution. This study is of great interest to health care providers, suggesting that health care providers should be vigilant about primiparas' awareness of and response to childbirth fear. This study shows that the fear of childbirth often begins to increase or decrease between 32 and 33 weeks of gestation. Screening and interventions should thus be initiated during this period, with follow-up mechanisms in place. Providers should also assess primiparas' capacity to cope with childbirth fear, offering targeted guidance and education to reduce uncertainty, enhance childbirth self-efficacy and ultimately alleviate fear.

Relaxation model for a homogeneous plasmas with spherically symmetric velocity space

Abstract We derive the transport equations from the Vlasov-Fokker-Planck equation when the velocity space is spherically symmetric. The Shkarofsky’s form of Fokker-Planck-Rosenbluth collision operator is employed in the Vlasov-FokkerPlanck equation. A closed-form relaxation model for homogeneous plasmas could be presented in terms of Gauss hypergeometric2F1 functions. This has been accomplished based on the Maxwellian mixture model. Furthermore, we demonstrate that classic models such as two-temperature thermal equilibrium model and thermodynamic equilibrium model are special cases of our relaxation model and the zeroth-order Braginskii heat transfer model can also be derived. The present relaxation model is a nonequilibrium model based on the hypothesis that the plasmas system possesses finitely distinguishable independent features, without relying on the conventional near-equilibrium assumption.