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

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1090 ◽  
Author(s):  
Branislav Panić ◽  
Jernej Klemenc ◽  
Marko Nagode

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.

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Yuwei Wang ◽  
Mofei Wen

This paper presents an in-depth analysis of tennis match scene classification using an adaptive Gaussian mixture model parameter estimation simulation algorithm. We divided the main components of semantic analysis into type of motion, distance of motion, speed of motion, and landing area of the tennis ball. Firstly, for the problem that both people and tennis balls in the video frames of tennis matches from the surveillance viewpoint are very small, we propose an adaptive Gaussian mixture model parameter estimation algorithm, which has good accuracy and speed on small targets. Secondly, in this paper, we design a sports player tracking algorithm based on role division and continuously lock the target player to be tracked and output the player region. At the same time, based on the displacement information of the key points of the player’s body and the system running time, the distance and speed of the player’s movement are obtained. Then, for the problem that tennis balls are small and difficult to capture in high-speed motion, this paper designs a prior knowledge-based algorithm for predicting tennis ball motion and landing area to derive the landing area of tennis balls. Finally, this paper implements a prototype system for semantic analysis of real-time video of tennis matches and tests and analyzes the performance indexes of the system, and the results show that the system has good performance in real-time, accuracy, and stability.


Energy ◽  
2020 ◽  
Vol 212 ◽  
pp. 118738
Author(s):  
Zixuan Yang ◽  
Qian Liu ◽  
Leiyu Zhang ◽  
Jialei Dai ◽  
Navid Razmjooy

2021 ◽  
pp. 096228022110175
Author(s):  
Jan P Burgard ◽  
Joscha Krause ◽  
Ralf Münnich ◽  
Domingo Morales

Obesity is considered to be one of the primary health risks in modern industrialized societies. Estimating the evolution of its prevalence over time is an essential element of public health reporting. This requires the application of suitable statistical methods on epidemiologic data with substantial local detail. Generalized linear-mixed models with medical treatment records as covariates mark a powerful combination for this purpose. However, the task is methodologically challenging. Disease frequencies are subject to both regional and temporal heterogeneity. Medical treatment records often show strong internal correlation due to diagnosis-related grouping. This frequently causes excessive variance in model parameter estimation due to rank-deficiency problems. Further, generalized linear-mixed models are often estimated via approximate inference methods as their likelihood functions do not have closed forms. These problems combined lead to unacceptable uncertainty in prevalence estimates over time. We propose an l2-penalized temporal logit-mixed model to solve these issues. We derive empirical best predictors and present a parametric bootstrap to estimate their mean-squared errors. A novel penalized maximum approximate likelihood algorithm for model parameter estimation is stated. With this new methodology, the regional obesity prevalence in Germany from 2009 to 2012 is estimated. We find that the national prevalence ranges between 15 and 16%, with significant regional clustering in eastern Germany.


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