scholarly journals Manipulation Testing Based on Density Discontinuity

2018 ◽  
Vol 18 (1) ◽  
pp. 234-261 ◽  
Author(s):  
Matias D. Cattaneo ◽  
Michael Jansson ◽  
Xinwei Ma
Keyword(s):  
Density Estimation ◽  
R Package ◽  
Estimation Technique ◽  
University Of Michigan ◽  
Working Paper ◽  
Local Polynomial ◽  
Density Discontinuity ◽  
Additional Assumptions ◽  
Density Estimators ◽  
Power Properties

In this article, we introduce two community-contributed commands, rddensity and rdbwdensity, that implement automatic manipulation tests based on density discontinuity and are constructed using the results for local-polynomial density estimators in Cattaneo, Jansson, and Ma (2017b, Simple local polynomial density estimators, Working paper, University of Michigan). These new tests exhibit better size properties (and more power under additional assumptions) than other conventional approaches currently available in the literature. The first command, rddensity, implements manipulation tests based on a novel local-polynomial density estimation technique that avoids prebinning of the data (improving size properties) and allows for restrictions on other features of the model (improving power properties). The second command, rdbwdensity, implements several bandwidth selectors specifically tailored for the manipulation tests discussed herein. We also provide a companion R package with the same syntax and capabilities as rddensity and rdbwdensity.

scholarly journals Improved Initialization of the EM Algorithm for Mixture Model Parameter Estimation

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 373
Author(s):  
Branislav Panić ◽  
Jernej Klemenc ◽  
Marko Nagode
Keyword(s):  
Em Algorithm ◽  
Density Estimation ◽  
Mixture Model ◽  
Expectation Maximization ◽  
State Of The Art ◽  
R Package ◽  
Likelihood Estimator ◽  
Local Optima ◽  
The Em Algorithm ◽  
Initialization Algorithm

A commonly used tool for estimating the parameters of a mixture model is the Expectation–Maximization (EM) algorithm, which is an iterative procedure that can serve as a maximum-likelihood estimator. The EM algorithm has well-documented drawbacks, such as the need for good initial values and the possibility of being trapped in local optima. Nevertheless, because of its appealing properties, EM plays an important role in estimating the parameters of mixture models. To overcome these initialization problems with EM, in this paper, we propose the Rough-Enhanced-Bayes mixture estimation (REBMIX) algorithm as a more effective initialization algorithm. Three different strategies are derived for dealing with the unknown number of components in the mixture model. These strategies are thoroughly tested on artificial datasets, density–estimation datasets and image–segmentation problems and compared with state-of-the-art initialization methods for the EM. Our proposal shows promising results in terms of clustering and density-estimation performance as well as in terms of computational efficiency. All the improvements are implemented in the rebmix R package.

scholarly journals Multivariate mixed kernel density estimators and their application in machine learning for classification of biological objects based on spectral measurements

2019 ◽  
Vol 43 (4) ◽  
pp. 677-691
Author(s):  
A.A. Sirota ◽  
A.O. Donskikh ◽  
A.V. Akimov ◽  
D.A. Minakov
Keyword(s):  
Machine Learning ◽  
Density Estimation ◽  
Data Augmentation ◽  
Kernel Density ◽  
Machine Learning Algorithms ◽  
Spectral Measurements ◽  
Density Estimates ◽  
Biological Objects ◽  
Density Estimators

A problem of non-parametric multivariate density estimation for machine learning and data augmentation is considered. A new mixed density estimation method based on calculating the convolution of independently obtained kernel density estimates for unknown distributions of informative features and a known (or independently estimated) density for non-informative interference occurring during measurements is proposed. Properties of the mixed density estimates obtained using this method are analyzed. The method is compared with a conventional Parzen-Rosenblatt window method applied directly to the training data. The equivalence of the mixed kernel density estimator and the data augmentation procedure based on the known (or estimated) statistical model of interference is theoretically and experimentally proven. The applicability of the mixed density estimators for training of machine learning algorithms for the classification of biological objects (elements of grain mixtures) based on spectral measurements in the visible and near-infrared regions is evaluated.

Nonparametric frequency polygon estimation for modeling input data

2019 ◽  
Author(s):  
Stephen Hague ◽  
Simaan AbouRizk
Keyword(s):  
Density Estimation ◽  
Kernel Density Estimation ◽  
Posterior Distribution ◽  
Input Data ◽  
Probability Distributions ◽  
Kernel Density ◽  
Simulation Environment ◽  
Frequency Polygon ◽  
Density Estimators

To construct valid probability distributions solely from input data, this paper compares three nonparametric density estimators: (1) histograms, (2) Kernel Density Estimation, and (3) Frequency Polygon Estimation. A pseudocode is implemented, a practical example is illustrated, and the Simphony.NET simulation environment is used to fit the nonparametric frequency polygon to a set of data to recreate it as a posterior distribution via the Metropolis-Hastings algorithm.

An Improved Adaptive Kernel-Based Object Tracking

2011 ◽  
Vol 383-390 ◽  
pp. 7588-7594
Author(s):  
Zheng Hua Liu ◽  
Li Han
Keyword(s):  
Object Tracking ◽  
Target Tracking ◽  
Density Estimation ◽  
Mean Shift ◽  
Multiple Scale ◽  
Tracking Algorithm ◽  
Estimation Technique ◽  
Scale Theory ◽  
Fixed Kernel ◽  
Adaptive Kernel

Kernel-based density estimation technique, especially Mean-shift based tracking technique, is a successful application to target tracking, which has the characteristics such as with few parameters, robustness, and fast convergence. However, classic Mean-shift based tracking algorithm uses fixed kernel-bandwidth, which limits the performance when the target’s orientation and scale change. An Improved adaptive kernel-based object tracking is proposed, which extend 2-dimentional mean shift to 3-dimentional, meanwhile combine multiple scale theory into tracking algorithm. Such improvements can enable the algorithm not only track zooming objects, but also track rotating objects. The experimental results validate that the new algorithm can adapt to the changes of orientation and scale of the target effectively.

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