• International Journal of Fuzzy Logic and Intelligent Systems
• /
• v.13 no.3
• /
• pp.186-199
• /
• 2013

We pose pattern classification as a density estimation problem where we consider mixtures of generative models under partially labeled data setups. Unlike traditional approaches that estimate density everywhere in data space, we focus on the density along the decision boundary that can yield more discriminative models with superior classification performance. We extend our earlier work on the recursive estimation method for discriminative mixture models to semi-supervised learning setups where some of the data points lack class labels. Our model exploits the mixture structure in the functional gradient framework: it searches for the base mixture component model in a greedy fashion, maximizing the conditional class likelihoods for the labeled data and at the same time minimizing the uncertainty of class label prediction for unlabeled data points. The objective can be effectively imposed as individual mixture component learning on weighted data, hence our mixture learning typically becomes highly efficient for popular base generative models like Gaussians or hidden Markov models. Moreover, apart from the expectation-maximization algorithm, the proposed recursive estimation has several advantages including the lack of need for a pre-determined mixture order and robustness to the choice of initial parameters. We demonstrate the benefits of the proposed approach on a comprehensive set of evaluations consisting of diverse time-series classification problems in semi-supervised scenarios.

• Journal of Korean Society for Quality Management
• /
• v.40 no.3
• /
• pp.347-358
• /
• 2012

Purpose: Given the mixture components - process variables experimental data, we propose the strategy to find the proper combined model. Methods: Process variables are factors in an experiment that are not mixture components but could affect the blending properties of the mixture ingredients. For example, the effectiveness of an etching solution which is measured as an etch rate is not only a function of the proportions of the three acids that are combined to form the mixture, but also depends on the temperature of the solution and the agitation rate. Efficient designs for the mixture components - process variables experiments depend on the mixture components - process variables model which is called a combined model. We often use the product model between the canonical polynomial model for the mixture and process variables model as a combined model. Results: First we choose the reasonable starting models among the class of admissible product models and practical combined models suggested by Lim(2011) based on the model selection criteria and then, search for candidate models which are subset models of the starting model by the sequential variables selection method or all possible regressions procedure. Conclusion: Good candidate models are screened by the evaluation of model selection criteria and checking the residual plots for the validity of the model assumption. The strategy to find the proper combined model is illustrated with examples in this paper.

• Communications for Statistical Applications and Methods
• /
• v.20 no.5
• /
• pp.395-404
• /
• 2013

This paper studies the skewness of the absolute value GARCH(1, 1) models with Gaussian mixture innovations (Gaussian mixture AVGARCH(1, 1) models). The maximum estimated-likelihood estimator (MELE) employed (a two- step estimation method in order to estimate the skewness of Gaussian mixture AVGARCH(1, 1) models. Through the real data analysis, the adequacy of adopting Gaussian mixture innovations is exhibited in reflecting the skewness of two major Korean stock indices.

• Communications for Statistical Applications and Methods
• /
• v.22 no.6
• /
• pp.589-598
• /
• 2015

In longitudinal studies missing data are common and require a complicated analysis. There are two popular modeling frameworks, pattern mixture model (PMM) and selection models (SM) to analyze the missing data. We focus on the PMM and we also propose Bayesian pattern mixture models using generalized linear mixed models (GLMMs) for longitudinal binary data. Sensitivity analysis is used under the missing not at random assumption.

• The Korean Journal of Applied Statistics
• /
• v.24 no.2
• /
• pp.425-433
• /
• 2011

Reject inference in credit scoring is a statistical approach to adjust for nonrandom sample bias due to rejected applicants. Function estimation approaches are based on the assumption that rejected applicants are not necessary to be included in the estimation, when the missing data mechanism is missing at random. On the other hand, the density estimation approach by using mixture models indicates that reject inference should include rejected applicants in the model. When mixture models are chosen for reject inference, it is often assumed that data follow a normal distribution. If data include missing values, an application of the normal mixture model to fully observed cases may cause another sample bias due to missing values. We extend reject inference by a multivariate normal mixture model to handle incomplete characteristic variables. A simulation study shows that inclusion of incomplete characteristic variables outperforms the function estimation approaches.

• International Journal of Reliability and Applications
• /
• v.6 no.2
• /
• pp.101-115
• /
• 2005

This article provides a new class of multivariate linear failure rate distributions where every component is a mixture of linear failure rate distribution. The new class includes several multivariate and bivariate models including Marslall and Olkin type. The approach in this paper is based on the introducing a linear failure rate distributed latent random variable. The distribution of minimum in a competing risk model is discussed.

• International Journal of Reliability and Applications
• /
• v.7 no.1
• /
• pp.55-69
• /
• 2006

This paper presents a new class of multivariate distributions with Pareto where dependence among the components is characterized by a latent random variable. The new class includes several multivariate and bivariate models of Marshall and Olkin type. It is found the bivariate distribution with Pareto is positively quadrant dependent and its mixture. Some important structural properties of the bivariate distributions with Pareto are discussed. The distribution of minimum in a competing risk Pareto model is derived.

• The Korean Journal of Applied Statistics
• /
• v.21 no.5
• /
• pp.835-843
• /
• 2008

In this paper, we investigate a Bayesian inference for software reliability models based on mean value functions which take the form of the mixture of beta distribution functions. The posterior simulation via the Markov chain Monte Carlo approach is used to produce estimates of posterior properties. Its applicability is illustrated with two real data sets. We compute the predictive distribution and the marginal likelihood of various models to compare the performance of them. The model comparison results show that the model based on the beta-mixture performs better than other models.

• Journal of the Korean Data and Information Science Society
• /
• v.28 no.3
• /
• pp.685-695
• /
• 2017

The traditional mixture of experts (ME) modeled the gate network using a certain parametric function. However, if the assumed parametric function does not properly reflect the true nature, the prediction strength of ME would become weak. For example, the parametric ME often uses logistic or multinomial logistic models for the network model. However, this could be very misleading if the true nature of the data is quite different from those models. Although, in this case, we may develop more flexible parametric models by extending the model at hand, we will never be free from such misspecification problems. In order to alleviate such weakness of the parametric ME, we propose to use the semi-parametric mixture of experts (SME) in which the gate network is estimated in a non-parametrical way. Based on this, we compared the performance of the SME with those of ME and neural networks via several simulation experiments and real data examples.

• Communications for Statistical Applications and Methods
• /
• v.21 no.2
• /
• pp.161-168
• /
• 2014

In mixture experiments with process variables, we consider the case that some of process variables are either uncontrollable or hard to control, which are called noise variables. Given the such mixture experimental data with process variables, first we study how to search for candidate models. Good candidate models are screened by the sequential variables selection method and checking the residual plots for the validity of the model assumption. Two methods, which use numerical optimization methods proposed by Derringer and Suich (1980) and minimization of the weighted expected loss, are proposed to find a cost-effective robust optimal condition in which the performance of the mean as well as the variance of the response for each of the candidate models is well-behaved under the cost restriction of the mixture. The proposed methods are illustrated with the well known fish patties texture example described by Cornell (2002).