scholarly journals Bayesian Sparse Estimation Using Double Lomax Priors

2013 ◽  
Vol 2013 ◽  
pp. 1-17 ◽  
Author(s):  
Xiaojing Gu ◽  
Henry Leung ◽  
Xingsheng Gu
Keyword(s):  
Bayesian Inference ◽  
Latent Variable ◽  
Linear Models ◽  
Model Identification ◽  
Ar Model ◽  
Smoothing Effect ◽  
Inference Procedure ◽  
Sparse Estimation ◽  
Automatic Relevance Determination ◽  
Convergence Performance

Sparsity-promoting prior along with Bayesian inference is an effective approach in solving sparse linear models (SLMs). In this paper, we first introduce a new sparsity-promoting prior coined as Double Lomax prior, which corresponds to a three-level hierarchical model, and then we derive a full variational Bayesian (VB) inference procedure. When noninformative hyperprior is assumed, we further show that the proposed method has one more latent variable than the canonical automatic relevance determination (ARD). This variable has a smoothing effect on the solution trajectories, thus providing improved convergence performance. The effectiveness of the proposed method is demonstrated by numerical simulations including autoregressive (AR) model identification and compressive sensing (CS) problems.

Constructing Generative Topographic Mapping by Variational Bayes with ARD Hierarchical Prior

2013 ◽  
Vol 17 (4) ◽  
pp. 473-479 ◽  
Author(s):  
Nobuhiko Yamaguchi ◽  
Keyword(s):  
Bayesian Inference ◽  
Latent Variable ◽  
Regularization Parameter ◽  
Topographic Mapping ◽  
Generative Topographic Mapping ◽  
Variable Model ◽  
Variational Bayesian ◽  
Variational Bayesian Inference ◽  
Hierarchical Prior ◽  
Automatic Relevance Determination

Generative Topographic Mapping (GTM) is a nonlinear latent variable model introduced as a data visualization technique by Bishop et al. In this paper, we focus on variational Bayesian inference in GTM. Variational Bayesian GTM, first proposed by Olier et al., uses a single regularization term and regularization parameter to avoid overfitting and therefore cannot be used to control the degree of regularization locally. To overcome this problem, we propose variational Bayesian inference with Automatic Relevance Determination (ARD) hierarchical prior for use with GTM. The proposed model uses multiple regularization parameters and therefore can be used to control the degree of regularization in local areas of data space individually. Several experiments show that GTM that we propose provides better visualization than conventional GTM approaches.

A new approach for subset 2-D AR model identification for describing textures

1997 ◽  
Vol 6 (3) ◽  
pp. 407-413 ◽  
Author(s):  
A. Sarkar ◽  
K.M.S. Sharma ◽  
R.V. Sonak
Keyword(s):  
Model Identification ◽  
Ar Model ◽  
New Approach

scholarly journals Bayesian Inference on Order-Constrained Parameters in Generalized Linear Models

Biometrics ◽  
2003 ◽  
Vol 59 (2) ◽  
pp. 286-295 ◽  
Author(s):  
David B. Dunson ◽  
Brian Neelon
Keyword(s):  
Bayesian Inference ◽  
Generalized Linear Models ◽  
Linear Models

Mixed frequency structured AR model identification

2013 ◽  
Author(s):  
Mohsen Zamani ◽  
Elisabeth Felsenstein ◽  
Brian D. O. Anderson ◽  
Manfred Deistler
Keyword(s):  
Model Identification ◽  
Ar Model ◽  
Mixed Frequency

AR model identification with unknown process order

1990 ◽  
Vol 38 (5) ◽  
pp. 872-876 ◽  
Author(s):  
S.K. Katsikas ◽  
S.D. Likothanassis ◽  
D.G. Lainiotis
Keyword(s):  
Model Identification ◽  
Ar Model

A Growth Model for Multilevel Ordinal Data

2005 ◽  
Vol 30 (4) ◽  
pp. 369-396 ◽  
Author(s):  
Eisuke Segawa
Keyword(s):  
Latent Variable ◽  
Ordinal Data ◽  
Linear Models ◽  
Growth Models ◽  
Simulated Data ◽  
Real Data ◽  
Analytic Structure ◽  
Data Sets ◽  
Data Set ◽  
Time Points

Multi-indicator growth models were formulated as special three-level hierarchical generalized linear models to analyze growth of a trait latent variable measured by ordinal items. Items are nested within a time-point, and time-points are nested within subject. These models are special because they include factor analytic structure. This model can analyze not only data with item- and time-level missing observations, but also data with time points freely specified over subjects. Furthermore, features useful for longitudinal analyses, “autoregressive error degree one” structure for the trait residuals and estimated time-scores, were included. The approach is Bayesian with Markov Chain and Monte Carlo, and the model is implemented in WinBUGS. They are illustrated with two simulated data sets and one real data set with planned missing items within a scale.

A New Method for Discharge State Prediction of Micro-EDM Using Empirical Mode Decomposition

2009 ◽  
Vol 132 (1) ◽  
Author(s):  
Zhenyuan Jia ◽  
Lingxuan Zhang ◽  
Fuji Wang ◽  
Wei Liu
Keyword(s):  
Empirical Mode Decomposition ◽  
Linear Prediction ◽  
Electrical Discharge Machining ◽  
Model Identification ◽  
Prediction Method ◽  
Ar Model ◽  
Micro Edm ◽  
Multisensor Data Fusion ◽  
State Prediction ◽  
Mode Decomposition

The property of high frequency in micro-EDM (electrical discharge machining) causes the discharge states to vary much faster than in conventional EDM, and discharge states of micro-EDM have the characteristics of nonstationarity, nonlinearity, and internal coupling, all of this makes it very difficult to carry out stable control. Thus empirical mode decomposition is adopted to conduct the prediction of the discharge states obtained through multisensor data fusion and fuzzy logic in micro-EDM. Combined with the autoregressive (AR) model identification and linear prediction, the mathematical model for EDM discharge state prediction using empirical mode decomposition is established and the corresponding prediction method is presented. Experiments demonstrate that the new prediction method with short identification data is highly accurate and operates quickly. Even using short model identification data, the accuracy of empirical mode decomposition prediction can stably reach a correlation of 74%, which satisfies statistical expectations. Additionally, the new process can also effectively eliminate the lag of conventional prediction methods to improve the efficiency of micro-EDM, and it provides a good basis to enhance the stability of the control system.

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