scholarly journals A Parametric Bayesian Approach in Density Ratio Estimation

Stats ◽  
2019 ◽  
Vol 2 (2) ◽  
pp. 189-201
Author(s):  
Abdolnasser Sadeghkhani ◽  
Yingwei Peng ◽  
Chunfang Lin
Keyword(s):  
Loss Function ◽  
Bayesian Approach ◽  
Risk Function ◽  
Density Ratio ◽  
Ratio Estimation ◽  
Function Estimation ◽  
Different Types ◽  
Ratio Estimators

This paper is concerned with estimating the ratio of two distributions with different parameters and common supports. We consider a Bayesian approach based on the log–Huber loss function, which is resistant to outliers and useful for finding robust M-estimators. We propose two different types of Bayesian density ratio estimators and compare their performance in terms of frequentist risk function. Some applications, such as classification and divergence function estimation, are addressed.

scholarly journals A Parametric Bayesian Approach in Density Ratio Estimation

2019 ◽  
Author(s):  
Abdolnasser Sadeghkhani ◽  
Yingwei Peng ◽  
Devon Lin
Keyword(s):  
Loss Function ◽  
Bayesian Approach ◽  
Risk Function ◽  
Density Ratio ◽  
Ratio Estimation ◽  
Function Estimation ◽  
Bayesian Risk ◽  
Different Types ◽  
Ratio Estimators

This paper considers estimating the ratio of two distributions with different parameters and common supports. We consider a Bayesian approach based on the Log--Huber loss function which is resistant to outliers and useful to find robust M-estimators. We propose two different types of Bayesian density ratio estimators and compare their performance in terms of Bayesian risk function with themselves as well as the usual plug-in density ratio estimators. Some applications such as classification and divergence function estimation are addressed.

scholarly journals A Bayesian Approach for Estimating Parameter of Rayleigh Distribution

2019 ◽  
Vol 11 (1) ◽  
pp. 23-39
Author(s):  
J. Mahanta ◽  
M. B. A. Talukdar
Keyword(s):  
Weibull Distribution ◽  
Loss Function ◽  
Bayesian Approach ◽  
Rayleigh Distribution ◽  
Loss Functions ◽  
Bayes Risk ◽  
Squared Error ◽  
Different Types ◽  
Two Parameters ◽  
Special Case

This paper is concerned with estimating the parameter of Rayleigh distribution (special case of two parameters Weibull distribution) by adopting Bayesian approach under squared error (SE), LINEX, MLINEX loss function. The performances of the obtained estimators for different types of loss functions are then compared. Better result is found in Bayesian approach under MLINEX loss function. Bayes risk of the estimators are also computed and presented in graphs.

Inlier-Based Outlier Detection via Direct Density Ratio Estimation

2008 ◽  
Author(s):  
Shohei Hido ◽  
Yuta Tsuboi ◽  
Hisashi Kashima ◽  
Masashi Sugiyama ◽  
Takafumi Kanamori
Keyword(s):  
Outlier Detection ◽  
Density Ratio ◽  
Ratio Estimation

scholarly journals Condition assessment of electro-mechanical actuators for aerospace using relative density-ratio estimation

2018 ◽  
Vol 51 (15) ◽  
pp. 957-962 ◽  
Author(s):  
M. Mazzoleni ◽  
M. Scandella ◽  
Y. Maccarana ◽  
F. Previdi ◽  
G. Pispola ◽  
...  
Keyword(s):  
Relative Density ◽  
Density Ratio ◽  
Condition Assessment ◽  
Ratio Estimation

Online Direct Density-Ratio Estimation Applied to Inlier-Based Outlier Detection

2015 ◽  
Vol 27 (9) ◽  
pp. 1899-1914
Author(s):  
Marthinus Christoffel du Plessis ◽  
Hiroaki Shiino ◽  
Masashi Sugiyama
Keyword(s):  
Outlier Detection ◽  
Density Estimation ◽  
Density Ratio ◽  
Learning Problems ◽  
Conditional Density ◽  
Ratio Estimation ◽  
Data Set ◽  
Step Procedure ◽  
Training Samples ◽  
Probability Densities

Many machine learning problems, such as nonstationarity adaptation, outlier detection, dimensionality reduction, and conditional density estimation, can be effectively solved by using the ratio of probability densities. Since the naive two-step procedure of first estimating the probability densities and then taking their ratio performs poorly, methods to directly estimate the density ratio from two sets of samples without density estimation have been extensively studied recently. However, these methods are batch algorithms that use the whole data set to estimate the density ratio, and they are inefficient in the online setup, where training samples are provided sequentially and solutions are updated incrementally without storing previous samples. In this letter, we propose two online density-ratio estimators based on the adaptive regularization of weight vectors. Through experiments on inlier-based outlier detection, we demonstrate the usefulness of the proposed methods.

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