Joint bilinear transformation space based maximum a posteriori linear regression adaptation using prior with variance function

2011 ◽  
Author(s):  
Hwa Jeon Song ◽  
Yunkeun Lee ◽  
Hyung Soon Kim
Keyword(s):  
Linear Regression ◽  
Variance Function ◽  
Maximum A Posteriori ◽  
A Posteriori ◽  
Bilinear Transformation ◽  
Transformation Space

scholarly journals New approach to Bayesian high-dimensional linear regression

2018 ◽  
Vol 7 (4) ◽  
pp. 605-655 ◽  
Author(s):  
Shirin Jalali ◽  
Arian Maleki
Keyword(s):  
Linear Regression ◽  
Sampling Rate ◽  
High Dimensional ◽  
Maximum A Posteriori ◽  
Map Estimation ◽  
A Posteriori ◽  
Fundamental Limits ◽  
New Approach ◽  
Estimation Scheme ◽  
Response Variables

Abstract Consider the problem of estimating parameters $X^n \in \mathbb{R}^n $, from $m$ response variables $Y^m = AX^n+Z^m$, under the assumption that the distribution of $X^n$ is known. Lack of computationally feasible algorithms that employ generic prior distributions and provide a good estimate of $X^n$ has limited the set of distributions researchers use to model the data. To address this challenge, in this article, a new estimation scheme named quantized maximum a posteriori (Q-MAP) is proposed. The new method has the following properties: (i) In the noiseless setting, it has similarities to maximum a posteriori (MAP) estimation. (ii) In the noiseless setting, when $X_1,\ldots,X_n$ are independent and identically distributed, asymptotically, as $n$ grows to infinity, its required sampling rate ($m/n$) for an almost zero-distortion recovery approaches the fundamental limits. (iii) It scales favorably with the dimensions of the problem and therefore is applicable to high-dimensional setups. (iv) The solution of the Q-MAP optimization can be found via a proposed iterative algorithm that is provably robust to error (noise) in response variables.

Maximum A Posteriori Linear Regression for language recognition

2012 ◽  
Vol 39 (4) ◽  
pp. 4287-4291 ◽  
Author(s):  
Jinchao Yang ◽  
Xiang Zhang ◽  
Hongbin Suo ◽  
Li Lu ◽  
Jianping Zhang ◽  
...  
Keyword(s):  
Linear Regression ◽  
Maximum A Posteriori ◽  
A Posteriori ◽  
Language Recognition

Structural maximum a posteriori linear regression for fast HMM adaptation

2002 ◽  
Vol 16 (1) ◽  
pp. 5-24 ◽  
Author(s):  
Olivier Siohan ◽  
Tor André Myrvoll ◽  
Chin-Hui Lee
Keyword(s):  
Linear Regression ◽  
Maximum A Posteriori ◽  
A Posteriori
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