scholarly journals High-Dimensional Elliptical Sliced Inverse Regression in non-Gaussian Distributions

2021 ◽  
pp. 1-39
Author(s):  
Xin Chen ◽  
Jia Zhang ◽  
Wang Zhou
Keyword(s):  
Sliced Inverse Regression ◽  
High Dimensional ◽  
Inverse Regression ◽  
Gaussian Distributions ◽  
Non Gaussian

On Sliced Inverse Regression With High-Dimensional Covariates

2006 ◽  
Vol 101 (474) ◽  
pp. 630-643 ◽  
Author(s):  
Lixing Zhu ◽  
Baiqi Miao ◽  
Heng Peng
Keyword(s):  
Sliced Inverse Regression ◽  
High Dimensional ◽  
Inverse Regression

scholarly journals Analysis of microarray right-censored data through fused sliced inverse regression

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Jae Keun Yoo
Keyword(s):  
Dimension Reduction ◽  
Censored Data ◽  
Sliced Inverse Regression ◽  
High Dimensional ◽  
Sufficient Dimension Reduction ◽  
Inverse Regression ◽  
Right Censored Data ◽  
Practical Advantage ◽  
Linear Projection ◽  
Lower Dimensional

Abstract Sufficient dimension reduction (SDR) for a regression pursue a replacement of the original p-dimensional predictors with its lower-dimensional linear projection. The so-called sliced inverse regression (SIR; [5]) arguably has the longest history in SDR methodologies, but it is still one of the most popular one. The SIR is known to be easily affected by the number of slices, which is one of its critical deficits. Recently, a fused approach for SIR is proposed to relieve this weakness, which fuses the kernel matrices computed by the SIR application from various numbers of slices. In the paper, the fused SIR is applied to a large-p-small n regression of a high-dimensional microarray right-censored data to show its practical advantage over usual SIR application. Through model validation, it is confirmed that the fused SIR outperforms the SIR with any number of slices under consideration.

scholarly journals A convex formulation for high-dimensional sparse sliced inverse regression

Biometrika ◽  
2018 ◽  
Author(s):  
Kean Ming Tan ◽  
Zhaoran Wang ◽  
Tong Zhang ◽  
Han Liu ◽  
R Dennis Cook
Keyword(s):  
Sliced Inverse Regression ◽  
High Dimensional ◽  
Inverse Regression ◽  
Convex Formulation

scholarly journals A Nonlinear Maximum Correntropy Information Filter for High-Dimensional Neural Decoding

Entropy ◽  
2021 ◽  
Vol 23 (6) ◽  
pp. 743
Author(s):  
Xi Liu ◽  
Shuhang Chen ◽  
Xiang Shen ◽  
Xiang Zhang ◽  
Yiwen Wang
Keyword(s):  
State Estimation ◽  
Measurement Model ◽  
High Dimensional ◽  
Neural Firing ◽  
The Neural Network ◽  
Information Filter ◽  
Critical Technology ◽  
Dimensional Measurements ◽  
Non Gaussian ◽  
Low Dimensional

Neural signal decoding is a critical technology in brain machine interface (BMI) to interpret movement intention from multi-neural activity collected from paralyzed patients. As a commonly-used decoding algorithm, the Kalman filter is often applied to derive the movement states from high-dimensional neural firing observation. However, its performance is limited and less effective for noisy nonlinear neural systems with high-dimensional measurements. In this paper, we propose a nonlinear maximum correntropy information filter, aiming at better state estimation in the filtering process for a noisy high-dimensional measurement system. We reconstruct the measurement model between the high-dimensional measurements and low-dimensional states using the neural network, and derive the state estimation using the correntropy criterion to cope with the non-Gaussian noise and eliminate large initial uncertainty. Moreover, analyses of convergence and robustness are given. The effectiveness of the proposed algorithm is evaluated by applying it on multiple segments of neural spiking data from two rats to interpret the movement states when the subjects perform a two-lever discrimination task. Our results demonstrate better and more robust state estimation performance when compared with other filters.

scholarly journals Emergence of skewed non-Gaussian distributions of velocity increments in isotropic turbulence

2019 ◽  
Vol 4 (6) ◽  
Author(s):  
W. Sosa-Correa ◽  
R. M. Pereira ◽  
A. M. S. Macêdo ◽  
E. P. Raposo ◽  
D. S. P. Salazar ◽  
...  
Keyword(s):  
Isotropic Turbulence ◽  
Gaussian Distributions ◽  
Velocity Increments ◽  
Non Gaussian
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