Bayesian inverse regression for supervised dimension reduction with small datasets
Xin Cai,Guang Lin,Jinglai Li +2 more
2
TL;DR: This work proposes a Bayesian framework to compute the conditional distribution where the likelihood function is constructed using the Gaussian process regression model and can then be computed directly via Monte Carlo sampling.
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Abstract: We consider supervised dimension reduction problems, namely to identify a low dimensional projection of the predictors x which can retain the statistical relationship between x and the response var...
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Citations
Shrinkage for extreme partial least-squares
Julyan Arbel,Stéphane Girard,Hadrien Lorenzo +2 more
TL;DR: This study adapts partial least squares for extreme value modeling, introducing a Bayesian framework for dimension reduction and shrinkage, and demonstrates its effectiveness in high-dimensional settings through simulation and real-world data analysis.
Shrinkage for Extreme Partial Least-Squares
Julyan Arbel,Stéphane Girard,Hadrien Lorenzo +2 more
- 20 Mar 2024
TL;DR: Dimension-reduction techniques for extreme value modelling using Extreme Partial Least Squares (EPLS) are investigated. EPLS is an adaptation of PLS tailored to extreme values, and its directions are interpreted as maximum likelihood estimators. The Bayesian paradigm is employed to incorporate prior information into the projection direction estimation. The method is shown to be effective in moderate data problems within high-dimensional settings.
References
Gaussian Processes For Machine Learning
Tanja Hueber
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TL;DR: The gaussian processes for machine learning is universally compatible with any devices to read, and is available in the digital library an online access to it is set as public so you can get it instantly.
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Gaussian Processes for Regression
Christopher Williams,Carl Edward Rasmussen +1 more
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TL;DR: This paper investigates the use of Gaussian process priors over functions, which permit the predictive Bayesian analysis for fixed values of hyperparameters to be carried out exactly using matrix operations.
•Posted Content
Finite Mixture Models
TL;DR: Finite mixture models as mentioned in this paper provide a natural way of modeling continuous or discrete outcomes that are observed from populations consisting of a finite number of homogeneous subpopulations, which are abundant in the social and behavioral sciences, biological and environmental sciences, engineering and finance.