منابع مشابه
Bayesian Compressed Regression
As an alternative to variable selection or shrinkage in high dimensional regression, we propose to randomly compress the predictors prior to analysis. This dramatically reduces storage and computational bottlenecks, performing well when the predictors can be projected to a low dimensional linear subspace with minimal loss of information about the response. As opposed to existing Bayesian dimens...
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Recent research has studied the role of sparsity in high dimensional regression and signal reconstruction, establishing theoretical limits for recovering sparse models from sparse data. In this paper we study a variant of this problem where the original n input variables are compressed by a random linear transformation to m ≪ n examples in p dimensions, and establish conditions under which a sp...
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We consider the problem of learning, from K data, a regression function in a linear space of high dimensionN using projections onto a random subspace of lower dimension M . From any algorithm minimizing the (possibly penalized) empirical risk, we provide bounds on the excess risk of the estimate computed in the projected subspace (compressed domain) in terms of the excess risk of the estimate b...
متن کاملRobust Bayesian Compressed sensing
We consider the problem of robust compressed sensing whose objective is to recover a high-dimensional sparse signal from compressed measurements corrupted by outliers. A new sparse Bayesian learning method is developed for robust compressed sensing. The basic idea of the proposed method is to identify and remove the outliers from sparse signal recovery. To automatically identify the outliers, w...
متن کاملCompressed Gaussian Process Manifold Regression
Nonparametric regression for massive numbers of samples (n) and features (p) is an important problem. We propose a Bayesian approach for scaling up Gaussian process (GP) regression to big n and p settings using random compression. The proposed compressed GP is particularly motivated by the setting in which features can be projected to a low-dimensional manifold with minimal loss of information ...
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ژورنال
عنوان ژورنال: Journal of the American Statistical Association
سال: 2015
ISSN: 0162-1459,1537-274X
DOI: 10.1080/01621459.2014.969425