Loading...
Please wait, while we are loading the content...
Similar Documents
Compressed regression (2007)
| Content Provider | CiteSeerX |
|---|---|
| Author | Zhou, Shuheng Lafferty, John Wasserman, Larry |
| Abstract | 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. This line of work shows that ℓ1-regularized least squares regression can accurately estimate a sparse linear model from n noisy examples in p dimensions, even if p is much larger than n. 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 sparse linear model can be successfully recovered from the compressed data. A primary motivation for this compression procedure is to anonymize the data and preserve privacy by revealing little information about the original data. We characterize the number of random projections that are required for ℓ1-regularized compressed regression to identify the nonzero coefficients in the true model with probability approaching one, a property called “sparsistence. ” In addition, we show that ℓ1-regularized compressed regression asymptotically predicts as well as an oracle linear model, a property called “persistence.” |
| File Format | |
| Language | English |
| Publisher Date | 2007-01-01 |
| Access Restriction | Open |
| Subject Keyword | 1-regularized Compressed Regression Sparse Linear Model Random Projection 1-regularized Least Square Regression Sparse Model Little Information Recent Research Signal Reconstruction Nonzero Coefficient Oracle Linear Model True Model Compression Procedure Noisy Example Original Data Sparse Data Primary Motivation Theoretical Limit Work Show High Dimensional Regression Original Input Variable Random Linear Transformation |
| Content Type | Text |
| Resource Type | Technical Report |
