Compressed Regression
- Shuheng Zhou (5415173)
- John Lafferty (5399966)
- Larry Wasserman (5362715)
DOIAbstract
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<1-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.” Finally, we characterize the privacy properties of the compression procedure in information-theoretic terms, e...
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