sparse_proj: Sparse projections using the square-root Lasso In RPtests: Goodness of Fit Tests for High-Dimensional Linear Regression Models

Description

Regresses each column of `x` against all others in turn, using the square-root Lasso, and outputs residuals from the regressions. Thus it outputs a form of sparse projection of each column on all others. Alternatively, given two matrices `x_null` and `x_alt`, it regresses each column of `x_null` on `x_alt` in a similar fashion.

Usage

 `1` ```sparse_proj(x, x_null, x_alt, mc.cores = 1L, rescale = FALSE, ...) ```

Arguments

 `x` Matrix with each row an observation vector. Need not be supplied if `x_alt` and `x_null` are given. `x_null` Matrix whose columns are to be regressed on to `x_alt`. `x_alt` Matrix which the columns of `x_null` are regressed on to. Must be specified if `x_null` is given. `mc.cores` The number of cores to use. Will always be 1 in Windows. `rescale` Should the columns of the output be rescaled to have l_2-norm the square-root of the number of observations? Default is `FALSE`. `...` Additional arguments to be passed to `sqrt_lasso`.

Value

A matrix where each column gives the residuals.

References

A. Belloni, V. Chernozhukov, and L. Wang. (2011) Square-root lasso: pivotal recovery of sparse signals via conic programming. Biometrika, 98(4):791-806. http://biomet.oxfordjournals.org/content/98/4/791.refs T. Sun and C.-H. Zhang. (2012) Scaled sparse linear regression. Biometrika, 99(4):879-898. http://biomet.oxfordjournals.org/content/early/2012/09/24/biomet.ass043.short T. Sun and C.-H. Zhang. (2013) Sparse matrix inversion with scaled lasso. The Journal of Machine Learning Research, 14(1):3385-3418. www.jmlr.org/papers/volume14/sun13a/sun13a.pdf

See Also

`sqrt_lasso` and `RPtest_single`.

Examples

 ```1 2``` ```x <- matrix(rnorm(50*100), 50, 100) out <- sparse_proj(x) ```

RPtests documentation built on May 29, 2017, 9:06 a.m.