I'm using the Dantzig Selector on high dimensional data and my matrix is ill conditioned (condition number on the order of magnitude of 10^17). I know there are ways to improve the conditioning, namely adding lambda to the diagonals. But I'd rather remove features (columns) of my matrix than distort the data. Or if there was a more numerically stable method to perform Dantzig (I'm using the L1 magic package that Candes wrote), that would be great too. Wondering if anyone has any ideas. Thanks

  • $\begingroup$ I should add, I standardized the variables to be normal with standard deviation 1 and it still did not help much. $\endgroup$ – www3 Apr 20 '16 at 22:16
  • $\begingroup$ This doesn't deal with the root cause of ill-conditioning, and drastically increases computation time, but you might want to consider doing calculations in higher precision, such as quad precision. In quad precision, a condition number of 1e17 might not cause significant problems (presuming you don't square the condition number before doing a calculation). $\endgroup$ – Mark L. Stone Apr 20 '16 at 22:23
  • $\begingroup$ Presuming you're able to do the necessary calculations in higher precision, that is. $\endgroup$ – Mark L. Stone Apr 20 '16 at 22:47

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