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. Author manuscript; available in PMC: 2016 Aug 4.
Published in final edited form as: Technometrics. 2016 Jul 8;58(3):285–293. doi: 10.1080/00401706.2015.1054436

Table 5.

Average runtime comparison (seconds) of OEM for various large-scale penalized and unpenalized least squares problems. All penalized models are fit for 100 values of the tuning parameter. Matrix Sparsity = 0 corresponds to a matrix with all nonzero values.

Matrix Sparsity p  n  OLS Lasso MCP Lasso, SCAD, MCP
0 100 1 × 108 140.140 140.141 140.140 140.143
1 × 109 1, 394.577 1, 394.578 1, 394.578 1, 394.580
1 × 1010 14, 267.520 14, 267.520 14, 267.520 14, 267.520
0 1, 000 1 × 107 946.168 946.266 946.265 946.463
5 × 107 4, 625.954 4, 626.046 4, 626.045 4, 626.232
1 × 108 9, 231.134 9, 231.223 9, 231.223 9, 231.405
0.999 10, 000 1 × 108 676.078 708.447 703.409 776.048
5 × 108 3, 009.860 3, 047.521 3, 034.636 3, 098.680
1 × 109 6, 119.103 6, 150.690 6, 144.003 6, 203.088
0.999 25, 000 1 × 108 2, 817.139 10, 584.220 3, 322.415 11, 924.730
5 × 108 21, 630.780 22, 081.390 21, 866.760 22, 614.350
1 × 109 40, 605.580 40, 952.200 40, 812.850 41, 382.630
0.995 10, 000 1 × 108 4, 221.646 4, 230.995 4, 321.926 4, 350.699
5 × 108 20, 737.900 20, 732.570 20, 772.450 20, 789.470
1 × 109 43, 202.950 43, 350.960 43, 313.470 43, 406.450