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. Author manuscript; available in PMC: 2013 May 1.
Published in final edited form as: J Multivar Anal. 2012 May 1;107:119–140. doi: 10.1016/j.jmva.2012.01.005

Table 2.

Comparison of the performance for simulated data sets of different dimensions when l1 penalty functions are used.

Precision Matrix Measure MNGM GGM-I GGM-C GGM-R
Model 3, n = 100, p = 150, q = 150
A ||ΔA|| 0.12(0.014) 0.31(0.013) 0.78(0.094)
|||ΔA||| 0.32(0.028) 0.59(0.027) 1.45(0.092)
||ΔA|| 0.05(0.011) 0.20(0.010) 0.49(0.074)
||ΔA||F 0.61(0.069) 2.26(0.120) 4.72(0.802)
SPEA 0.84(0.005) 0.80(0.004) 1.00(0.000)
SENA 1.00(0.000) 1.00(0.000) 0.00(0.000)
MCCA 0.45(0.006) 0.40(0.004) 0.05(0.022)
B ||ΔB|| 0.10(0.009) 0.10(0.009) 0.77(0.186)
|||ΔB||| 0.29(0.022) 0.32(0.025) 1.38(0.208)
||ΔB|| 0.04(0.007) 0.04(0.007) 0.58(0.236)
||ΔB||F 0.53(0.025) 0.56(0.024) 4.25(0.856)
SPEB 0.83(0.005) 0.80(0.003) 1.00(0.000)
SENB 1.00(0.000) 1.00(0.000) 0.01(0.000)
MCCB 0.43(0.007) 0.40(0.004) 0.07(0.021)
Model 4, n = 100, p = 500, q = 500
A ||ΔA|| 0.10(0.008) 0.22(0.008) 3.69(0.521)
|||ΔA||| 0.27(0.018) 0.45(0.019) 4.23(0.502)
||ΔA|| 0.04(0.007) 0.14(0.006) 3.63(0.581)
||ΔA||F 0.95(0.078) 2.94(0.131) 43.68(6.153)
SPEA 0.99(0.001) 0.95(0.001) 1.00(0.002)
SENA 1.00(0.00) 1.00(0.00) 0.01(0.038)
MCCA 0.76(0.008) 0.52(0.003) 0.13(0.030)
B ||ΔB|| 0.08(0.006) 0.08(0.006) 1.17(0.026)
|||ΔB||| 0.26(0.019) 0.26(0.019) 6.88(0.809)
||ΔB|| 0.03(0.003) 0.03(0.004) 0.34(0.088)
||ΔB||F 0.79(0.028) 0.76(0.031) 13.07(0.773)
SPEB 0.98(0.001) 0.97(0.001) 0.64(0.055)
SENB 1.00(0.000) 1.00(0.000) 0.65(0.095)
MCCB 0.75(0.007) 0.62(0.003) 0.06(0.015)

MNGM: the matrix normal graphical model with l1 penalties; GGM-I: Gaussian graphical model treating rows or columns as independent; GGM-R/GGM-C: Gaussian graphical model that uses only data from the first column or the first row. For each measurement, mean and standard deviation are calculated over 50 replications.