Group Selection and Shrinkage: Structured Sparsity for Semiparametric Additive Models

Figures & data

Figure 1 Comparisons of estimators for sparse semiparametric regression. Metrics are aggregated over 30 synthetic datasets generated with n = 1000, p = 10,000, and g = 5000. Solid points represent averages and error bars denote (one) standard errors. Dashed lines indicate the true number of nonzero functions.

Figure 2 Comparisons of estimators for sparse semiparametric classification. Metrics are aggregated over 30 synthetic datasets generated with n = 1000, p = 10,000, and g = 5000. Solid points represent averages and error bars denote (one) standard errors. Dashed lines indicate the true number of nonzero functions.

Figure 3 Comparisons of grpsel and grpreg, and their estimators. Metrics are aggregated over 30 synthetic datasets generated with $\text{SNR}=1$, $\rho =0.5$, and n = 1000. Vertical bars represent averages and error bars denote (one) standard errors.

Table 1 Comparisons of methods for modeling supermarket foot traffic.

		Sparsity
	Mean square loss	Total	Linear	Nonlinear
Group subset + shrinkage	0.650 (0.026)	178.6 (2.3)	115.7 (1.2)	62.9 (2.0)
Group lasso	0.651 (0.025)	267.0 (12.9)	132.9 (2.3)	134.1 (11.0)
Group MCP	0.658 (0.026)	215.1 (6.1)	120.9 (1.2)	94.1 (5.5)
Lasso	0.712 (0.028)	165.2 (5.0)	165.2 (5.0)	–
Random forest	1.330 (0.057)	–	–	–
Mean	9.856 (0.367)	–	–	–

NOTE: Metrics are aggregated over 30 splits of the data into training and testing sets. Averages are reported next to (one) standard errors in parentheses.

Table 2 Comparisons of methods for modeling economic recessions.

		Sparsity
	Mean logistic loss	Total	Linear	Nonlinear
Group subset + shrinkage	0.968 (0.103)	44.0 (2.5)	16.2 (0.9)	27.8 (1.8)
Group lasso	1.063 (0.102)	57.5 (1.5)	30.7 (0.7)	26.8 (1.0)
Group MCP	1.141 (0.092)	31.5 (0.7)	18.7 (0.5)	12.8 (0.4)
Lasso	1.093 (0.107)	56.8 (1.1)	56.8 (1.1)	–
Random forest	1.294 (0.039)	–	–	–
Mean	3.703 (0.000)	–	–	–

NOTE: Metrics are aggregated over 30 splits of the data into training and testing sets. Averages are reported next to (one) standard errors in parentheses.

Data Availability Statement

Our implementation grpsel is available on the R repository CRAN.