Complexity

Research Article

A Two-Stage Regularization Method for Variable Selection and Forecasting in High-Order Interaction Model

Table 1

The statistical performance of TSSRHR, TSLASSO, TSSCAD, and TSSRL. The performances are measured by number of nonzero elements of main effects, two-way interactions, three-way interactions, MSE (×100), RMSE (×100), and computational costs (CC, in seconds, unless otherwise specified).


	Nz()	Nz()	Nz()	MSE	RMSE	CC		Nz()	Nz()	Nz()	MSE	RMSE	CC
Scenario 1							Scenario 2

TSSRHR	3.00	1.00	3.00	93.47	96.68	10.62	TSSRHR	3.00	1.00	5.00	82.71	91.13	5.82
TSLASSO	5.00	59.50	3505.50	145.72	119.13	6.94	TSLASSO	7.00	46.00	3596.00	156.48	124.12	4.12
TSSCAD	2.00	1.00	8.00	127.40	112.92	18.77	TSSCAD	14.00	21.50	3678.00	185.49	132.81	20.73
TSSRL	3.00	0.00	1.00	102.71	101.36	5.26	TSSRL	2.00	0.00	4.00	86.78	91.98	8.13

	Nz()	Nz()	Nz()	MSE	RMSE	CC		Nz()	Nz()	Nz()	MSE	RMSE	CC
Scenario 3							Scenario 4

TSSRHR	2.00	1.00	6.00	80.21	89.38	11.72	TSSRHR	3.00	0.00	0.00	87.92	93.13	20.46
TSLASSO	12.00	20.00	4796.00	137.54	117.13	4.32	TSLASSO	35.00	0.00	31458.00	264.13	161.81	11.12
TSSCAD	4.00	0.00	15.00	101.92	100.83	19.72	TSSCAD	19.00	0.00	6661.00	237.35	152.51	52.15
TSSRL	2.00	0.00	1.00	88.86	93.53	25.43	TSSRL	2.00	0.00	1.00	96.92	97.43	1215.93

	Nz()	Nz()	Nz()	MSE	RMSE	CC		Nz()	Nz()	Nz()	MSE	RMSE	CC
Scenario 5							Scenario 6

TSSRHR	3.00	0.00	4.00	413.85	200.94	4.21	TSSRHR	3.00	0.00	4.00	418.72	205.19	4.92
TSLASSO	6.00	7.00	94.00	533.48	228.12	3.98	TSLASSO	5.00	2.00	50.50	438.59	207.14	4.01
TSSCAD	3.00	2.50	6.00	470.83	215.94	20.15	TSSCAD	6.00	1.00	94.00	473.21	216.83	25.13
TSSRL	3.00	0.00	1.00	468.10	215.18	2.13	TSSRL	2.00	0.00	3.00	428.13	206.89	3.72

	Nz()	Nz()	Nz()	MSE	RMSE	CC		Nz()	Nz()	Nz()	MSE	RMSE	CC
Scenario 7							Scenario 8

TSSRHR	2.00	0.00	3.00	405.13	201.98	10.98	TSSRHR	3.00	0.00	2.00	407.95	201.34	28.13
TSLASSO	5.00	0.00	77.50	436.82	207.92	4.35	TSLASSO	16.00	0.00	1195.50	870.94	294.48	7.19
TSSCAD	9.00	28.00	451.50	434.12	206.15	30.95	TSSCAD	28.00	0.00	29113	454.79	211.83	72.49
TSSRL	2.00	0.00	1.00	430.93	205.73	3.43	TSSRL	2.00	0.00	1.00	445.23	209.89	1529.38

	Nz()	Nz()	Nz()	MSE	RMSE	CC		Nz()	Nz()	Nz()	MSE	RMSE	CC
Scenario 9							Scenario 10

TSSRHR	3.00	1.00	4.00	147.33	121.38	14.03	TSSRHR	3.00	1.00	3.00	142.62	119.42	19.66
TSLASSO	3.00	1.00	12.00	194.07	139.31	4.09	TSLASSO	4.00	0.00	19.00	183.93	135.62	6.28
TSSCAD	3.00	4.00	18.00	195.77	139.92	8.73	TSSCAD	3.00	1.00	15.00	165.67	128.71	14.62
TSSRL	3.00	0.00	3.00	183.71	135.54	2.84	TSSRL	3.00	0.00	3.00	174.79	132.21	3.91