Feature Weighting Improves Pool-Based Sequential Active Learning for Regression

Dongrui Wu

cs.LGApr 2, 2026

Feature Weighting Improves Pool-Based Sequential Active Learning for Regression

Authors: Dongrui Wu

Organizations: Ministry of Education Key Laboratory of Image Processing and Intelligent Control, and Hubei Key Laboratory of Brain-inspired Intelligent Systems, School of Artificial Intelligence and Automation, Huazhong University of Science and Technology, Wuhan, 430074 China.

Abstract

Pool-based sequential active learning for regression (ALR) optimally selects a small number of samples sequentially from a large pool of unlabeled samples to label, so that a more accurate regression model can be constructed under a given labeling budget. Representativeness and diversity, which involve computing the distances among different samples, are important considerations in ALR. However, previous ALR approaches do not incorporate the importance of different features in inter-sample distance computation, resulting in inaccurate distances and hence sub-optimal sample selection. This paper proposes four feature weighted single-task ALR approaches and three feature weighted multi-task ALR approaches, where the ridge regression coefficients trained from a small amount of previously labeled samples are used to weight the corresponding features in inter-sample distance computation. Extensive experiments showed that this intuitive and easy-to-implement enhancement almost always improves the performance of five existing ALR approaches, in both single-task and multi-task regression problems. The feature weighting strategy may also be easily extended to stream-based ALR, and classification algorithms.

Figures & tables

		# of	# of	# of	# of	# of
Dataset	Source	samples	raw	numerical	categorical	total
			features	features	features	features
Yacht 1	UCI	308	6	6	0	6
autoMPG 2	UCI	392	7	6	1	9
NO2 3	StatLib	500	7	7	0	7
PM10 3	StatLib	500	7	7	0	7

TABLE I: Summary of the 11 single-task regression datasets.

Panel of Figure 2 — Fig. 1: Performance of the 11 single-task ALR algorithms on the 11 datasets, averaged over 100 runs. (a) Yacht; (b) autoMPG; (c) NO2; (d) PM110; (e) Housing; (f) CPS; (g) EE-Cooling; (h) Concrete; (i) Airfoil; (j) Wine-white; and, (k) BikeSharing.

Dataset	RMSE											CC
					FW		FW		FW		FW					FW		FW		FW		FW
	BL	EMCM	QBC	RD	-RD	GSx	-GSx	iGS	-iGS	GALR	-GALR	BL	EMCM	QBC	RD	-RD	GSx	-GSx	iGS	-iGS	GALR	-GALR
Yacht	1.00	1.14	1.12	0.97	0.88	1.22	0.97	0.95	0.91	1.17	0.99	1.00	1.02	1.02	1.10	1.07	1.04	1.05	1.06	1.07	1.05	1.05
autoMPG	1.00	0.87	0.84	0.79	0.79	0.73	0.72	0.76	0.75	0.75	0.73	1.00	1.01	1.02	1.03	1.02	1.05	1.05	1.04	1.04	1.05	1.05
NO2	1.00	0.97	0.95	1.00	0.98	0.95	0.93	0.93	0.93	0.94	0.93	1.00	1.00	1.02	1.00	1.01	1.01	1.00	0.99	0.98	1.00	1.01
PM10	1.00	0.93	0.92	0.99	0.97	0.96	0.89	0.89	0.89	0.92	0.89	1.00	1.22	1.26	0.69	0.78	1.34	1.40	1.32	1.27	1.49	1.43

TABLE II: Normalized AUCs of RMSEs and CCs of different algorithms on the 11 datasets.

Approach	RMSE										CC
Approach	BL	EMCM	QBC	RD	FW-RD	GSx	FW-GSx	iGS	FW-iGS	GALR	BL	EMCM	QBC	RD	FW-RD	GSx	FW-GSx	iGS	FW-iGS	GALR
EMCM	0.04										0.01
QBC	0.03	0.41									0.02	0.12
RD	0.28	1.00	0.97								0.37	1.00	0.97
FW-RD	0.00	0.21	0.12	0.03							0.17	0.41	0.58	0.58
GSx	0.02	0.17	0.32	0.46	0.70						0.02	0.02	0.05	0.46	0.97

TABLE III:

p

-values of Wilcoxon paired signed-rank test on the AUCs of RMSEs and CCs across the 11 datasets.

p

-values smaller than 0.05 are in bold.

Panel of Figure 5 — Fig. 2: Computational cost of the 11 algorithms on BikeSharing, for $M\in[20,60]$ , averaged over 100 runs. (a) $d=39$ , while $N$ increases from 100 to 15,000; and, (b) $N=10,000$ , while $d$ increases from 5 to 39.

Fig. 3: True and estimated feature weights on Housing. Results for first four of the 13 features are shown.

Panel of Figure 7 — Fig. 4: Performance of the 11 single-task ALR algorithms, averaged over 100 runs. (a) Yacht; and, (b) autoMPG. Two redundant features were added to each dataset.

	RMSE				CC
Algorithm	Yacht		AutoMPG		Yacht		AutoMPG
	Before	After	Before	After	Before	After	Before	After
BL	1.00	1.18	1.00	0.95	1.00	0.98	1.00	1.00
EMCM	1.14	1.19	0.87	0.85	1.02	1.02	1.01	1.01
QBC	1.12	1.18	0.84	0.81	1.02	1.01	1.02	1.02
RD	0.97	1.00	0.79	0.79	1.10	1.11	1.03	1.02

TABLE IV: Normalized AUCs of RMSE and CC before and after adding correlated/redundant features.

Panel of Figure 9 — Fig. 5: Performance of the 11 single-task ALR algorithms, averaged over 100 runs. (a) Yacht; and, (b) autoMPG. Two irrelevant features were added to each dataset.

	RMSE				CC
Algorithm	Yacht		AutoMPG		Yacht		AutoMPG
	Before	After	Before	After	Before	After	Before	After
BL	1.00	1.12	1.00	1.01	1.00	0.93	1.00	0.98
EMCM	1.14	1.12	0.87	0.90	1.02	0.96	1.01	1.01
QBC	1.12	1.11	0.84	0.86	1.02	0.96	1.02	1.01
RD	0.97	1.02	0.79	0.84	1.10	1.05	1.03	1.00

TABLE V: Normalized AUCs of RMSE and CC before and after adding irrelevant features.

Panel of Figure 11 — Fig. 6: Effect of different number of initially labeled samples, $n_{\min}$ (averaged over 100 runs). (a) Yacht, where $d=6$ ; and, (b) autoMPG, where $d=9$ .

Fig. 7: Performance of different initialization approaches on the EE-Cooling dataset, averaged over 100 runs. iGS (iRDM) and FW-iGS (iRDM) used iRDM [ 32 ] to select the first 5 samples to label. iGS (IRD) and FW-iGS (IRD) used IRD [ 33 ] to select the first 5 samples to label.

Panel of Figure 13 — Fig. 8: Performance of the nine single-task ALR algorithms, averaged over 200 runs. Linear ridge regression was used to estimate the feature weights in FW-RD , FW-GSx , FW-iGS and FW-GALR , and a nonlinear regression tree was trained for new sample prediction. (a) Yacht; (b) autoMPG; and, (c) NO2.

Panel of Figure 14 — Fig. 9: Performance of the nine single-task ALR algorithms, averaged over 200 runs. A nonlinear regression tree was used in both feature weight estimation in FW-RD , FW-GSx , FW-iGS and FW-GALR , and for new sample prediction. (a) Yacht; (b) autoMPG; and, (c) NO2.

Fig. 10: Performance of the seven multi-task ALR algorithms on the VAM dataset, averaged over 100 runs.

Fig. 11: Performance of the seven multi-task ALR algorithms on the EE dataset, averaged over 100 runs.

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