基于池的无监督线性回归主动学习

刘子昂; 蒋雪; 伍冬睿

doi:10.16383/j.aas.c200071

基于池的无监督线性回归主动学习

doi: 10.16383/j.aas.c200071 cstr: 32138.14.j.aas.c200071

1.
华中科技大学人工智能与自动化学院图像信息处理与智能控制教育部重点实验室武汉 430074

基金项目: 湖北省技术创新专项基金(2019AEA171), 国家自然科学基金(61873321), NSFC-深圳机器人基础研究中心重点项目基金(U1913207), 科技部政府间国际科技创新合作重点专项基金(2017YFE0128300)资助

详细信息

作者简介:
刘子昂：2017年获得武汉理工大学自动化专业学士学位, 2020年获得华中科技大学控制科学与工程硕士学位. 主要研究方向为机器学习. E-mail: ziangliu@hust.edu.cn

蒋雪：华中科技大学人工智能与自动化学院博士研究生. 2019年获得西南大学电子信息工程学院学士学位. 主要研究方向为机器学习, 脑机接口和情感计算. E-mail: xuejiang@hust.edu.cn

伍冬睿：华中科技大学人工智能与自动化学院教授. 主要研究方向为机器学习, 脑机接口, 计算智能, 情感计算. 本文通信作者. E-mail: drwu@hust.edu.cn

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出版历程
- 收稿日期: 2020-02-17
- 录用日期: 2020-08-14
- 网络出版日期: 2021-10-26
- 刊出日期: 2021-12-23

Unsupervised Pool-Based Active Learning for Linear Regression

1.
Ministry of Education Key Laboratory on Image Information Processing and Intelligent Control, School of Artificial Intelligence and Automation, Huazhong University of Science and Technology, Wuhan 430074

Funds: Supported by Technology Innovation Project of Hubei Province of China (2019AEA171), National Natural Science Foundation of China (61873321), NSFC-Shenzhen Robotics Basic Research Center (U1913207), and International Science and Technology Cooperation Program of China (2017YFE0128300)

More Information

Author Bio:
LIU Zi-Ang　Received his bachelor degree in automation from Wuhan University of Technology in 2017, and his master degree in control science and engineering from Huazhong University of Science and Technology in 2020. His main research interest is machine learning

JIANG Xue　Ph.D. candidate at the School of Artificial Intelligence and Automation, Huazhong University of Science and Technology. She received her bachelor degree in communications engineering from Southwest University in 2019. Her research interest covers machine learning, brain-computer interfaces, and affective computing

WU Dong-Rui　Professor at the School of Artificial Intelligence and Automation, Huazhong University of Science and Technology. His research interest covers machine learning, brain-computer interfaces, computational intelligence, and affective computing. Corresponding author of this paper

摘要

摘要: 在许多现实的机器学习应用场景中, 获取大量未标注的数据是很容易的, 但标注过程需要花费大量的时间和经济成本. 因此, 在这种情况下, 需要选择一些最有价值的样本进行标注, 从而只利用较少的标注数据就能训练出较好的机器学习模型. 目前, 主动学习(Active learning)已广泛应用于解决这种场景下的问题. 但是, 大多数现有的主动学习方法都是基于有监督场景: 能够从少量带标签的样本中训练初始模型, 基于模型查询新的样本, 然后迭代更新模型. 无监督情况下的主动学习却很少有人考虑, 即在不知道任何标签信息的情况下最佳地选择要标注的初始训练样本. 这种场景下, 主动学习问题变得更加困难, 因为无法利用任何标签信息. 针对这一场景, 本文研究了基于池的无监督线性回归问题, 提出了一种新的主动学习方法, 该方法同时考虑了信息性、代表性和多样性这三个标准. 本文在3个不同的线性回归模型(岭回归、LASSO (Least absolute shrinkage and selection operator)和线性支持向量回归)和来自不同应用领域的12个数据集上进行了广泛的实验, 验证了其有效性.
- 主动学习 /
- 无监督学习 /
- 线性回归 /
- 支持向量回归 /
- LASSO /
- 岭回归
Abstract: In many real-world machine learning applications, unlabeled data can be easily obtained, but it is very time-consuming and/or expensive to label them. So, it is desirable to be able to select the optimal samples to label, so that a good machine learning model can be trained from a minimum number of labeled data. Active learning (AL) has been widely used for this purpose. However, most existing AL approaches are supervised: they train an initial model from a small number of labeled samples, query new samples based on the model, and then update the model iteratively. Few of them have considered the completely unsupervised AL problem, i.e., starting from zero, how to optimally select the very first few samples to label, without knowing any label information at all. This problem is very challenging, as no label information can be utilized. This paper studies unsupervised pool-based AL for linear regression problems. We propose a novel AL approach that considers simultaneously the informativeness, representativeness, and diversity, three essential criteria in AL. Extensive experiments on 12 datasets from various application domains, using three different linear regression models (ridge regression, LASSO (least absolute shrinkage and selection operator), and linear support vector regression), demonstrated the effectiveness of our proposed approach.
- Active learning (AL) /
- unsupervised learning /
- linear regression /
- support vector regression /
- least absolute shrinkage and selection operator (LASSO) /
- ridge regression
注释:

1) ¹$ \theta $并不是$ H $和$ H' $之间的真实角度, 当满足$ \overrightarrow{\bar{{\boldsymbol{x}}} _v\bar{{\boldsymbol{x}}}_n'}\perp\overrightarrow{\bar{{\boldsymbol{x}}}_1\bar{{\boldsymbol{x}}}_2} $时, $ \theta $才是$ H $和$ H' $间的夹角, 通常$ \bar{{\boldsymbol{x}}}_n' $并不满足这一条件. 然而, 如同$ H $和$ H' $之间的真实角度, $ \theta $会随着$ H' $和$ H $越来越接近而单调递减, 因此可以用它来度量$ H' $和$ H $之间的接近程度. 我们使用这样的$ \theta ,$ 而不是$ H $和$ H' $之间的真实角度来进行计算, 将会使得推导更加容易. ²我们还考虑了其他兼顾代表性、信息性和多样性的方法, 例如$ {\boldsymbol{x}} _n^* = $$ \arg\min_{{\boldsymbol{x}}_n}(\frac{1}{N}\sum_{i = 1}^N|{\boldsymbol{x}}_i-{\boldsymbol{x}}_n|^2)^{1/2}+\lambda\cdot |{\boldsymbol{x}}_v-{\boldsymbol{x}}_n| $, 但这种方法会引入超参数$ \lambda $, 并且我们的实验表明, 从最佳的$ \lambda $获得的性能要比式(11)差. 因此, 由于其简单性和准确性, 我们最终使用式(11)作为选择准则.

2) 收稿日期 2020-02-17 录用日期 2020-08-14 Manuscript received February 17, 2020; accepted August 14,2020 湖北省技术创新专项基金 (2019AEA171), 国家自然科学基金 (61873321), NSFC-深圳机器人基础研究中心重点项目基金 (U1913207), 科技部政府间国际科技创新合作重点专项基金 (2017YFE0128300) 资助 Supported by Technology Innovation Project of Hubei Province of China (2019AEA171), National Natural Science Foundation of China (61873321), NSFC-Shenzhen Robotics Basic Research Center (U1913207), and International Science and Technology Cooperation Program of China (2017YFE0128300) 本文责任编委王立威 Recommended by Associate Editor WANG Li-Wei 1. 华中科技大学人工智能与自动化学院图像信息处理与智能控制教育部重点实验室武汉 430074

3) ³http://archive.ics.uci.edu/ml/index.php⁴http://lib.stat.cmu.edu/datasets/

4) 1. Ministry of Education Key Laboratory on Image Information Processing and Intelligent Control, School of Artificial Intelligence and Automation, Huazhong University of Science and Technology, Wuhan 430074

5) ⁵对普通最小二乘法(Ordinary least squares, OLS)回归也进行了尝试, IRD依然取得了最佳表现. 但当训练样本较少时, OLS非常不稳定, 因此在实际中不是一个合理的选择, 本文不讨论其结果.

6) ⁶由于页面限制, 只展示了RR的详细结果, 因为它通常表现更稳定. 其他两个回归模型上的结果类似.

HTML全文

图 1 基于池的ALR中样本的代表性与多样性^[17]

Fig. 1 Illustration of representativeness and diversity in pool-based ALR^[17]

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图 2 当$d=2$时IRD算法图示

Fig. 2 Illustration of IRD when $d=2$

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图 3 12个数据集上的平均RMSE和CC (mRMSE和mCC; 重复运行100次) (回归模型为RR ($\lambda=0.5$))

Fig. 3 Mean of the RMSEs and the CCs on the 12 datasets, averaged over 100 runs (RR ($\lambda=0.5$) was used as the regression model)

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图 4 12个数据集上归一化AUC-mRMSE和AUC-mCC

Fig. 4 Normalized AUCs of the mean RMSEs and the mean CCs on the 12 datasets

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图 5 对于不同的$M,$ 4种ALR方法的mRMSE和mCC相对于RS在12个数据集上的平均比率

Fig. 5 Ratios of the mean RMSEs and the mean CCs for different $M,$ averaged across 12 datasets

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图 6 在Housing数据集上不同ALR算法所选样本(星号)的t-SNE可视化

Fig. 6 t-SNE visualization of the selected samples (asterisks) from different ALR approaches on Housing dataset

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图 7 对于不同的$c_{\max},$ 4种ALR算法的AUC-mRMSE和AUC-mCC相对于RS在12个数据集上的平均比率

Fig. 7 Ratios of AUCs of the mean RMSEs and the mean CCs for different $c_{\max},$ averaged across 12 datasets

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图 8 对于不同的$\lambda$(RR和LASSO)和$C$(线性SVR),4种ALR算法的AUC-mRMSE和AUC-mCC相对于RS在12个数据集上的平均比率

Fig. 8 Ratios of the AUCs of the mean RMSEs and the mean CCs, averaged across 12 datasets, for different $\lambda$(RR and LASSO) and $C $(linear SVR)

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图 9 对于不同的$M,$ IRD及其变体的mRMSE和mCC相对于RS在12个数据集上的平均比率

Fig. 9 Ratios of the mean RMSEs and the mean CCs w.r.t. different $M,$ averaged across 12 datasets

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表 1 基于池的无监督ALR方法中考虑的标准

Table 1 Criteria considered in the three existing and the proposed unsupervised pool-based ALR approaches

	方法	信息性	代表性	多样性
现有方法	P-ALICE	$\checkmark$	$-$	$-$
	GSx	$-$	$-$	$\checkmark$
	RD	$-$	$\checkmark$	$\checkmark$
本文方法	IRD	$\checkmark$	$\checkmark$	$\checkmark$

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表 2 12个数据集的总结

Table 2 Summary of the 12 regression datasets

数据集	来源	样本个数	原始特征个数	数字型特征个数	类别型特征个数	总的特征个数
Concrete-CS^a	UCI	103	7	7	0	7
Yacht^b	UCI	308	6	6	0	6
autoMPG^c	UCI	392	7	6	1	9
NO2^d	StatLib	500	7	7	0	7
Housing^e	UCI	506	13	13	0	13
CPS^f	StatLib	534	10	7	3	19
EE-Cooling^g	UCI	768	7	7	0	7
VAM-Arousal^h	ICME	947	46	46	0	46
Concreteⁱ	UCI	1030	8	8	0	8
Airfoil^j	UCI	1503	5	5	0	5
Wine-Red^k	UCI	1599	11	11	0	11
Wine-White^l	UCI	4898	11	11	0	11
^a https://archive.ics.uci.edu/ml/datasets/Concrete+Slump+Test ^b https://archive.ics.uci.edu/ml/datasets/Yacht+Hydrodynamics ^c https://archive.ics.uci.edu/ml/datasets/auto+mpg ^d http://lib.stat.cmu.edu/datasets/ ^e https://archive.ics.uci.edu/ml/machine-learning-databases/housing/ ^f http://lib.stat.cmu.edu/datasets/CPS_85_Wages				^g http://archive.ics.uci.edu/ml/datasets/energy+efficiency ^h https://dblp.uni-trier.de/db/conf/icmcs/icme2008.html ⁱ https://archive.ics.uci.edu/ml/datasets/Concrete+Compressive+ Strength ^j https://archive.ics.uci.edu/ml/datasets/Airfoil+Self-Noise ^k https://archive.ics.uci.edu/ml/datasets/Wine+Quality

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表 3 AUC-mRMSE/sRMSE和AUC-mCC/sCC的提升百分比

Table 3 Percentage improvements of the AUCs of the mean/std RMSEs and the mean/std CCs

回归模型	性能指标		相对于 RS 的提升百分比
回归模型	性能指标		P-ALICE	GSx	RD	IRD
RR	RMSE	Mean	2.58	−2.57	4.15	8.63
	RMSE	std	2.75	3.98	36.60	34.84
	CC	Mean	6.54	−3.43	10.39	18.70
	CC	std	12.74	29.47	35.03	42.97
LASSO	RMSE	Mean	4.22	0.84	7.58	10.81
	RMSE	std	6.77	0.85	43.45	39.84
	CC	Mean	25.06	69.41	25.67	60.63
	CC	std	6.39	31.05	22.46	29.82
SVR	RMSE	Mean	4.21	0.66	5.23	12.12
	RMSE	std	6.62	−0.19	33.99	38.69
	CC	Mean	9.71	−1.65	12.46	28.99
	CC	std	11.10	25.78	34.97	43.25

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表 4 非参数多重检验的$p$值($\alpha=0.05$; 如果 $p<\alpha/2$拒绝$H_0$).

Table 4 $p$-values of non-parametric multiple comparisons ($\alpha=0.05$; reject $H_0$ if $p<\alpha/2$)

回归模型	性能指标	IRD versus
回归模型	性能指标	RS	P-ALICE	GSx	RD
RR	RMSE	0.0000	0.0003	0.0000	0.0284
RR	CC	0.0000	0.0000	0.0000	0.0005
LASSO	RMSE	0.0000	0.0004	0.0000	0.0596
LASSO	CC	0.0000	0.0000	0.0000	0.0000
SVR	RMSE	0.0000	0.0000	0.0000	0.0018
SVR	CC	0.0000	0.0000	0.0000	0.0000

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