一种噪声容错弱监督矩阵补全的生存分析方法

陈蕾; 邵楷; 林腾涛; 陈兴国

doi:10.16383/j.aas.c190740

一种噪声容错弱监督矩阵补全的生存分析方法

doi: 10.16383/j.aas.c190740

陈蕾^{1, 2, 3,},
邵楷^1,,
林腾涛^1,,
陈兴国^{1, 2,}

1.
南京邮电大学计算机学院南京 210023
2.
南京航空航天大学模式分析与机器智能工业和信息化部重点实验室南京 211106
3.
江苏省大数据安全与智能处理重点实验室南京 210023

基金项目: 国家自然科学基金(61872190, 61772285, 61572263), 南京航空航天大学模式分析与机器智能工业和信息化部重点实验室开放基金(TK219016)资助

详细信息

作者简介:
陈蕾：南京邮电大学教授. 主要研究方向为大规模机器学习, 基于医学影像的脑疾病分析. 本文通信作者.E-mail: chenlei@njupt.edu.cn

邵楷：南京邮电大学计算机学院硕士研究生. 主要研究方向为机器学习.E-mail: sk1017041210@163.com

林腾涛：南京邮电大学计算机学院硕士研究生. 主要研究方向为机器学习.E-mail: ltt1995711@126.com

陈兴国：南京邮电大学讲师. 主要研究方向为机器学习, 强化学习, 智能游戏. E-mail: chenxg@njupt.edu.cn

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出版历程
- 收稿日期: 2019-10-26
- 录用日期: 2020-03-11
- 网络出版日期: 2021-10-28
- 刊出日期: 2021-12-23

Noise-tolerant Weakly Supervised Matrix Completion for Survival Analysis

CHEN Lei^{1, 2, 3
,},
SHAO Kai^1
,,
LIN Teng-Tao^1
,,
CHEN Xing-Guo^{1, 2
,}

1.
School of Computer Science, Nanjing University of Posts and Telecommunications, Nanjing 210023
2.
MIIT Key Laboratory of Pattern Analysis and Machine Intelligence, Nanjing University of Aeronautics and Astronautics, Nanjing 211106
3.
Jiangsu Key Laboratory of Big Data Security and Intelligent Processing, Nanjing 210023

Funds: Supported by National Natural Science Foundation of China (61872190, 61772285, 61572263) and Open Fund of Ministry of Industry and Information Technology (MIIT) Key Laboratory of Pattern Analysis and Machine Intelligence of Nanjing University of Aeronautics and Astronautics (NUAA) (TK219016)

More Information

Author Bio:
CHEN Lei　Professor at Nanjing University of Posts and Telecommunications. His research interest covers large-scale machine learning, and brain diseases analysis based on medical imaging. Corresponding author of this paper

SHAO Kai　Master student at Nanjing University of Posts and Telecommunications. His main research interest is machine learning

LIN Teng-Tao　Master student at Nanjing University of Posts and Telecommunications. His main research interest is machine learning

CHEN Xing-Guo　Lecturer at Nanjing University of Posts and Telecommunications. His research interest covers machine learning, reinforcement learning, and intelligent games

摘要

摘要: 生存分析旨在预测某个感兴趣事件发生前的延续等待时间, 已广泛应用于临床治疗中患者的生存状态分析. 然而, 受限于研究代价高昂和环境因素的影响, 现有的生存分析方法不可避免地面临着高维小样本挑战以及复杂环境所引起的噪声敏感等问题. 为了克服上述缺陷, 本文提出一类噪声容错弱监督直推式矩阵补全(Weakly supervised transductive matrix completion, WSTMC)生存分析方法. 该方法首先将生存分析问题建模为多任务直推式矩阵补全模型, 然后引入高斯混合分布拟合真实数据中的复杂噪声以减轻模型的噪声敏感性, 同时设计了一类多任务直推式特征选择机制来缓解高维小样本所带来的过拟合缺陷. 此外, 设计了一类有效的拟期望最大化优化算法用于求解所提出的WSTMC模型. 最后, 5个微阵列基因表达数据集上的实验结果证实了所提出的WSTMC模型优于当前广泛使用的18种生存分析方法.
- 生存分析 /
- 弱监督学习 /
- 多任务学习 /
- 噪声容错 /
- 矩阵补全
Abstract: Survival analysis aims to predict the time of an event of interest, which has been widely applied in survival status prediction of patients in clinical treatment. However, limited to the high cost of research and the influence of environments, the existing survival analysis methods inevitably suffer the over-fitting defects caused by high dimensional small-sample-size and the noise sensitivity caused by complex environments. To address these challenges, we propose a novel noise-tolerant weakly supervised transductive matrix completion (WSTMC) model to predict survival statuses of the censored instances and new instances. Specifically, we first formulate the original survival analysis problem as a multitask matrix completion model. Then the MoG (mixture of Gaussians distribution) model is employed to fit the unknown complex noise, and thus alleviate the noise sensitivity. Meanwhile, we design a novel multitask transductive feature selection mechanism to adaptively select the sharing discriminant features across tasks. Furthermore, an efficient expectation-maximization-like optimization algorithm is designed to solve the proposed WSTMC model. Finally, the experimental results conducted on 5 real microarray gene expression datasets verify that our proposed WSTMC model outperforms 18 widely-used competing methods.
- Survival analysis /
- weakly supervised learning /
- multi-task learning /
- noise-tolerant /
- matrix completion

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图 1 生存分析问题建模为弱监督多任务学习问题的图示

Fig. 1 Illustration of formulating the survival analysis problem as a weakly supervised multi-task learning problem

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表 1 WSTMC及其他相关模型的时间复杂度比较

Table 1 Time complexity comparison of the proposed WSTMC and the other related models

模型	时间复杂度
Multi-LASSO^[27]	${\rm{O} }\left({dtm}_{{\rm{tr}}}\right)$
Multi-${\ell }_{{2,1}}$^[27]	${\rm{O} }\left({dtm}_{{\rm{tr}}}\right)$
MTLSA^[7]	${\rm{O} }\left(N{dtm}_{{\rm{tr}}}\right)$
MTLSA.V2^[7]	${\rm{O} }\left(N{dtm}_{{\rm{tr}}}\right)$
MTMC^[8]	${\rm{O} }(Nmd\;{\rm{m} }{\rm{i} }{\rm{n} }\{m,d\left\}\right)$
NLMC^[28]	${\rm{O}}\left(Nmdt\right)$
WSTMC	${\rm{O} }\left({N}_{{\rm{EM}}}{N}_{{\rm{BPL}}}\right(m{d}^{2}+{m}^{2}d\left)\right)$
注: $m$表示样本数 (包括训练样本和测试样本); ${m}_{{\rm{tr}}}$表示训练样本数; $d$表示样本特征维数; $t$表示任务数; $N$表示迭代次数.

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表 2 实验所用数据集概述

Table 2 Details of datasets used in this study

Dataset	#Instances	#Features	#Censored	#Labels	#Ratios
NSBCD	115	549	77	188	0.2094
DBCD	295	4919	216	18	0.0599
Lung	86	7129	62	110	0.0120
DLBCL	240	7399	102	21	0.0137
MCL	92	8810	28	14	0.0104

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表 3 对比模型的特征比较

Table 3 Comparison of characteristics for the competing models

	噪声容错性	直推式学习机制	时序稳定性	自适应特征选择	多任务学习机制
COX	$\times$	$\times$	$\surd$	$\times$	$\times$
LASSO-COX	$\times$	$\times$	$\surd$	$\surd$	$\times$
EN-COX	$\times$	$\times$	$\surd$	$\surd$	$\times$
Cox-${l}_{{2,1}}$	$\times$	$\times$	$\surd$	$\surd$	$\times$
Cox-Trace	$\times$	$\times$	$\surd$	$\times$	$\times$
Logistic	$\times$	$\times$	$\surd$	$\times$	$\times$
Weibull	$\times$	$\times$	$\surd$	$\times$	$\times$
Log-gaussian	$\times$	$\times$	$\surd$	$\times$	$\times$
Log-logistic	$\times$	$\times$	$\surd$	$\times$	$\times$
OLS	$\times$	$\times$	$\times$	$\times$	$\times$
Tobit	$\times$	$\times$	$\surd$	$\times$	$\times$
RWRSS	$\times$	$\times$	$\surd$	$\surd$	$\times$
Multi-LASSO	$\times$	$\times$	$\times$	$\times$	$\surd$
Multi-${l}_{{2,1}}$	$\times$	$\times$	$\times$	$\surd$	$\surd$
MTLSA	$\times$	$\times$	$\surd$	$\surd$	$\surd$
MTLSA.V2	$\times$	$\times$	$\surd$	$\surd$	$\surd$
NLMC	$\times$	$\surd$	$\times$	$\times$	$\surd$
MTMC	$\times$	$\surd$	$\times$	$\times$	$\surd$
WSTMC	$\surd$	$\surd$	$\surd$	$\surd$	$\surd$

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表 4 所提出的WSTMC模型和其他比较模型在C-index指标上的性能比较(标准差)

Table 4 Comparison of the WSTMC and competing models using C-index (standard deviations)

		NSBCD	Lung	DBCD	DLBCL	MCL
COX based	COX	0.4411 (0.0589)	0.5158 (0.1333)	0.5539 (0.1233)	0.4553 (0.0718)	0.5773 (0.0591)
	LASSO-COX	0.5910 (0.1086)	0.6698 (0.0910)	0.6880 (0.0429)	0.6344 (0.0421)	0.6824 (0.0701)
	EN-COX	0.6046 (0.1000)	0.6652 (0.0702)	0.7214 (0.0306)	0.6488 (0.0394)	0.6734 (0.0733)
	Cox-${l}_{{2,1}}$	0.7453 (0.0742)	0.7470 (0.0450)	0.7548 (0.0640)	0.6499 (0.0474)	0.7229 (0.0379)
	Cox-Trace	0.7550 (0.0737)	0.7348 (0.0431)	0.6946 (0.0576)	0.6478 (0.0387)	0.7127 (0.0902)
Parametric models	Logistic	0.3787 (0.0195)	0.5714 (0.0596)	0.4908 (0.0872)	0.4840 (0.0496)	0.4827 (0.0682)
	Weibull	0.3045 (0.1528)	0.4287 (0.1023)	0.4555 (0.1046)	0.2507 (0.0627)	0.4735 (0.0747)
	Log-gaussian	0.4435 (0.0539)	0.4122 (0.0754)	0.4875 (0.0553)	0.3167 (0.0914)	0.2564 (0.0715)
	Log-logistic	0.2378 (0.0500)	0.5924 (0.0655)	0.5257 (0.0232)	0.4246 (0.1243)	0.4802 (0.0724)
Linear models	OLS	0.6333 (0.1108)	0.5743 (0.0658)	0.5690 (0.0744)	0.5024 (0.1023)	0.5007 (0.1059)
	Tobit	0.3733 (0.0214)	0.4689 (0.1358)	0.4869 (0.0762)	0.4969 (0.0527)	0.4591 (0.0322)
	RWRSS	0.6766 (0.1277)	0.6969 (0.0430)	0.7216 (0.0446)	0.6265 (0.0657)	0.7118 (0.0737)
Multi-task based	Multi-LASSO	0.6117 (0.1493)	0.4410 (0.1655)	0.6256 (0.0749)	0.6104 (0.0512)	0.6539 (0.0140)
	Multi-${l}_{{2,1}}$	0.6100 (0.1700)	0.5248 (0.1130)	0.6899 (0.0720)	0.6115 (0.0512)	0.6912 (0.0602)
	MTLSA.V2	0.6858 (0.0834)	0.6769 (0.0271)	0.7515 (0.0625)	0.6545 (0.0600)	0.7079 (0.0963)
	MTLSA	0.6820 (0.0446)	0.6327 (0.0753)	0.7581 (0.0304)	0.6527 (0.0713)	0.7274 (0.1257)
	NLMC	0.6827 (0.1415)	0.6939 (0.1500)	0.7563 (0.0565)	0.6178 (0.0702)	0.7232 (0.1035)
	MTMC	0.7620 (0.0576)	0.6958 (0.0217)	0.4292 (0.0660)	0.6611 (0.0491)	0.7223 (0.0284)
	WSTMC	0.7970 (0.0135)	0.8153 (0.0992)	0.7705 (0.0562)	0.6810 (0.0571)	0.7336 (0.0697)

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表 5 所提出的WSTMC模型和其他比较模型在Weighted average AUC指标上的性能比较(标准差)

Table 5 Comparison of the WSTMC and competing models using Weighted average AUC (standard deviations)

		NSBCD	Lung	DBCD	DLBCL	MCL
COX based	Cox	0.4611 (0.1893)	0.5464 (0.1632)	0.5334 (0.1620)	0.4480 (0.1079)	0.4695 (0.1701)
	LASSO-COX	0.5986 (0.1589)	0.7499 (0.1780)	0.7068 (0.0292)	0.7104 (0.0533)	0.7401 (0.0166)
	EN-COX	0.6479 (0.0970)	0.7540 (0.1398)	0.7494 (0.0189)	0.7260 (0.0618)	0.7350 (0.0025)
	Cox-${l}_{{2,1}}$	0.7752 (0.0450)	0.8079 (0.0462)	0.7545 (0.0365)	0.7157 (0.0795)	0.8215 (0.0737)
	Cox-Trace	0.6729 (0.0883)	0.7074 (0.0455)	0.7078 (0.0465)	0.6768 (0.0903)	0.7197 (0.0209)
Parametric models	Logistic	0.4597 (0.1742)	0.6301 (0.0924)	0.4840 (0.1086)	0.5011 (0.0489)	0.2986 (0.0501)
	Weibull	0.4575 (0.2622)	0.4379 (0.1018)	0.4707 (0.0809)	0.4320 (0.1080)	0.3240 (0.0484)
	Log-gaussian	0.4992 (0.2378)	0.4182 (0.0680)	0.4742 (0.0763)	0.4270 (0.0977)	0.4457 (0.0161)
	Log-logistic	0.3304 (0.1057)	0.5822 (0.1544)	0.5302 (0.0298)	0.4712 (0.0627)	0.2983 (0.0505)
Linear models	OLS	0.6599 (0.1042)	0.5677 (0.1120)	0.5998 (0.1096)	0.4934 (0.1952)	0.5594 (0.1191)
	Tobit	0.4567 (0.1812)	0.4708 (0.1422)	0.4668 (0.1021)	0.5243 (0.0691)	0.5074 (0.0283)
	RWRSS	0.7016 (0.1369)	0.6821 (0.0840)	0.6928 (0.0183)	0.5622 (0.0127)	0.7056 (0.1367)
Multi-task based	Multi-LASSO	0.6495 (0.1226)	0.4410 (0.1655)	0.6402 (0.0572)	0.5876 (0.1047)	0.6079 (0.0696)
	Multi-${l}_{{2,1}}$	0.6501 (0.1314)	0.5589 (0.1486)	0.7125 (0.0775)	0.6001 (0.0528)	0.6476 (0.0653)
	MTLSA.V2	0.6822 (0.0576)	0.8076 (0.0559)	0.7569 (0.0645)	0.7405 (0.0719)	0.7639 (0.0651)
	MTLSA	0.7032 (0.0427)	0.7169 (0.0964)	0.8003 (0.0425)	0.7385 (0.0638)	0.8095 (0.0367)
	NLMC	0.5724 (0.0705)	0.5842 (0.0994)	0.6212 (0.0687)	0.6130 (0.0657)	0.7175 (0.0664)
	MTMC	0.8206 (0.0929)	0.6035 (0.1422)	0.4334 (0.0506)	0.6989 (0.0351)	0.8255 (0.0729)
	WSTMC	0.8662 (0.0788)	0.8629 (0.0519)	0.8007 (0.0549)	0.7064 (0.0563)	0.8430 (0.0767)

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表 6 在两种评价指标C-index和Weighted average AUC上的消融性实验性能比较(标准差)

Table 6 Comparison of the ablation experiments using C-index and Weighted average AUC (standard deviations)

		NSBCD	Lung	DBCD	DLBCL	MCL
C-index	MTMC	0.7620 (0.0576)	0.6958 (0.0217)	0.4292 (0.0660)	0.6611 (0.0491)	0.7223 (0.0284)
	WSTMC-nM	0.7633 (0.0406)	0.7053 (0.1566)	0.6847 (0.0454)	0.6661 (0.0670)	0.7241 (0.1023)
	WSTMC-nT	0.7642 (0.0650)	0.7345 (0.0767)	0.7270 (0.0422)	0.6659 (0.0529)	0.7234 (0.0729)
	WSTMC-nF	0.7664 (0.0164)	0.7293 (0.1086)	0.7123 (0.0586)	0.6641 (0.0497)	0.7273 (0.0934)
	WSTMC	0.7970 (0.0135)	0.8153 (0.0992)	0.7705 (0.0562)	0.6810 (0.0571)	0.7336 (0.0697)
Weighted average AUC	MTMC	0.8206 (0.0929)	0.6035 (0.1422)	0.4334 (0.0506)	0.6989 (0.0351)	0.8255 (0.0729)
	WSTMC-nM	0.8547 (0.0441)	0.6674 (0.0777)	0.6353 (0.0467)	0.6994 (0.0526)	0.8256 (0.1488)
	WSTMC-nT	0.8557 (0.0447)	0.7676 (0.0531)	0.6061 (0.0726)	0.6998 (0.0535)	0.8334 (0.1075)
	WSTMC-nF	0.8421 (0.0915)	0.7420 (0.0433)	0.6560 (0.0435)	0.7053 (0.0467)	0.8268 (0.0230)
	WSTMC	0.8662 (0.0788)	0.8629 (0.0519)	0.8007 (0.0549)	0.7064 (0.0563)	0.8430 (0.0767)

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