Predicting the occurrence of a particular event of interest at future time points is the primary goal of survival analysis. The presence of incomplete observations due to time limitations or loss of data traces is known as censoring which brings unique challenges in this domain and differentiates survival analysis from other standard regression methods. The popularly used survival analysis methods such as Cox proportional hazard model and parametric survival regression suffer from some strict assumptions and hypotheses that are not realistic in most of the real-world applications. To overcome the weaknesses of these two types of methods, in this paper, we reformulate the survival analysis problem as a multi-task learning problem and propose a new multi-task learning based formulation to predict the survival time by estimating the survival status at each time interval during the study duration. We propose an indicator matrix to enable the multi-task learning algorithm to handle censored instances and incorporate some of the important characteristics of survival problems such as non-negative non-increasing list structure into our model through max-heap projection. We employ the L2,1-norm penalty which enables the model to learn a shared representation across related tasks and hence select important features and alleviate over-fitting in high-dimensional feature spaces; thus, reducing the prediction error of each task. To efficiently handle the two non-smooth constraints, in this paper, we propose an optimization method which employs Alternating Direction Method of Multipliers (ADMM) algorithm to solve the proposed multi-task learning problem. We demonstrate the performance of the proposed method using real-world microarray gene expression high-dimensional benchmark datasets and show that our method outperforms state-of-the-art methods.
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Tensor-based Temporal Multi-Task Survival Analysis
Survival analysis aims at predicting time to event of interest along with its probability on longitudinal data. It is commonly used to make predictions for a single specific event of interest at a given time point. However, predicting the occurrence of multiple events simultaneously and dynamically is needed in many applications. An intuitive way to solve this problem is to simply apply the regular survival analysis method independently to each task at each time point. However, it often leads to a suboptimal solution since the underlying dependencies between tasks are ignored, which motivates us to analyze these tasks jointly to select common features shared across all tasks. In this paper, we formulate a temporal Multi-Task learning framework (MTMT) using tensor representation. More specifically, given a survival dataset and a sequence of time points, which are considered as the monitored time points, we model each task at each time point as a regular survival analysis problem and optimize them simultaneously. We demonstrate the performance of MTMT model on two real-world datasets. We show the superior performance of the MTMT model compared to several state-of-the-art models. We also provide the list of important features selected to demonstrate the interpretability of our model.
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- PAR ID:
- 10143376
- Date Published:
- Journal Name:
- IEEE Transactions on Knowledge and Data Engineering
- ISSN:
- 1041-4347
- Page Range / eLocation ID:
- 1 to 1
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1109/TKDE.2020.2967700
