Machine Learning for Survival Analysis: A Survey <s> Transfer Learning. <s> In survival analysis, the primary goal is to monitor several entities and model the occurrence of a particular event of interest. In such applications, it is quite often the case that the event of interest may not always be observed during the study period and this gives rise to the problem of censoring which cannot be easily handled in the standard regression approaches. In addition, obtaining sufficient labeled training instances for learning a robust prediction model is a very time consuming process and can be extremely difficult in practice. In this paper, we propose a transfer learning based Cox method, called Transfer-Cox, which uses auxiliary data to augment learning when there are insufficient amount of training examples. The proposed method aims to extract "useful" knowledge from the source domain and transfer it to the target domain, thus potentially improving the prediction performance in such time-to-event data. The proposed method uses the l_2,1-norm penalty to encourage multiple predictors to share similar sparsity patterns, thus learns a shared representation across source and target domains, potentially improving the model performance on the target task. To speedup the computation, we apply the screening approach and extend the strong rule to sparse survival analysis models in multiple high-dimensional censored datasets. We demonstrate the performance of the proposed transfer learning method using several synthetic and high-dimensional microarray gene expression benchmark datasets and compare with other related competing state-of-the-art methods. Our results show that the proposed screening approach significantly improves the computational efficiency of the proposed algorithm without compromising the prediction performance. We also demonstrate the scalability of the proposed approach and show that the time taken to obtain the results is linear with respect to both the number of instances and features. <s> BIB001 </s> Machine Learning for Survival Analysis: A Survey <s> Transfer Learning. <s> 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. <s> BIB002
Collecting labeled information for survival problems is very timeconsuming as it is necessary to wait for the event to occur in a sufficient number of training instances to build robust models. A naive solution for this insufficient data problem is to merely integrate the data from related tasks into a consolidated form and build prediction models on this integrated dataset. However, such approaches often do not perform well because the target task (for which the predictions are to be made) will be overwhelmed by auxiliary data with different distributions. In such scenarios, knowledge transfer between related tasks will usually produce much better results. Transfer learning methods have been extensively studied to solve standard regression and classification problems (Pan and Yang 2010). Recently, Li and coworkers BIB001 proposed the use of a regularized Cox PH model named Transfer-Cox to improve the prediction performance of the Cox model in the target domain through knowledge transfer from the source domain in the context of survival models built on multiple high-dimensional datasets. The Transfer-Cox model employs 2,1 -norm to penalize the sum of the loss functions (negative partial log-likelihood) for both source and target domains. Thus, the model, which has time complexity O (N P ), will not only select important features but will also learn shared representations across source and target domains to improve the model performance on the target task. BIB002 reformulated the survival time prediction problem as a multitask learning problem. In survival data, the outcome labeling matrix is necessarily incomplete since the event label of each censored instance is unavailable after its corresponding censoring time. This means that it is not possible to handle censored information using the standard multitask learning methods. To address this problem, the Multitask Learning Model for Survival Analysis (MTLSA) translates the original event labels into an N × K indicator matrix I , where K = max (y i ) (∀i = 1, . . . , N ) is the maximum follow-up time for all the instances in the dataset. Element I i j (i = 1, . . . , N ; j = 1, . . . , K ) of the indicator matrix will be 1 if the event occurred before time y j for instance i; otherwise it will be 0. One of the major advantages of the MTLSA approach is that it can capture the dependency between the outcomes at various time points by using a shared representation across the related tasks in the transformation, which will reduce the prediction error for each task. In addition, the model can simultaneously learn from both uncensored and censored instances based on the indicator matrix. One important characteristic of non-recurring events (namely, that once the event occurs it will not occur again) is encoded via the non-negative non-increasing list structure constraint. In the MTLSA algorithm, the 2,1 -norm penalty is employed to learn a shared representation, with time complexity O (N PK ), across related tasks and hence compute the relatedness between the individual models built for various unique event time points.