Machine Learning for Survival Analysis: A Survey <s> Support Vector Machines <s> Censored targets, such as the time to events in survival analysis, can generally be represented by intervals on the real line. In this paper, we propose a novel support vector technique (named SVCR) for regression on censored targets. SVCR inherits the strengths of support vector methods, such as a globally optimal solution by convex programming, fast training speed and strong generalization capacity. In contrast to ranking approaches to survival analysis, our approach is able not only to achieve superior ordering performance, but also to predict the survival time very well. Experiments show a significant performance improvement when the majority of the training data is censored. Experimental results on several survival analysis datasets demonstrate that SVCR is very competitive against classical survival analysis models. <s> BIB001 </s> Machine Learning for Survival Analysis: A Survey <s> Support Vector Machines <s> A crucial challenge in predictive modeling for survival analysis is managing censored observations in the data. The Cox proportional hazards model is the standard tool for the analysis of continuous censored survival data. We propose a novel machine learning algorithm, support vector regression for censored data (SVRc) for improved analysis of medical survival data. SVRc leverages the high-dimensional capabilities of traditional SVR while adapting it for use with censored data through a modified asymmetric loss/penalty function which allows censored (left and right censored) data to be processed. We applied the new algorithm to predict the recurrence and disease progression of prostate cancer, breast cancer and lung cancer. Compared with the traditional Cox model, SVRc achieves significant improvement in overall accuracy as well as in the ability to identify high-risk and low-risk patient populations. <s> BIB002 </s> Machine Learning for Survival Analysis: A Survey <s> Support Vector Machines <s> Condition monitoring (CM) of machines health or industrial components and systems that can detect, classify and predict the impending faults is critical in reducing operating and maintenance cost. Many papers have reported the valuable models and methods of prognostic systems. However, it was rarely found the papers deal with censored data, which was common in machine condition monitoring practice. This work deals with development of machine degradation assessment system that utilizes censored and complete data collected from CM routine. Relevance vector machine (RVM) is selected as intelligent system then trained by input data obtained from run-to-failure bearing data and target vectors of survival probability estimated by Kaplan-Meier (KM) and probability density function estimators. After validation process, RVM is employed to predict survival probability of individual unit of machine component. The plausibility of the proposed method is shown by applying the proposed method to bearing degradation data in predicting survival probability of individual unit. <s> BIB003 </s> Machine Learning for Survival Analysis: A Survey <s> Support Vector Machines <s> An accelerated failure time (AFT) model has been widely used for the analysis of censored survival or failure time data. However, the AFT imposes the restrictive log-linear relation between the survival time and the explanatory variables. In this paper, we introduce a relevance vector machine survival (RVMS) model based on Weibull AFT model that enables the use of kernel framework to automatically learn the possible nonlinear effects of the input explanatory variables on target survival times. We take advantage of the Bayesian inference technique in order to estimate the model parameters. We also introduce two approaches to accelerate the RVMS training. In the first approach, an efficient smooth prior is employed that improves the degree of sparsity. In the second approach, a fast marginal likelihood maximization procedure is used for obtaining a sparse solution of survival analysis task by sequential addition and deletion of candidate basis functions. These two approaches, denoted by smooth RVMS and fast RVMS, typically use fewer basis functions than RVMS and improve the RVMS training time; however, they cause a slight degradation in the RVMS performance. We compare the RVMS and the two accelerated approaches with the previous sparse kernel survival analysis method on a synthetic data set as well as six real-world data sets. The proposed kernel survival analysis models have been discovered to be more accurate in prediction, although they benefit from extra sparsity. The main advantages of our proposed models are: 1) extra sparsity that leads to a better generalization and avoids overfitting; 2) automatic relevance sample determination based on data that provide more accuracy, in particular for highly censored survival data; and 3) flexibility to utilize arbitrary number and types of kernel functions (e.g., non-Mercer kernels and multikernel learning). <s> BIB004
Support Vector Machines (SVM), a very successful supervised learning approach, are used mostly for classification and can also be modified for regression problems  . They have also been successfully adapted for use in survival analysis problems. A naive approach is to consider only those instances that actually have events in the Support Vector Regression (SVR), where the ϵ-insensitive loss function f (X i ) = max (0, | f (X i ) − y i | − ϵ ) is minimized with a regularizer  . However, the main disadvantage of this approach is that the order information included in the censored instances will then be completely ignored BIB001 ). Another possible way to handle censored data is to apply support vector classification using the constraint classification approach  . This imposes constraints on the SVM formulation for two comparable instances in order to maintain the required order. However, the computational complexity for this algorithm is quadratic with respect to the number of instances, which for large datasets is clearly impractical. In addition, it only examines the ordering among the instances and ignores the actual values of the outputs. To counter this, BIB002 proposed the use of SVR for Censored Data (SVRc), as this takes advantage of the standard SVR and also adapts it for censored cases by using an updated asymmetric loss function. In this case, it considers both the uncensored and censored instances in the model.  studied a learning machine designed for the predictive modeling of independently right-censored survival data by introducing a health index, which serves as a proxy between the instance's covariates and the outcome. The same group ) then went on to introduce an SVR-based approach that combines the ranking and regression methods in the context of survival analysis. On average, the time complexity of these methods is O (N 3 ), which follows the time complexity of the standard SVM. The Relevance Vector Machine (RVM) proposed by others BIB003 BIB004 ) obtains parsimonious estimates for regression and probabilistic problems using Bayesian inference utilizing the same formulation as SVM but adding a probabilistic classification. RVM adopts a Bayesian approach by considering the prior over the weights controlled by various parameters. Each of these parameters corresponds to a weight, the most probable value of which can be estimated iteratively based on the data. The Bayesian representation of the RVM can avoid these parameters in SVM as optimization methods based on cross-validation are usually used. However, it is also possible for RVMs to converge to a local minimum since an EM algorithm is used to learn the parameters. This differs from the regular Sequential Minimal Optimization (SMO) algorithm used in SVM, which guarantees convergence to a global minimum.