Machine learning methods which takes time-to-event into account? My vague understanding is that machine learning methods are based on classification labels. How about a survival type of problem? That is to say, not only "have event" or "have no event", but also "time to event".
In statistics, we can perform e.g. Cox PH regression, but we can then only combine the multiple baseline characteristics in a linear manner (multivariable Cox analysis). If we want to look at a more advanced way to combine them, such as nonlinear, kernel-based, etc., is there corresponding machine learning methods which takes time-to-event into account?
Thanks for any comments.
 A: You may might be interested in Random Survival Forests and the corresponding R package randomForestSRC:
http://www.ccs.miami.edu/~hishwaran/papers/randomSurvivalForests.pdf
https://cran.r-project.org/web/packages/randomForestSRC/
I believe the main limitation of the approach is that it doesn't deal with time varying predictors. 
A: The majority of the linear models based in the likelihood function have extension to the Cox regression. For example, penalized regression models (lasso, rigde regression, elastic net) or partial least squares. In other hand, there are extensions from the classification trees to survival trees. This means all the ensemble methods based in trees are also extended to survival data in a natural way: random forest, bagging, gradient boosting machines, …. Finally, other methods, like support vector machines or neural networks have some theoretical versions for survival data, but there are difficult to apply in the practice.
A: Any linear survival analysis method can be straightforwardly kernelised to generate a non-linear equivalent.  I did something like this a while back for modelling the time-to-growth of microbial pathogens from spores in foods.
G. C. Cawley, N. L. C. Talbot, G. J. Janacek and M. W. Peck, Sparse Bayesian kernel survival analysis for modelling the growth domain of microbial pathogens, IEEE Transactions on Neural Networks, volume 17, number 2, pp. 471-481, March 2006. (www)
A: It is a mistake to assume that the Cox proportional hazards model makes simple assumptions such as linearity.  All regression models have been extended for decades using regression splines, tensor interaction splines, and other approaches to allow for great flexibility in the low- to mid-dimensional case.  As others have said, penalization is instrumental in handling higher-dimensional cases.  [One problem is how to scale nonlinear terms when using penalization and regression splines simultaneously.]
Note also that the term 'multivariate' is inappropriate in this context as there is only one $Y$.
More to the original question, one of the amazing things about statistics is the ability of statistical approaches to extend models in various ways based on sound principles.  Faraggi and Simon (Statistics in Medicine, 1995) did just that to develop a likelihood function for obtaining an artificial neural network Cox model.
