Survival Kernets: Scalable and Interpretable Deep Kernel Survival Analysis with an Accuracy Guarantee

TL;DR

Survival kernets introduce a scalable, interpretable deep kernel survival analysis model that provides theoretical guarantees and performs well on large datasets, combining clustering, neural networks, and kernel methods.

Contribution

We develop a novel survival kernel net model that scales to large datasets, offers interpretability through clustering, and includes theoretical error bounds.

Findings

Achieves high concordance index on large survival datasets

Provides finite-sample error bounds for survival predictions

Scales efficiently with dataset size using kernel netting and neural architecture search

Abstract

Kernel survival analysis models estimate individual survival distributions with the help of a kernel function, which measures the similarity between any two data points. Such a kernel function can be learned using deep kernel survival models. In this paper, we present a new deep kernel survival model called a survival kernet, which scales to large datasets in a manner that is amenable to model interpretation and also theoretical analysis. Specifically, the training data are partitioned into clusters based on a recently developed training set compression scheme for classification and regression called kernel netting that we extend to the survival analysis setting. At test time, each data point is represented as a weighted combination of these clusters, and each such cluster can be visualized. For a special case of survival kernets, we establish a finite-sample error bound on predicted survival distributions that is, up to a log factor, optimal. Whereas scalability at test time is achieved using the aforementioned kernel netting compression strategy, scalability during training is achieved by a warm-start procedure based on tree ensembles such as XGBoost and a heuristic approach to accelerating neural architecture search. On four standard survival analysis datasets of varying sizes (up to roughly 3 million data points), we show that survival kernets are highly competitive compared to various baselines tested in terms of time-dependent concordance index. Our code is available at: https://github.com/georgehc/survival-kernets