  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
