  Kernel survival analysis methods predict subject-specific survival curves and
times using information about which training subjects are most similar to a
test subject. These most similar training subjects could serve as forecast
evidence. How similar any two subjects are is given by the kernel function. In
this paper, we present the first neural network framework that learns which
kernel functions to use in kernel survival analysis. We also show how to use
kernel functions to construct prediction intervals of survival time estimates
that are statistically valid for individuals similar to a test subject. These
prediction intervals can use any kernel function, such as ones learned using
our neural kernel learning framework or using random survival forests. Our
experiments show that our neural kernel survival estimators are competitive
with a variety of existing survival analysis methods, and that our prediction
intervals can help compare different methods' uncertainties, even for
estimators that do not use kernels. In particular, these prediction interval
widths can be used as a new performance metric for survival analysis methods.
