  In this paper we describe an algorithm for estimating the provenance of hacks
on websites. That is, given properties of sites and the temporal occurrence of
attacks, we are able to attribute individual attacks to joint causes and
vulnerabilities, as well as estimating the evolution of these vulnerabilities
over time. Specifically, we use hazard regression with a time-varying additive
hazard function parameterized in a generalized linear form. The activation
coefficients on each feature are continuous-time functions over time. We
formulate the problem of learning these functions as a constrained variational
maximum likelihood estimation problem with total variation penalty and show
that the optimal solution is a 0th order spline (a piecewise constant function)
with a finite number of known knots. This allows the inference problem to be
solved efficiently and at scale by solving a finite dimensional optimization
problem. Extensive experiments on real data sets show that our method
significantly outperforms Cox's proportional hazard model. We also conduct a
case study and verify that the fitted functions are indeed recovering
vulnerable features and real-life events such as the release of code to exploit
these features in hacker blogs.
