abstract
this paper addresses detecting anomalous patterns in images, time-series, and tensor data
when the location and scale of the pattern is unknown a priori. the multiscale scan statistic
convolves the proposed pattern with the image at various scales and returns the maximum of
the resulting tensor. scale corrected multiscale scan statistics apply different standardizations
at each scale, and the limiting distribution under the null hypothesis—that the data is only
noise—is known for smooth patterns. we consider the problem of simultaneously learning and
detecting the anomalous pattern from a dictionary of smooth patterns and a database of many
tensors. to this end, we show that the multiscale scan statistic is a subexponential random
variable, and prove a chaining lemma for standardized suprema, which may be of independent
interest. then by averaging the statistics over the database of tensors we can learn the pattern
and obtain bernstein-type error bounds. we will also provide a construction of an -net of
the location and scale parameters, providing a computationally tractable approximation with
similar error bounds.