  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 $\epsilon$-net of the location and scale parameters,
providing a computationally tractable approximation with similar error bounds.
