  We propose a non-parametric anomaly detection algorithm for high dimensional
data. We score each datapoint by its average $K$-NN distance, and rank them
accordingly. We then train limited complexity models to imitate these scores
based on the max-margin learning-to-rank framework. A test-point is declared as
an anomaly at $\alpha$-false alarm level if the predicted score is in the
$\alpha$-percentile. The resulting anomaly detector is shown to be
asymptotically optimal in that for any false alarm rate $\alpha$, its decision
region converges to the $\alpha$-percentile minimum volume level set of the
unknown underlying density. In addition, we test both the statistical
performance and computational efficiency of our algorithm on a number of
synthetic and real-data experiments. Our results demonstrate the superiority of
our algorithm over existing $K$-NN based anomaly detection algorithms, with
significant computational savings.
