  We make two contributions to the Isolation Forest method for anomaly and
outlier detection. The first contribution is an information-theoretically
motivated generalisation of the score function that is used to aggregate the
scores across random tree estimators. This generalisation allows one to take
into account not just the ensemble average across trees but instead the whole
distribution. The second contribution is an alternative scoring function at the
level of the individual tree estimator, in which we replace the depth-based
scoring of the Isolation Forest with one based on hyper-volumes associated to
an isolation tree's leaf nodes.
  We motivate the use of both of these methods on generated data and also
evaluate them on 34 datasets from the recent and exhaustive ``ADBench''
benchmark, finding significant improvement over the standard isolation forest
for both variants on some datasets and improvement on average across all
datasets for one of the two variants. The code to reproduce our results is made
available as part of the submission.
