Random cut trees are generated with respective to respective samples of a baseline set of data records of a data set for which outlier detection is to be performed. To construct a particular random cut tree, an iterative splitting technique is used, in which the attribute along which a given set of data records is split is selected based on its value range. With respect to a newly-received data record of the stream, an outlier score is determined based at least partly on a potential insertion location of a node representing the data record in a particular random cut tree, without necessarily modifying the random cut tree.