1. A method comprising: over time adding new data points to a streaming window of data points and removing existing data points from the streaming window, each data point having a value for each dimension of one or more dimensions; each time a given new data point is added to the streaming window or a given existing data point is removed from the streaming window, updating, by a processor of a computing device, one or more outlier detection data structures, each outlier detection data structure encompassing the data points within the streaming window for a corresponding dimension; and, using the outlier detection data structures to detect one or more outlier data points within the streaming window over selected one or more dimensions.