Some good and bad properties of
histograms as density estimators
• There is no need to fit a model to the data.
– We just compute some very simple statistics (the
number of datapoints in each bin) and store them.
• The number of bins is exponential in the dimensionality
of the dataspace. So high-dimensional data is tricky:
– We must either use big bins or get lots of zero counts
(or adapt the local bin-width to the density)
• The density has silly discontinuities at the bin
boundaries.
– We must be able to do better by some kind of
smoothing.