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AverageShiftedHistograms.jl

An Average Shifted Histogram (ASH) estimator is essentially a kernel density estimator calculated over a fine-partition histogram.

Benefits Over KDE

  • The histogram component can be constructed on-line.
  • Adding new data is an O(nbins) operation vs. O(n) for KDE, nbins << n.
  • ASH is considerably faster even for small datasets. See below with a comparison with KernelDensity.jl.
julia> @btime kde(x) setup=(x=randn(100));
  169.523 μs (106 allocations: 56.05 KiB)

julia> @btime ash(x) setup=(x=randn(100));
  4.173 μs (3 allocations: 8.22 KiB)
<img width = 600 src = "https://cloud.githubusercontent.com/assets/8075494/17938441/ce8815e4-69da-11e6-8f19-33052e2ef21e.gif">

Usage

The main function exported by AverageShiftedHistograms is ash.

ash

Gotchas

!!! warning Beware oversmoothing by setting the m parameter too large. Note that "too large" is relative to the width of the bin edges.

using AverageShiftedHistograms, Plots

y = randn(10 ^ 6)

o = ash(y; rng = -5:.1:5, m = 20)

plot(o)

savefig("indexplot.svg"); nothing # hide