bhtt

Ben-Haim/Tom-Tov (BHTT) streaming histogram sketch implementation (http://www.jmlr.org/papers/volume11/ben-haim10a/ben-haim10a.pdf).

A BHTT histogram is an ordered list of bins that is a compact approximate representation of a numerical data distribution.

The desired size of the list is chosen at histogram creation time (larger histograms give more accurate estimates of quantiles, but use more memory and are generally slower). Each bin is a (value, count) pair, where value is a weighted average of count numbers (or bins) merged together.

To insert a new value to the histogram, a new (value, 1) bin is added first, preserving the ascending order of bins in the list. If the total number of bins exceeds the configured histogram size, then the two closest bins are merged together to restore the size invariant.

Unlike traditional histograms, which require one to specify both the histogram size and the bin boundaries configuration at histogram creation time, BHTT streaming histograms automatically adjust the bins as new values are inserted.

Typical operations on the constructed histograms include approximations of quantiles and counts.

BHTT histograms are mergeable but it's not possible to subtract one histogram from another (bin by bin) to get a difference between the two.

Examples

use bhtt::Histogram;

let values = vec![1.0, 0.0, -5.4, -2.1, 8.5, 10.0, 8.6, 4.3, 7.8, 5.2];

// create a new Histogram with (up to) 5 bins and insert some values
let mut h = Histogram::new(5);
for value in values {
    h.insert(value);
}

// the histogram keeps track of the total number of inserted values,
// as well as the exact minimum and maximum values
assert_eq!(h.size(), 5);
assert_eq!(h.count(), 10);
assert_eq!(h.min(), Some(-5.4));
assert_eq!(h.max(), Some(10.0));

// the histogram allows to get approximations of arbitrary quantiles
assert_eq!(h.quantile(0.0), Some(-5.4));
assert_eq!(h.quantile(0.5), Some(4.75));
assert_eq!(h.quantile(1.0), Some(10.0));

// or estimate how many values are less than or equal to the given value
assert_eq!(h.count_less_than_or_equal_to(-7.4), 0);
assert_eq!(h.count_less_than_or_equal_to(5.0), 5);
assert_eq!(h.count_less_than_or_equal_to(13.0), 10);

// if two histograms have been built separately, it's possible to merge them together
h.merge(&Histogram::from_iter(5, &[1.0, -7.6, 0.0, 5.8, 4.3, 2.1, 11.6]));
assert_eq!(h.count(), 17);
assert_eq!(h.min(), Some(-7.6));
assert_eq!(h.max(), Some(11.6));

Development

Running tests

Unit tests are put directly to the code modules in src/.

Integration tests are in tests/ directory with input data and utility functions stored in utilities/ (so that they can be shared between integration tests and benchmarks).

$ cargo test

Running benchmarks

$ cargo bench