PyTDigest: Fast streaming calculation of approximate quantiles

Python package for fast TDigest calculation.

• C implementation and thin Python wrapper
• suitable for big data and streaming and distributed settings
• developed for smooth compatibility with Pandas and numpy

Based on previous work of Ted Dunning and Andrew Werner.

• https://github.com/tdunning/t-digest
• https://github.com/ajwerner/tdigestc

Warning

The package relies on C implementation that is compiled on host machine. I tested the compilation on Linux and on Windows 11, but I cannot ensure the compatibility with all operating systems. Let me know if you have encountered any issues.

Basic example

from pytdigest import TDigest
import numpy as np
import pandas as pd

rng = np.random.default_rng(12354)
n = 100_000
x = rng.normal(loc=0, scale=10, size=n)
w = rng.exponential(scale=1, size=n)

# estimation from data is simple:
td = TDigest.compute(x, w, compression=1_000)
# td now contains "compressed" distribution: centroids with their means and weights

# TDigest can be used to provide mean or approximate quantiles (i.e. inverse CDF):
td.mean
quantiles = [0., 0.01, 0.05, 0.25, 0.5, 0.75, 0.95, 0.99, 1.]
td.inverse_cdf(quantiles)

# these results are close to numpy values (note that numpy provides only unweighted quantiles)
np.average(x, weights=w)  # mean should be exact
np.quantile(x, quantiles)

# TDigest can be copied
td2 = td.copy()

# and multiple TDigests can be added together to provide approximate quantiles for the overall dataset
td + td2

Installation

From PyPI:

$ pip install pytdigest

Performance

Ted Dunning's original algorithm in Java takes about ~140 ns per addition on average. This package needs about ~200 ns per addition when called from Python on numpy arrays, so the performance is fairly comparable with the original implementation. All other tested TDigest implementations in Python are much slower.

import numpy as np
from pytdigest import TDigest
import time

rng = np.random.Generator(np.random.PCG64(12345))

for n in [100_000, 1_000_000, 10_000_000]:
    x = rng.normal(size=n)
    w = rng.exponential(size=n)

    start = time.time()
    td = TDigest.compute(x, w)
    end = time.time()
    print(f'PyTDigest, n = {n:,}: {end - start:.3g} seconds')

# PyTDigest, n = 100,000: 0.0222 seconds
# PyTDigest, n = 1,000,000: 0.21 seconds
# PyTDigest, n = 10,000,000: 2.02 seconds

Similar packages

Several Python packages or wrappers exist for the TDigest algorithm.

tdigest

The most popular on GitHub is a pure Python tdigest package. Pure Python implementation is indeed very slow – more than 100x slower than this package:

import numpy as np
from pytdigest import TDigest
from tdigest import TDigest as TDigestPython
import time

rng = np.random.Generator(np.random.PCG64(12345))
n = 100_000
x = rng.normal(size=n)
w = rng.exponential(size=n)

start = time.time()
td = TDigest.compute(x, w)
end = time.time()
print(f'PyTDigest: {end - start:.3g} seconds')
# PyTDigest: 0.0246 seconds

tdp = TDigestPython()
start = time.time()
tdp.batch_update(x)
end = time.time()
print(f'TDigest: {end - start:.3g} seconds')
# TDigest: 7.26 seconds

Different weights for can be used in tdigest only with update method for adding a single observation.

t-digest CFFI

Other package is t-digest CFFI, a thin Python wrapper over C implementation. It does not pass batch updates into the C layer, so the iteration has to be done in python:

import numpy as np
from tdigest import TDigest as TDigestCFFI
import time

rng = np.random.Generator(np.random.PCG64(12345))
n = 100_000
x = rng.normal(size=n)

tdcffi = TDigestCFFI()
start = time.time()
for xx in x:
    tdcffi.insert(xx)
end = time.time()
print(f'TDigest-CFFI: {end - start:.3g} seconds')

Hence this package is still almost 20x slower than this package when used over numpy arrays. In addition, t-digest CFFI package allows only for integer weights.

qtdigest

qtdigest's own benchmarking states that 100 000 additions take about 1.7 s, so it is again almost 100x slower than this package.

tdigestc

tdigestc by ajwerner is a simple C implementation with wrappers for different languages. The Python wrapper is very basic, it is not published on PyPI and some functionality was missing in the underlying C implementation (for instance support for batch updates based on numpy arrays), so I took this package as the starting point and added several useful features for use as a standalone Python package.

Future plans

There are several improvements that can be done in the future:

• TDigest can calculate exact variance in addition to mean.
• Alternating merging procedure (the centroids are always merged left to right in the C implementation, however Ted Dunning states that alternating merging improves the precision).
• Scaling function for merging centroids is hard-coded at the moment. Ted Dunning mentions several possible functions that can be used in merging.
• Centroids can store information about their variance - the resulting TDigest should be still composable and fast and it can work much better for discrete distributions.

Documentation

• https://protivinsky.github.io/pytdigest/index.html

Legal stuff

Apache License, Version 2.0, http://www.apache.org/licenses/LICENSE-2.0

Copyright (c) 2015 Ted Dunning, All rights reserved.

https://github.com/tdunning/t-digest

Copyright (c) 2018 Andrew Werner, All rights reserved.

https://github.com/ajwerner/tdigestc

Copyright (c) 2022 Tomas Protivinsky, All rights reserved.

https://github.com/protivinsky/pytdigest