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Microsynthesis using quasirandom sampling and/or IPF

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Latest news

The 2.1.3 release is a non-functional change that affects the python version only:

  • migrate to pybind11 from the native C python API, to reduce and simplify the code, and
  • provide improved python API documentation.

2.1 release

  • now available on conda.
  • adds new functionality for multidimensional integerisation.
  • removes previously deprecated functionality: synthPop and synthPopG functions.

Multidimensional integerisation

Building on the prob2IntFreq function - which takes a discrete probability distribution and a count, and returns the closest integer population to the distribution that sums to the count - a multidimensional equivalent integerise is introduced. In one dimension, for example:

>>> import numpy as np
>>> import humanleague
>>> p=np.array([0.1, 0.2, 0.3, 0.4])
>>> humanleague.prob2IntFreq(p, 11)
{'freq': array([1, 2, 3, 5]), 'rmse': 0.3535533905932736}

produces the optimal (i.e. closest possible) integer population to the discrete distribution.

The integerise function generalises this problem and applies it to higher dimensions: given an n-dimensional array of real numbers where the 1-d marginal sums in every dimension are integral (and thus the total population is too), it attempts to find an integral array that also satisfies these constraints.

The QISI algorithm is repurposed to this end. As it is a sampling algorithm it cannot guarantee that a solution is found, and if so, whether the solution is optimal. If it fails this does not prove that a solution does not exist for the given input.

>>> a = np.array([[ 0.3,  1.2,  2. ,  1.5],
                  [ 0.6,  2.4,  4. ,  3. ],
                  [ 1.5,  6. , 10. ,  7.5],
                  [ 0.6,  2.4,  4. ,  3. ]])
# marginal sums
>> sum(a)
array([ 3., 12., 20., 15.])
>>> sum(a.T)
array([ 5., 10., 25., 10.])
# perform integerisation
>>> r = humanleague.integerise(a)
>>> r["conv"]
>>> r["result"]
array([[ 0,  2,  2,  1],
       [ 0,  3,  4,  3],
       [ 2,  6, 10,  7],
       [ 1,  1,  4,  4]])
>>> r["rmse"]
# check marginals are preserved
>>> sum(r["result"]) == sum(a)
array([ True,  True,  True,  True])
>>> sum(r["result"].T) == sum(a.T)
array([ True,  True,  True,  True])

Removed functions

The functions synthPop and synthPopG implement restricted versions of algorithms that are available in other functions. Use qis ins place of synthPop, and qisi in place of synthPopG.


humanleague is a python and an R package for microsynthesising populations from marginal and (optionally) seed data. The package is implemented in C++ for performance.

The package contains algorithms that use a number of different microsynthesis techniques:

The latter provides a bridge between deterministic reweighting and combinatorial optimisation, offering advantages of both techniques:

  • generates high-entropy integral populations
  • can be used to generate multiple populations for sensitivity analysis
  • goes some way to address the 'empty cells' issues that can occur in straight IPF
  • relatively fast computation time

The algorithms:

  • support arbitrary dimensionality* for both the marginals and the seed.
  • produce statistical data to ascertain the likelihood/degeneracy of the population (where appropriate).

The package also contains the following utility functions:

  • a Sobol sequence generator
  • construct a closest integer population from a discrete univariate probability distribution.
  • an algorithm for sampling an integer population from a discrete multivariate probability distribution, constrained to the marginal sums in every dimension.
  • 'flatten' a multidimensional population into a table: this converts a multidimensional array containing the population count for each state into a table listing individuals and their characteristics.

Version 1.0.1 reflects the work described in the Quasirandom Integer Sampling (QIS) paper.


Requires Python 3.5 or newer.


python3 -m pip install humanleague --user


conda install -c conda-forge humanleague

Build, install and test (from cloned repo)

python install --user
python test


Official release:

> install.packages("humanleague")

For a development version

> devtools::install_github("virgesmith/humanleague")

Or, for the legacy version

> devtools::install_github("virgesmith/humanleague@1.0.1")

Documentation and Examples


Consult the package documentation, e.g.

> library(humanleague)
> ?humanleague


See here, or

>>> import humanleague as hl
>>> help(hl)

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