Sampling

The Sampling module provides functions for resampling and search methods suitable for functions found in the Estimators module.

References

conaction.sampling.heuristic_downward_closure_search(f, X, tau=0.1, abscomp=False, leastarity=2)

Search via the downward closure heuristic.

Parameters:

f (function) – A permutation-invariant multiary function.
X (ndarray) – m x n data matrix.
tau (float) – Downward closure threshold.
abscomp (Bool) – Whether to compare threshold to absolute value of f.
leastarity (int (default=2)) – The function arity to start search.

Returns:

d – Computing values of f.

Return type:

dict[dict]

conaction.sampling.isoarity_search(f, X, arity)

For a given arity of relation, compute set function on all sets whose cardinality equals that arity.

Parameters:

f (function) – Estimator
X (np.ndarray-like) – Data matrix
arity (int) – Arity to compute f at; number of variables.

Returns:

results – Results of computing function f on columns of X.

Return type:

dict

conaction.sampling.permute_columns(x)

Permutes the columns of a data matrix.

Parameters:: x (array-like) – An m x n data matrix.
Returns:: Permuted matrix.
Return type:: array-like

References

Examples

>>> import numpy as np
>>> np.random.seed(0)
>>> data = np.arange(100).reshape(10,10)
>>> permute_columns(data)
array([[60, 61, 82, 43, 34, 75, 16, 97, 78, 99],
   [30, 81, 92, 53, 14, 15, 26, 87, 48, 69],
   [80, 41, 32, 63, 24, 55, 46, 67, 58, 79],
   [90, 51, 22,  3, 64, 95, 76, 77, 28, 59],
   [40, 71, 12, 33, 54, 85,  6, 47, 88, 49],
   [ 0, 11,  2, 73, 94, 65, 86, 57, 18,  9],
   [50, 91, 62, 83,  4, 35, 96, 37, 98, 29],
   [10,  1, 42, 93, 84, 25, 36, 17, 68, 39],
   [70, 31, 72, 23, 44,  5, 56,  7, 38, 19],
   [20, 21, 52, 13, 74, 45, 66, 27,  8, 89]])

conaction.sampling.powerset_search(f, X, leastarity=1)

Computes a set function on the whole powerset of sets of variables.

Parameters:

f (function) – Estimator
X (np.ndarray-like) – Data matrix

Returns:

results – Computing values of f.

Return type:

dict

conaction.sampling.statistic_permute(X, stat_func=<function <lambda>>, iters=100)

Performs a permutation Monte Carlo of a statistical function applied to a given dataset.

Parameters:

X (array-like) – An m x n data matrix.
stat_func (function) – Function to be calculated on new samples. (default=lambda x: x)

Returns:

y – Resulting permutation statistics.

Return type:

list

Notes

This function wraps around the permute_columns function to sample a function of a data matrix multiple times under pseudo-randomly sampled permutations within the columns.

References

Examples

>>> import numpy as np
>>> data = np.arange(9).reshape(3,3)
>>> statistic_permute(data, np.mean, 2)
[4.0, 4.0]