PermutationImportance 1.0.5.1

Important variables determined through permutation selection

PermutationImportance

Provides an efficient method to compute variable importance through the permutation of input variables. Uses multithreading and supports both Windows and Unix systems and Python 2 and 3.

This repository provides the stand-alone functionality of a permutation-based method of computing variable importance in an arbitrary model. Importance for a given variable is computed in accordance with Lakshmanan et al. (2015)'s paper[1]. Variables which, when their values are permuted, cause the worst resulting score are considered most important. This implementation provides the functionality for an arbitrary method for computing the "worst" score and for using an arbitrary scoring metric. The most common case of this is to chose the variable which most negatively impacts the accuracy of the model.

Functionality is provided not only for returning the most important variable (along with the raw scores for each variable) but also for returning the sequential importance of variables. To do this, the most important variable is determined and then it is left permuted while the next most important variable is determined. In the extreme case, this is continued until the sequential ordering of all variables is determined, but this can be terminated at an earlier level by choice.

¹Lakshmanan, V., C. Karstens, J. Krause, K. Elmore, A. Ryzhkov, and S. Berkseth, 2015: Which Polarimetric Variables Are Important for Weather/No-Weather Discrimination?. J. Atmos. Oceanic Technol., 32, 1209–1223, https://doi.org/10.1175/JTECH-D-13-00205.1

Setup

PermutationImportance is now available on pip, so you can simply install with

pip install PermutationImportance

and import the desired method with

from permutation_importance.variable_importance import permutation_selection_importance

Example Usage

For these examples, I will assume a particular model (FakeModel below), but any python object with a predict method can be used.

class FakeModel(object):
    """Computes a particular linear combination of the input variables of a dataset"""

    def __init__(self, cutoff, *coefs):
        """Store the coeficients to multiply the input variables by"""
        self.cutoff = cutoff
        self.coefs = coefs

    def predict(self, input_data):
        return np.array([sum([self.coefs[i]*data[i] for i in range(len(data))]) > self.cutoff for data in input_data])

model = FakeModel(20, 3, 2, 0, 1)

You will also need the testing inputs and outputs, both of which should be numpy.ndarrays. Similarly, a classes object containing the possible outputs of the model is required for some scoring function. For my example, I am using

# Binary classification with 4 input variables
# x is most important (scaled by a factor of 3)
# y is next most important (scaled by a factor of 2)
# z is not important at all
# w is slightly important (scaled by 1)
def population_def(x, y, z, w): return int(3*x + 2*y + w > 20)
    fake_model_input = np.random.randint(0, 10, size=(1000, 4))
    fake_model_output = [population_def(*data_point)
                         for data_point in fake_model_input]
    classes = 20

Lastly, for the most simple usage of the model, you also require the number of permutations to perform. Generally, this should be at least 30 to ensure better statistics. Here is the simplest call:

results = permutation_selection_importance(model, classes, fake_model_input, fake_model_output, npermute=30)
# Returns a list of triples which is as long as the number of input variables
len(results)
# 4
(important_variable_indices_ordered, score_before_permuting, all_scores_after_permuting) = results[i]

For the triple in the kth element of results, important_variable_indices_ordered contains a list of the indices of the k variables which are most important together. results[0][0] is a list containing only the index of the most important individual variable. results[1][0] contains the index of the most important variable and then the index of the variable which is most important after the first variable has been removed. results[2][0] contains those same two indices followed by the index of the variable which is most important after those two variables have been removed, etc. So for the example above

results[0][0]
# [0]
results[1][0]
# [0, 1]
results[2][0]
# [0, 1, 3]
results[3][0]
# [0, 1, 3, 2]

In this manner, results[k][0] contains the ordering of the "ranks" of the k+1 most important variables (Section 2.e of the paper).

score_before_permuting is the score after permuting all variables of a "rank" before the (k+1)th variable, and all_scores_after_permuting is a list of the scores for all of the variables, with None for the scores of the variables of "rank" lower than k+1. (These may be handy for plotting the results.)

There are two typical ways to determine the relative importances of each variable:

1. Use the "ranks" of all the variables: results[-1][0]. This takes O(n2) time
2. Use the ordering of the scores after each variable is permuted only once: np.argsort(results[0][2])[::-1]. This takes O(n) time

results = permutation_selection_importance(model, classes, fake_model_input, fake_model_output, npermute=30)

rank_importances = results[-1][0]
# Reverse the order here because the variable with the worst score is the most important
permutation_importances = np.argsort(results[0][2])[::-1]

Options

nimportant_variables

By default, the algorithm will execute the O(n2) version of the algorithm (1. above), but if you only want the first m entries of results, you can specify nimportant_variables=m in the function call. To execute the O(n) version of the algorithm (2. above), set nimportant_variables=1. e.g.

results = permutation_selection_importance(model, classes, fake_model_input, fake_model_output, npermute=30, nimportant_variables=1)
importances = np.argsort(results[0][2])[::-1]

subsample

By default, the algorithm will use the entire data for each permutation iteration, but you will typically want to only use a smaller fraction (say half). For this, you can specify subsample=0.5

results = permutation_selection_importance(model, classes, fake_model_input, fake_model_output, npermute=30, subsample=0.5)

score_fn

Any arbitrary callable can be used for scoring, so long as it has the form (new_predictions, truths, classes) -> number. Normally, this defaults to accuracy. Some example scorers are provided in the scorers.py file. For example, to use Peirce Skill Score

from permutation_importance.scorers import peirce_skill_scorer
results = permutation_selection_importance(model, classes, fake_model_input, fake_model_output, npermute=30, score_fn=peirce_skill_scorer)

optimization

A different strategy can be used for determining which variable is the most important, given a list of scores by specifying optimization=<string or callable>. By default, the score which is lowest after permuting indicates that variable was most important ("minimize"), but ("maximize") is also supported. Further, an arbitrary callable can be used, so long as it has the form (list_of_scores) -> index. This is particularly useful for scoring function like bias, where a bias of 1 is best and a bias near 0 or +infinity indicates the model is doing poorly. Assuming some sort of "error" function where a lower score is better, the example usage is

error_fn # some arbitrary error function where a lower score is better
results = permutation_selection_importance(model, classes, fake_model_input, fake_model_output, npermute=30, score_fn=error_fn, optimization='maximize')

njobs and share_vars

The implementation can be multithreaded by specifying a number of jobs (njobs). Additionally, for optimization, as many variables as possible can be shared between threads share_vars=True. Sadly, this feature only works on Unix systems, so the parameter share_vars will be ignored on Windows systems. To multithread the algorithm for a Unix machine with 8 cores, call

results = permutation_selection_importance(model, classes, fake_model_input, fake_model_output, npermute=30, njobs=8, share_vars=True)

This same command will also run for a Windows machine with 8 cores, as the share_vars parameter will be safely ignored.