| Multivariate Pattern Analysis in Python

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This content refers to the previous stable release of PyMVPA. Please visit www.pymvpa.org for the most recent version of PyMVPA and its documentation.

# Monte-Carlo testing of Classifier-based Analyses

It is often desirable to be able to make statements like “Performance is significantly above chance-level”. PyMVPA supports NULL (aka H0) hypothesis testing for transfer errors and all dataset measures. In both cases the object computing the measure or transfer error takes an optional constructor argument null_dist. The value of this argument is an instance of some `NullDist` estimator. If NULL distribution is luckily a-priori known, it is possible to reuse any distribution specified in scipy.stats module. If the parameters of the distribution are known, such distribution instance can be used to initialize FixedNullDist instance to be specified in null_dist parameter.

However, as with other applications of statistics in classifier-based analyses there is the problem that we do not know the distribution of a variable like error or performance under the NULL hypothesis to assign the adored p-values, i.e. the probability of a result given that there is no signal. Even worse, the chance-level or guess probability of a classifier depends on the content of a validation dataset, e.g. balanced or unbalanced number of samples per label and total number of labels).

One approach to deal with this situation is to estimate the NULL distribution. A generic way to do this are permutation tests (aka Monte Carlo, Nichols et al. (2006)). Then NULL distribution is estimated by computing some measure multiple times using datasets with no relevant signal in them. These datasets are generated by permuting the labels of all samples in the training dataset each time the measure is computed, and therefore randomizing/removing any possible relevant information.

Given the measures computed using the permuted datasets one can now determine the probability of the empirical measure (i.e. the one computed from the original training dataset) under the no signal condition. This is simply the fraction of measures from the permutation runs that is larger or smaller than the emprical (depending on whether on is looking at performances or errors).

If the family of the distribution is known (e.g. Gaussian/Normal) and provided in dist_class parameter of MCNullDist, then permutation tests done by MCNullDist allow to determine the distribution parameters. Under strong assumption of Gaussian distribution, 20-30 permutations should be sufficient to get sensible estimates of the distribution parameters. If no distribution family can be assumed, with a larger number of permutations, derivation of CDF out of population is possible with Nonparametric probability function (which is the default value of dist_class for MCNullDist). If null_dist is provided, the respective `TransferError` or `DatasetMeasure` instance will automatically use it to estimate the NULL distribution and store the associated p-values in a state variable named null_prob.

    # lazy import
    from mvpa.suite import *

    # enable progress output for MC estimation
    if __debug__:
        debug.active += ["STATMC"]

    # some example data with signal
    train = normalFeatureDataset(perlabel=50, nlabels=2, nfeatures=3,
                                 nonbogus_features=[0,1], snr=0.3, nchunks=1)

    # define class to estimate NULL distribution of errors
    # use left tail of the distribution since we use MeanMatchFx as error
    # function and lower is better
    # in a real analysis the number of permutations should be larger
    # to get stable estimates
    terr = TransferError(clf=SMLR(),
                         null_dist=MCNullDist(permutations=100,
                                              tail='left'))

    # compute classifier error on training dataset (should be low :)
    err = terr(train, train)
    print 'Error on training set:', err

    # check that the result is highly significant since we know that the
    # data has signal
    print 'Corresponding p-value: ',  terr.null_prob

See also

The full source code of this example is included in the PyMVPA source distribution (doc/examples/permutation_test.py).

### Navigation

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