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Diverse (co-)moment statistics

This class implements (co)-moment statistics, covering both clasical product-moment statistics, as well as more recently developed energy statistics. The dicomo class also serves as a plug-in into capi and ppdire. It has been written consistently with ppdire such that it provides a wide range of projection indices based on (co-)moments.

Description

The dicomo folder contains

  • The class object (dicomo.py)
  • Ancillary functions for (co-)moment estimation (_dicomo_utils.py)

The dicomo class

Parameters

  • est, str: mode of estimation. The set of options are 'arithmetic' (product-moment) or 'distance' (energy statistics)
  • mode, str: type of moment. Options are:
    • 'mom': moment
    • 'var': variance
    • 'std': standard deviation
    • 'skew': skewness
    • 'kurt': kurtosis
    • 'com': co-moment
    • 'M3': shortcut for third order co-moment
    • 'cov': covariance
    • 'cos': co-skewness
    • 'cok': co-kurtosis
    • 'corr': correlation,
    • 'continuum': continuum association
    • 'mdd': martingale difference divergence (requires est = 'distance')
    • 'mdc': martingale difference correlation (requires est = 'distance')
    • 'ballcov': ball covariance (requires installing Ball and uncommenting the import statement)
  • center: internal centring used in calculation. Options are mean or median.

Attributes

Attributes always provided

  • moment_: The resulting (co-)moment

Depending on the options picked, intermediate results are stored as well, as x_moment_, y_moment_ or co_moment_

Methods

  • fit(X, *args, **kwargs): fit model

The fit function takes several optional input arguments. These are options that apply to individual settings:

  • biascorr, Bool, when True, correct for bias. For classical product-moment statistics, this is the small sample correction. For energy statistics, this leads to the estimates that are unbiased in high dimension (but not preferred in low dimension).
  • alpha, float, parameter for continuum association. Has no effect for other options.
  • option, int, determines which higher order co-moment to calculate, e.g. for co-skewness, option=1 calciulates CoS(x,x,y)
  • order, int, which order (co-)moment to calculate. Can be overruled by mode, e.g. if mode='var', order is set to 2.
  • calcmode, str, to use the efficient or naive algorithm to calculate distance statistics. Defaults to fast when available.

Examples

Check out the dicomo examples notebook
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