Median absolute deviation from numpy ndarray

Question

I work with a 4D numpy array where I compute statistics mean, meadin, std along the 3rd dimension of the array like so:

import numpy as np
input_shape = (1, 10, 4)
n_sample =20
X = np.random.uniform(0,1, (n_sample,)+input_shape)
X.shape
(20, 1, 10, 4)

Then I compute the mean, med, and std-dev this way:

sta_fuc = (np.mean, np.median, np.std)
stat = np.concatenate([func(X, axis=2, keepdims=True) for func in sta_fuc], axis=2)

So that:

stat.shape
(20, 1, 3, 4)

represent the values of the mean, median and std along that dimension.

But then I would like to add the value of the column’s mean absolute deviation mad so that the statistics is (mean, median, std, mad), but it appears numpy doesn’t provide a function for that. How do I add madto my statistics?

EDIT

As far the first answer, using the defined function, i.e.:

def mad(arr, axis=None, keepdims=True):
    median = np.median(arr, axis=axis, keepdims=True)
    mad = np.median(np.abs(arr-median, axis=axis, keepdims=keepdims),
                    axis=axis, keepdims=keepdims)
    return mad

Then adding mad to the statistics, which generate an error, like so:

sta_fuc = (np.mean, np.median, np.std, mad)
stat = np.concatenate([func(X, axis=2, keepdims=True) for func in sta_fuc], axis=2)

---------------------------------------------------------------------------

TypeError                                 Traceback (most recent call last)

<ipython-input-22-dab51665f952> in <module>()
      1 sta_fuc = (np.mean, np.median, np.std, mad)
----> 2 stat = np.concatenate([func(X, axis=2, keepdims=True) for func in sta_fuc], axis=2)

1 frames

<ipython-input-21-84d735c8c516> in mad(arr, axis, keepdims)
      1 def mad(arr, axis=None, keepdims=True):
      2     median = np.median(arr, axis=axis, keepdims=True)
----> 3     mad = np.median(np.abs(arr-median, axis=axis, keepdims=keepdims),
      4                     axis=axis, keepdims=keepdims)
      5     return mad

TypeError: 'axis' is an invalid keyword to ufunc 'absolute'

EDIT-2

Using the scipy function suggested by @Jussi also generates error as below:
from scipy.stats import median_absolute_deviation as mad

sta_fuc = (np.mean, np.median, np.std, mad)
stat = np.concatenate([func(X, axis=2, keepdims=True) for func in sta_fuc], axis=2)

TypeError: median_absolute_deviation() got an unexpected keyword argument 'keepdims'

Asked By: super_ask

||

Source

Answer 1

Usually, I’ve seen MAD referring to median absolute deviation. If that’s what you want, it’s available in the SciPy library as scipy.stats.median_absolute_deviation().

It’s also pretty easy to write a suitable function yourself.

Edit: here’s a MAD function that takes a keepdims argument:

def mad(data, axis=None, scale=1.4826, keepdims=False):
    """Median absolute deviation (MAD).
    
    Defined as the median absolute deviation from the median of the data. A
    robust alternative to stddev. Results should be identical to
    scipy.stats.median_absolute_deviation(), which does not take a keepdims
    argument.

    Parameters
    ----------
    data : array_like
        The data.
    scale : float, optional
        Scaling of the result. By default, it is scaled to give a consistent
        estimate of the standard deviation of values from a normal
        distribution.
    axis : numpy axis spec, optional
        Axis or axes along which to compute MAD.
    keepdims : bool, optional
        If this is set to True, the axes which are reduced are left in the
        result as dimensions with size one.

    Returns
    -------
    ndarray
        The MAD.
    """
    # keep dims here so that broadcasting works
    med = np.median(data, axis=axis, keepdims=True)
    abs_devs = np.abs(data - med)
    return scale * np.median(abs_devs, axis=axis, keepdims=keepdims)

Answered By: Jussi Nurminen

Answer 2

I’m not aware of a built-in solution using numpy. But you can implement it based on numpy functions fairly easily, using mad = median(abs(a - median(a))).

def mad(arr, axis=None, keepdims=True):
    median = np.median(arr, axis=axis, keepdims=True)
    mad = np.median(np.abs(arr-median),axis=axis, keepdims=keepdims)
    return mad

Answered By: BurnNote

Median absolute deviation from numpy ndarray

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