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[英]Why the MAD that is calculated with the function scipy.stats.median_absolute_deviation it's different from the function i did?
[英]Median absolute deviation from numpy ndarray
我使用 4D numpy 數組,我在其中計算統計數據mean, meadin, std
沿數組的第 3 個維度,如下所示:
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)
然后我以這種方式計算mean, med,
和std-dev
:
sta_fuc = (np.mean, np.median, np.std)
stat = np.concatenate([func(X, axis=2, keepdims=True) for func in sta_fuc], axis=2)
以便:
stat.shape
(20, 1, 3, 4)
表示沿該維度的mean, median
和std
的值。
但后來我想添加該列的平均絕對偏差mad
的值,以便統計數據是( mean, median, std, mad
),但看起來numpy
沒有為此提供 function。 如何將mad
添加到我的統計數據中?
編輯
至於第一個答案,使用定義的 function,即:
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
然后將mad
添加到統計數據中,這會產生錯誤,如下所示:
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'
編輯-2
使用scipy
建議的 scipy function 也會產生如下錯誤: 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'
通常,我看到 MAD 指的是中位數絕對偏差。 如果這是您想要的,它可以在 SciPy 庫中作為scipy.stats.median_absolute_deviation()
。
自己編寫一個合適的 function 也很容易。
編輯:這是一個 MAD function,它帶有一個keepdims
參數:
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)
我不知道使用 numpy 的內置解決方案。但是您可以使用mad = median(abs(a - median(a)))
很容易地基於 numpy 函數實現它。
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
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