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pythonarraysnumpymeanmean-square-error
TheMeaningfulEngineer
TheMeaningfulEngineer

Reputation: 16359

Mean Squared Error in Numpy?

Is there a method in numpy for calculating the Mean Squared Error between two matrices?

I've tried searching but found none. Is it under a different name?

If there isn't, how do you overcome this? Do you write it yourself or use a different lib?

Upvotes: 115

Views: 337133

Answers (7)

Roger V.
Roger V.

Reputation: 733

The standard numpy methods for calculation mean squared error (variance) and its square root (standard deviation) are numpy.var() and numpy.std(), see here and here. They apply to matrices and have the same syntax as numpy.mean().

I suppose that the question and the preceding answers might have been posted before these functions became available.

Remarks on statistics
To answer the comment made by @Drew :
This answer is equivalent to the top answers in this thread. Technically, MSE differs from variance in that it uses "true" value of the parameter, rather than its estimate, see What's the difference between the variance and the mean squared error? and What is the Difference between Variance and MSE?. The two quantities then differ by the bias of our estimate of the central parameter. However, when calculating sample variance, as is done in the OP, we cannot really know the value of this parameter. I believe the OP uses term MSE in a loose sense.

Furthermore, the numpy functions proposed above allow for parameter ddof (the number of degrees of freedom), which allows to obtain unbiased variance estimates (contrary to what is claimed in some superficial comparisons between python and R.)

Upvotes: 2

Developer700
Developer700

Reputation: 36

What about this to keep with the np.operation style?

mse = np.mean(np.square(A - B))

Just keep in mind that np.mean() with no axis keyword argument specified will output a scalar, just like np.sum().

Upvotes: 0

Saullo G. P. Castro
Saullo G. P. Castro

Reputation: 58985

You can use:

mse = ((A - B)**2).mean(axis=ax)

Or

mse = (np.square(A - B)).mean(axis=ax)
  • with ax=0 the average is performed along the row, for each column, returning an array
  • with ax=1 the average is performed along the column, for each row, returning an array
  • with omitting the ax parameter (or setting it to ax=None) the average is performed element-wise along the array, returning a scalar value

Upvotes: 157

dcneuro
dcneuro

Reputation: 181

Just for kicks

mse = (np.linalg.norm(A-B)**2)/len(A)

Upvotes: 9

user4172036
user4172036

Reputation:

Another alternative to the accepted answer that avoids any issues with matrix multiplication:

 def MSE(Y, YH):
     return np.square(Y - YH).mean()

From the documents for np.square:

Return the element-wise square of the input.

Upvotes: 6

Mark Swardstrom
Mark Swardstrom

Reputation: 18100

Even more numpy

np.square(np.subtract(A, B)).mean()

Upvotes: 39

Charity Leschinski
Charity Leschinski

Reputation: 2906

This isn't part of numpy, but it will work with numpy.ndarray objects. A numpy.matrix can be converted to a numpy.ndarray and a numpy.ndarray can be converted to a numpy.matrix.

from sklearn.metrics import mean_squared_error
mse = mean_squared_error(A, B)

See Scikit Learn mean_squared_error for documentation on how to control axis.

Upvotes: 51

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