Error Evaluation

New in version 0.7.

Implemented functions:

• Mean absolute error (MAE, also known as MAD - mean absolute deviation)

  \(\textrm{MAE}=\frac{1}{n} \sum _{i=1}^{n}(e_{i})\).

• Mean squared error (MSE, also known as MSD)

  \(\textrm{MSE}=\frac{1}{n} \sum _{i=1}^{n}(e_{i})^{2}\).

• Root-mean-square error (RMSE, also known as RMSD)

  \(\textrm{RMSE} = \sqrt{\textrm{MSE}}\).

• Logarithmic squared error (returns a vector of values in dB!)

  \(\textbf{logSE} = 10 \log_{10} (\textbf{e}^{2})\)

all functions are often used for evaluation of an error rather than just the error itself or its mean value.

Usage instructions

For MAE evaluation from two time series use

mse = pa.misc.MAE(x1, x2)

If you have the error already calculated, then just

mse = pa.misc.MAE(e)

The same instructions apply for the MSE, RMSE a logarithmic squared error

mse = pa.misc.MSE(x1, x2)
rmse = pa.misc.RMSE(x1, x2)
logse = pa.misc.logSE(x1, x2)

and from error

mse = pa.misc.MSE(e)
rmse = pa.misc.RMSE(e)
logse = pa.misc.logSE(e)

Minimal working examples

In the following example is estimated MSE for two series (x1 and x1):

import numpy as np
import padasip as pa

x1 = np.array([1, 2, 3, 4, 5])
x2 = np.array([5, 4, 3, 2, 1])
mse = pa.misc.MSE(x1, x2)
print(mse)

You can easily check that the printed result 8.0 is correct MSE for given series.

The following example displays, that you can use directly the error series e if you already have it.

import numpy as np
import padasip as pa

# somewhere else in your project
x1 = np.array([1, 2, 3, 4, 5])
x2 = np.array([5, 4, 3, 2, 1])
e = x1 - x2
# you have just the error - e
mse = pa.misc.MSE(e)
print(mse)

Again, you can check the correctness of the answer easily.

Code Explanation

padasip.misc.error_evaluation.MAE(x1, x2=- 1)

Mean absolute error - this function accepts two series of data or directly one series with error.

Args:

• x1 - first data series or error (1d array)

Kwargs:

• x2 - second series (1d array) if first series was not error directly, then this should be the second series

Returns:

• e - MAE of error (float) obtained directly from x1, or as a difference of x1 and x2

padasip.misc.error_evaluation.MSE(x1, x2=- 1)

Mean squared error - this function accepts two series of data or directly one series with error.

Args:

• x1 - first data series or error (1d array)

Kwargs:

• x2 - second series (1d array) if first series was not error directly, then this should be the second series

Returns:

• e - MSE of error (float) obtained directly from x1, or as a difference of x1 and x2

padasip.misc.error_evaluation.RMSE(x1, x2=- 1)

Root-mean-square error - this function accepts two series of data or directly one series with error.

Args:

• x1 - first data series or error (1d array)

Kwargs:

• x2 - second series (1d array) if first series was not error directly, then this should be the second series

Returns:

• e - RMSE of error (float) obtained directly from x1, or as a difference of x1 and x2

padasip.misc.error_evaluation.get_mean_error(x1, x2=- 1, function='MSE')

This function returns desired mean error. Options are: MSE, MAE, RMSE

Args:

• x1 - first data series or error (1d array)

Kwargs:

• x2 - second series (1d array) if first series was not error directly, then this should be the second series

Returns:

• e - mean error value (float) obtained directly from x1, or as a difference of x1 and x2

padasip.misc.error_evaluation.get_valid_error(x1, x2=- 1)

Function that validates:

• x1 is possible to convert to numpy array

• x2 is possible to convert to numpy array (if exists)

• x1 and x2 have the same length (if both exist)

padasip.misc.error_evaluation.logSE(x1, x2=- 1)

10 * log10(e**2) This function accepts two series of data or directly one series with error.

Args:

• x1 - first data series or error (1d array)

Kwargs:

• x2 - second series (1d array) if first series was not error directly, then this should be the second series

Returns:

• e - logSE of error (1d array) obtained directly from x1, or as a difference of x1 and x2. The values are in dB!