Reverse Box-Cox transformation

Question

I am using SciPy's boxcox function to perform a Box-Cox transformation on a continuous variable.

from scipy.stats import boxcox
import numpy as np
y = np.random.random(100)
y_box, lambda_ = ss.boxcox(y + 1) # Add 1 to be able to transform 0 values

Then, I fit a statistical model to predict the values of this Box-Cox transformed variable. The model predictions are in the Box-Cox scale and I want to transform them to the original scale of the variable.

from sklearn.ensemble import RandomForestRegressor
rf = RandomForestRegressor()
X = np.random.random((100, 100))
rf.fit(X, y_box)
pred_box = rf.predict(X)

However, I can't find a SciPy function that performs a reverse Box-Cox transformation given transformed data and lambda. Is there such a function? I coded an inverse transformation for now.

pred_y = np.power((y_box * lambda_) + 1, 1 / lambda_) - 1

Answer 1

1. Here it is the code. It is working and just test. Scipy used neperian logarithm, i check the BoxCox transformation paper and it seens that they used log10. I kept with neperian, because it works with scipy

2. Follow the code:

   #Function
   def invboxcox(y,ld):
      if ld == 0:
         return(np.exp(y))
      else:
         return(np.exp(np.log(ld*y+1)/ld))
   
   # Test the code
   x=[100]
   ld = 0
   y = stats.boxcox(x,ld)
   print invboxcox(y[0],ld)
   

Answer 2

SciPy has added an inverse Box-Cox transformation.

https://docs.scipy.org/doc/scipy/reference/generated/scipy.special.inv_boxcox.html

scipy.special.inv_boxcox scipy.special.inv_boxcox(y, lmbda) =

Compute the inverse of the Box-Cox transformation.

Find x such that:

y = (x**lmbda - 1) / lmbda  if lmbda != 0
    log(x)                  if lmbda == 0

Parameters: y : array_like

Data to be transformed.

lmbda : array_like

Power parameter of the Box-Cox transform.

Returns:
x : array

Transformed data.

Notes

New in version 0.16.0.

Example:

from scipy.special import boxcox, inv_boxcox
y = boxcox([1, 4, 10], 2.5)
inv_boxcox(y, 2.5)

output: array([1., 4., 10.])

Answer 3

Thanks to @Warren Weckesser, I've learned that the current implementation of SciPy does not have a function to reverse a Box-Cox transformation. However, a future SciPy release may have this function. For now, the code I provide in my question may serve others to reverse Box-Cox transformations.