`KernelShap` returns no explanations when `link='logit'` and predicted proba is 0 or 1

[ascillitoe]

Issue

When the KernelShap explainer is configured with link='logit', and the predictor returns probabilities of 0 or 1, the logit link function raises errors due to logit(0) = -inf and logit(1) = inf.

Example error:

    240 @staticmethod
    241 def f(x):
--> 242     return np.log(x/(1-x))

ZeroDivisionError: float division by zero

This is a problem when batches of instances are passed to explain, because the errors raised by problem instances result in no instances being returned, even for instances where 0 > proba < 1.

Solution

When link='logit', we could patch the logit link function with something like:

from shap.utils._legacy import Link

class FixedLogitLink(Link):
    def __str__(self):
        return "logit"
    
    @staticmethod
    def f(x):
        with np.errstate(all='raise'):
            try:
                return np.log(x / (1 - x))
            except Exception as e:
                if x <= 0.0:
                    return -np.inf
                elif x >= 1.0:
                    return np.inf
                else:
                    raise e
            
    @staticmethod
    def finv(x):
        return 1/(1+np.exp(-x)) 

This would allow the explanations to run for instances who's predicted proba's are 0 < proba < 1. Problematic instances would just have np.nan explanations returned. For example:

>>> explanation.data['shap_values'][1]

array([[ 0.23972787, -0.01814982, -0.19931147, -0.70222757,  0.19566954,
        -0.52669155,  0.01747202, -0.41221566, -0.18493278, -0.04171934,
         0.19687651, -0.00301931],
       [        nan,         nan,         nan,         nan,         nan,
                nan,         nan,         nan,         nan,         nan,
                nan,         nan]])

Related issues

• Python Version of Tree SHAP gives ZeroDivisionError  shap/shap#183