Force_plot function with link=logit displays incorrect results for feature importance

[ehuijzer]

Description
Force_plot does not display correct feature importance in case of link=logit

• identical logit shap values result in different importance
• base value + feature importance effects <> output value

Steps/Code to Reproduce

import shap
import numpy as np
shap.force_plot(base_value=-3,
                shap_values=np.array([1,1,-1]),
                feature_names=['PosFeat1', 'PosFeat2', 'NegFeat1'],
                matplotlib=True,
                link="logit")

Expected Results
PosFeat1, PosFeat2 and NegFeat1 all have exactly the same shap value (either positive or negative).
Each feature is represented by same size effect in plot.
Difference in length of negative and positive effects should equal difference base value vs output value

Actual Results
PosFeat2 effect is smaller than PosFeat1 effect.
Sum PosFeat effect - NegFeat1 effect < Output value - Base value

Analysis
Logit function is not linear, therefore the calculation of the effect is dependent of the order (and base value) of the calculation.

Proposed solution

1. Approximate the logistic function by a linear function
2. Calculate the slope: (proba output value - proba base value) / sum shap values
   (Special case sum=0; use derivative of logistic: exp(shap) / (exp(shap) + 1)^2
3. Multiply all shap values by the slope

This way identical shap values result in identical probability effects.
Base value and feature effects sum up to the output value.

[ehuijzer]

@slundberg I've seen some discussion on this topic in #238 and #29
Do you agree with my comment and proposed fix in pull request #1148 ?

[slundberg]

Sorry have been getting back on top of things after being out sick. Great catch! But the right solution I think is to match the behavior of the JS version of the plot. In the JS version we leave the pixels in logit space, but then change the tick marks to reflect a non-linear progress of values from the logit. Will comment on the PR with more thoughts.