How SHAP value explains contribution of features for outliers event?

Question

I'm trying to understand and experiment with how the SHAP value can explain behaviour for each outlier events (rows) and how it can be related to shap.force_plot(). I already created a simple synthetic dataset with 7 outliers.

I didn't get how 4.85 calculated as output model.

outliers_df = temp_dataset.loc[synth_data_df[outdet.label_feature] == 1]
outliers_df

#Here is the frame of 7 outlier cases I input to SHAP: 

+----+-------------+--------------+---------------+
| id |      NF1    |      CF1     |outlier_scores |
+----+-------------+--------------+---------------+
|  1 |       904   |     2        | -0.192221     |
|  2 |       951   |     3        | -0.203116     |
|  3 |       125   |     5        | -0.076722     |
|  4 |       755   |     2        | -0.237189     |
|  5 |       983   |     2        | -0.213205     |
|  6 |       906   |     3        | -0.202074     |
|  7 |       999   |     5        | -0.266428     |
+----+-------------+--------------+---------------+

I applied IsolationForest using class OutlierDetector in my implementation to isolate outliers:

outdet = OutlierDetector(synth_data_df, label_feature="label", 
                         normalize_outlier_scores=True, standardize_outlier_scores=False, 
                         n_estimators=100, max_samples=1., contamination=0.1)
outdet.train_IF()

I got SHAP for each rows:

outdet.shap_values_outliers = outdet.explainer.shap_values(outliers_df)
outdet.shap_values_outliers
array([[-6.0205, -0.7785,  0.    ],
       [-6.3379, -0.7031,  0.    ],
       [-2.9014, -1.0911,  0.    ],
       [-6.6259, -1.1502,  0.    ],
       [-6.445 , -0.8171,  0.    ],
       [-6.2393, -0.7787,  0.    ],
       [-8.1958, -0.1862,  0.    ]])

This is simple shap.force_plot() for first row for 3 features. I already concatenate outlier_scores to the frame after I trained my model with NF1 and CF1 as follow:

How to get $\text{basic}_\text{value} = 11.65$ via a script, as explained here?
General interpretation considering $\text{basic}_\text{value} = 11.65$ and $\text{Model}_\text{output} = 4.85$ for first event or observation considering no features pushing the prediction higher are shownred by red color?
Reason for getting $\text{SHAP}_\text{outlier_scores} = 0$ ?

Edit I would also like to share the following plot, which may help to see if we can understand the contribution of one of these two features to explain outliers like $\text{SHAP}_\text{NF1} = [-8, -6]$:

outdet.plot_shap_values()

Base value depends on the average output, so it should be linked to 7/total population if it a classification problem. However it is not clear what you are calculating exactly. How do you get those outlier scores in the first place ? — Lucas Morin, Feb 19 '21 at 09:40
@lcrmorin, before applying SHAP, I used `IsolationForest` for outlier detection, and I was interested to see if SHAP can explain the outliers by monitoring the feature's contribution. I concatenated the `outlier_scores` output of `IsolationForest` as the 3rd feature before applying SHAP to experiment if it could be an interesting output, but it returns the `0` SHAP value! How can print **base value** and **output model** which has been shown in `shap.force_plot()`. I don't understand how these two are related? How I can interpret this plot for the Anomaly detection concept. — Mario, Feb 19 '21 at 23:15
Could you supply the rest of your code? I think maybe these numbers are (expected average impacts of) path lengths, but it'd be nice to do some testing. — Ben Reiniger, Feb 19 '21 at 23:33

How SHAP value explains contribution of features for outliers event?

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