Active Coalition of Variables (ACV):

ACV is a python library that aims to explain any machine learning models or data.

• It gives local rule-based explanations for any model or data.
• It provides a better estimation of Shapley Values for tree-based model (more accurate than path-dependent TreeSHAP). It also proposes new Shapley Values that have better local fidelity.
  • and the correct way of computing Shapley Values of categorical variables after encoding (eg., One Hot or Dummy, etc.)

We can regroup the different explanations in two groups: Agnostic Explanations and Tree-based Explanations.

See the papers here.

Installation

Requirements

Python 3.6+

OSX: ACV uses Cython extensions that need to be compiled with multi-threading support enabled. The default Apple Clang compiler does not support OpenMP. To solve this issue, obtain the lastest gcc version with Homebrew that has multi-threading enabled: see for example pysteps installation for OSX.

Windows: Install MinGW (a Windows distribution of gcc) or Microsoft’s Visual C

Install the acv package:

$ pip install acv-exp

A. Agnostic explanations

The Agnostic approaches explain any data (X, Y) or model (X, f(X)) using the following explanation methods:

• Same Decision Probability (SDP) and Sufficient Explanations
• Sufficient Rules

See the paper Consistent Sufficient Explanations and Minimal Local Rules for explaining regression and classification models for more details.

I. First, we need to fit our explainer (ACXplainers) to input-output of the data (X, Y) or model (X, f(X)) if we want to explain the data or the model respectively.

from acv_explainers import ACXplainer

# It has the same params as a Random Forest, and it should be tuned to maximize the performance.  
acv_xplainer = ACXplainer(classifier=True, n_estimators=50, max_depth=5)
acv_xplainer.fit(X_train, y_train)

roc = roc_auc_score(acv_xplainer.predict(X_test), y_test)

II. Then, we can load all the explanations in a webApp as follow:

import acv_app
import os

# compile the ACXplainer
acv_app.compile_ACXplainers(acv_xplainer, X_train, y_train, X_test, y_test, path=os.getcwd())

# Launch the webApp
acv_app.run_webapp(pickle_path=os.getcwd())

III. Or we can compute each explanation separately as follow:

Same Decision Probability (SDP)

The main tool of our explanations is the Same Decision Probability (SDP). Given <img src="https://latex.codecogs.com/gif.latex?x%20%3D%20%28x_S%2C%20x_%7B%5Cbar%7BS%7D%7D%29" />, the same decision probability <img src="https://latex.codecogs.com/gif.latex?SDP_S%28x%2C%20f%29" /> of variables <img src="https://latex.codecogs.com/gif.latex?x_S" /> is the probabilty that the prediction remains the same when we fixed variables <img src="https://latex.codecogs.com/gif.latex?X_S=x_S" /> or when the variables <img src="https://latex.codecogs.com/gif.latex?X_{\bar{S}}" /> are missing.

• How to compute <img src="https://latex.codecogs.com/gif.latex?SDP_S%28x%2C%20f%29" /> ?

sdp = acv_xplainer.compute_sdp_rf(X, S, data_bground) # data_bground is the background dataset that is used for the estimation. It should be the training samples.

Minimal Sufficient Explanations

The Sufficient Explanations is the Minimal Subset S such that fixing the values <img src="https://latex.codecogs.com/gif.latex?X_S=x_S" /> permit to maintain the prediction with high probability <img src="https://latex.codecogs.com/gif.latex?\pi" />. See the paper here for more details.

• How to compute the Minimal Sufficient Explanation <img src="https://latex.codecogs.com/gif.latex?S^\star" /> ?

  The following code return the Sufficient Explanation with minimal cardinality.

sdp_importance, min_sufficient_expl, size, sdp = acv_xplainer.importance_sdp_rf(X, y, X_train, y_train, pi_level=0.9)

• How to compute all the Sufficient Explanations ?

  Since the Minimal Sufficient Explanation may not be unique for a given instance, we can compute all of them.

sufficient_expl, sdp_expl, sdp_global = acv_xplainer.sufficient_expl_rf(X, y, X_train, y_train, pi_level=0.9)

Local Explanatory Importance

For a given instance, the local explanatory importance of each variable corresponds to the frequency of apparition of the given variable in the Sufficient Explanations. See the paper here for more details.

• How to compute the Local Explanatory Importance ?

lximp = acv_xplainer.compute_local_sdp(d=X_train.shape[1], sufficient_expl)

Local rule-based explanations

For a given instance (x, y) and its Sufficient Explanation S such that <img src="https://latex.codecogs.com/gif.latex?SDP_S(\boldsymbol{x};&space;y)&space;\geq&space;\pi" title="SDP_S(\boldsymbol{x}; y) \geq \pi" />, we compute a local minimal rule which contains x such that every observation z that satisfies this rule has <img src="https://latex.codecogs.com/gif.latex?SDP_S(\boldsymbol{z};&space;y)&space;\geq&space;\pi" title="SDP_S(\boldsymbol{z}; y) \geq \pi" />. See the paper here for more details

• How to compute the local rule explanations ?

sdp, rules, _, _, _ = acv_xplainer.compute_sdp_maxrules(X, y, data_bground, y_bground, S) # data_bground is the background dataset that is used for the estimation. It should be the training samples.

B. Tree-based explanations

ACV gives Shapley Values explanations for XGBoost, LightGBM, CatBoostClassifier, scikit-learn and pyspark tree models. It provides the following Shapley Values:

• Classic local Shapley Values (The value function is the conditional expectation <img src="https://latex.codecogs.com/gif.latex?E[f(x)&space;|&space;\boldsymbol{X}_S&space;=&space;\boldsymbol{x}_S]" title="E[f(x) | \boldsymbol{X}_S = \boldsymbol{x}_S]" />)
• Active Shapley values (Local fidelity and Sparse by design)
• Swing Shapley Values (The Shapley values are interpretable by design) (Coming soon)

In addition, we use the coalitional version of SV to properly handle categorical variables in the computation of SV.

See the papers here

To explain the tree-based models above, we need to transform our model into ACVTree.

from acv_explainers import ACVTree

forest = XGBClassifier() # or any Tree Based models
#...trained the model

acvtree = ACVTree(forest, data_bground) # data_bground is the background dataset that is used for the estimation. It should be the training samples.

Accurate Shapley Values

sv = acvtree.shap_values(X)

Note that it provides a better estimation of the tree-path dependent of TreeSHAP when the variables are dependent.

Accurate Shapley Values with encoded categorical variables

Let assume we have a categorical variable Y with k modalities that we encoded by introducing the dummy variables <img src="https://latex.codecogs.com/gif.latex?Y_1%2C%5Cdots%2C%20Y_%7Bk-1%7D" />. As shown in the paper, we must take the coalition of the dummy variables to correctly compute the Shapley values.

# cat_index := list[list[int]] that contains the column indices of the dummies or one-hot variables grouped 
# together for each variable. For example, if we have only 2 categorical variables Y, Z 
# transformed into [Y_0, Y_1, Y_2] and [Z_0, Z_1, Z_2]

cat_index = [[0, 1, 2], [3, 4, 5]]
forest_sv = acvtree.shap_values(X, C=cat_index)

In addition, we can compute the SV given any coalitions. For example, let assume we have 10 variables <img src="https://latex.codecogs.com/gif.latex?(\boldsymbol{X}_0,&space;\boldsymbol{X}_1,&space;\dots,&space;\boldsymbol{X}_{10})" title="(\boldsymbol{X}_0, \boldsymbol{X}_1, \dots, \boldsymbol{X}_{10})" /> and we want the following coalition <img src="https://latex.codecogs.com/gif.latex?C_0%20%3D%20%28X_0%2C%20X_1%2C%20X_2%29%2C%20C_1%3D%28X_3%2C%20X_4%29%2C%20C_2%3D%28X_5%2C%20X_6%29" />

coalition = [[0, 1, 2], [3, 4], [5, 6]]
forest_sv = acvtree.shap_values(X, C=coalition)

How to compute <img src="https://latex.codecogs.com/gif.latex?SDP_S%28x%2C%20f%29" /> for tree-based classifier ?

Recall that the <img src="https://latex.codecogs.com/gif.latex?SDP_S%28x%2C%20f%29" /> is the probability that the prediction remains the same when we fixed variables <img src="https://latex.codecogs.com/gif.latex?X_S=x_S" /> given the subset S.

sdp = acvtree.compute_sdp_clf(X, S, data_bground) # data_bground is the background dataset that is used for the estimation. It should be the training samples.

How to compute the Sufficient Coalition <img src="https://latex.codecogs.com/gif.latex?S^\star" /> and the Global SDP importance for tree-based classifier ?

Recall that the Minimal Sufficient Explanations is the Minimal Subset S such that fixing the values <img src="https://latex.codecogs.com/gif.latex?X_S=x_S" /> permit to maintain the prediction with high probability <img src="https://latex.codecogs.com/gif.latex?\pi" />.

sdp_importance, sdp_index, size, sdp = acvtree.importance_sdp_clf(X, data_bground) # data_bground is the background dataset that is used for t