Contrastive Reasons
Currently, contrastives reasons for Boosted trees are only available for binary classification.
Unlike abductive explanations that explain why an instance $x$ is classified as belonging to a given class, the contrastive explanations explains why $x$ has not been classified by the ML model as expected.
Let 𝑓 be a Boolean function represented by a random forest 𝑅𝐹, 𝑥 be an instance and 1 (resp. 0) the prediction of 𝑅𝐹 on 𝑥 (𝑓(𝑥)=1 (resp $f(x)=0$)), a contrastive reason for $x$ is a term $t$ such that:
- $t \subseteq t_{x}$, $t_{x} \setminus t$ is not an implicant of $f;$
- for every $\ell \in t$, $t \setminus {\ell}$ does not satisfy this previous condition (i.e., $t$ is minimal w.r.t. set inclusion).
Formally, a contrastive reason for $x$ is a subset $t$ of the characteristics of $x$ that is minimal w.r.t. set inclusion among those such that at least one instance $x’$ that coincides with $x$ except on the characteristics from $t$ is not classified by the decision tree as $x$ is. Stated otherwhise, a contrastive reason represents adjustments of the features that we have to do to change the prediction for an instance.
A contrastive reason is minimal w.r.t. set inclusion, i.e. there is no subset of this reason which is also a contrastive reason. A minimal contrastive reason for $x$ is a contrastive reason for $x$ that contains a minimal number of literals. In other words, a minimal contrastive reason has a minimal size.
| <ExplainerBT Object>.minimal_contrastive_reason(*, time_limit=None): |
|---|
This method computes a minimal contrastive reasons using a MIP solver. Return one minimal contrastive reason of the current instance. Supports the excluded features. The reasons are in the form of binary variables, you must use the to_features method if you want a representation based on the features considered at start. |
time_limit Integer None: The time limit of the method in seconds. Set this to None to give this process an infinite amount of time. Default value is None. |
Example from Building Trees
We show now how to get them with PyXAI. We start by building the Boosted Tree:
from pyxai import Builder, Explainer
node1_1 = Builder.DecisionNode(1, operator=Builder.GT, threshold=2, left=-0.2, right=0.3)
node1_2 = Builder.DecisionNode(3, operator=Builder.EQ, threshold=1, left=-0.3, right=node1_1)
node1_3 = Builder.DecisionNode(2, operator=Builder.GT, threshold=1, left=0.4, right=node1_2)
node1_4 = Builder.DecisionNode(4, operator=Builder.EQ, threshold=1, left=-0.5, right=node1_3)
tree1 = Builder.DecisionTree(4, node1_4)
node2_1 = Builder.DecisionNode(4, operator=Builder.EQ, threshold=1, left=-0.4, right=0.3)
node2_2 = Builder.DecisionNode(1, operator=Builder.GT, threshold=2, left=-0.2, right=node2_1)
node2_3 = Builder.DecisionNode(2, operator=Builder.GT, threshold=1, left=node2_2, right=0.5)
tree2 = Builder.DecisionTree(4, node2_3)
node3_1 = Builder.DecisionNode(1, operator=Builder.GT, threshold=2, left=0.2, right=0.3)
node3_2_1 = Builder.DecisionNode(1, operator=Builder.GT, threshold=2, left=-0.2, right=0.2)
node3_2_2 = Builder.DecisionNode(4, operator=Builder.EQ, threshold=1, left=-0.1, right=node3_1)
node3_2_3 = Builder.DecisionNode(4, operator=Builder.EQ, threshold=1, left=-0.5, right=0.1)
node3_3_1 = Builder.DecisionNode(2, operator=Builder.GT, threshold=1, left=node3_2_1, right=node3_2_2)
node3_3_2 = Builder.DecisionNode(2, operator=Builder.GT, threshold=1, left=-0.4, right=node3_2_3)
node3_4 = Builder.DecisionNode(3, operator=Builder.EQ, threshold=1, left=node3_3_1, right=node3_3_2)
tree3 = Builder.DecisionTree(4, node3_4)
BT = Builder.BoostedTrees([tree1, tree2, tree3], n_classes=2)
We compute a contrastive reason for these two instances:
explainer = Explainer.initialize(BT)
explainer.set_instance((4,3,2,1))
contrastive_reason = explainer.minimal_contrastive_reason()
print("target_prediction:", explainer.target_prediction)
print("minimal contrastive reason:", explainer.to_features(contrastive_reason))
assert explainer.is_contrastive_reason(contrastive_reason), "It is not a contrastive reason !"
target_prediction: 1
minimal contrastive reason: ('f4 == 1',)
# We can create a contrastive instance
explainer.set_instance((4,3,2,0))
print("target_prediction:", explainer.target_prediction)
# The prediction is 0 now.
target_prediction: 0
Example from Real Dataset
For this example, we take the compas.csv known to be biased. We create a model using the hold-out approach (by default, the test size is set to 30%) and select a wrong classified instance.
from pyxai import Learning, Explainer
learner = Learning.Xgboost("../../../dataset/compas.csv", learner_type=Learning.CLASSIFICATION)
model = learner.evaluate(method=Learning.HOLD_OUT, output=Learning.BT)
instance, prediction = learner.get_instances(model, n=1, correct=False)
data:
Number_of_Priors score_factor Age_Above_FourtyFive \
0 0 0 1
1 0 0 0
2 4 0 0
3 0 0 0
4 14 1 0
... ... ... ...
6167 0 1 0
6168 0 0 0
6169 0 0 1
6170 3 0 0
6171 2 0 0
Age_Below_TwentyFive Origin_African_American Origin_Asian \
0 0 0 0
1 0 1 0
2 1 1 0
3 0 0 0
4 0 0 0
... ... ... ...
6167 1 1 0
6168 1 1 0
6169 0 0 0
6170 0 1 0
6171 1 0 0
Origin_Hispanic Origin_Native_American Origin_Other Female \
0 0 0 1 0
1 0 0 0 0
2 0 0 0 0
3 0 0 1 0
4 0 0 0 0
... ... ... ... ...
6167 0 0 0 0
6168 0 0 0 0
6169 0 0 1 0
6170 0 0 0 1
6171 1 0 0 1
Misdemeanor Two_yr_Recidivism
0 0 0
1 0 1
2 0 1
3 1 0
4 0 1
... ... ...
6167 0 0
6168 0 0
6169 0 0
6170 1 0
6171 0 1
[6172 rows x 12 columns]
-------------- Information ---------------
Dataset name: ../../../dataset/compas.csv
nFeatures (nAttributes, with the labels): 12
nInstances (nObservations): 6172
nLabels: 2
--------------- Evaluation ---------------
method: HoldOut
output: BT
learner_type: Classification
learner_options: {'seed': 0, 'max_depth': None, 'eval_metric': 'mlogloss'}
--------- Evaluation Information ---------
For the evaluation number 0:
metrics:
accuracy: 66.73866090712744
precision: 66.66666666666666
recall: 53.855278766310796
f1_score: 59.580052493438316
specificity: 77.50247770069376
true_positive: 454
true_negative: 782
false_positive: 227
false_negative: 389
sklearn_confusion_matrix: [[782, 227], [389, 454]]
nTraining instances: 4320
nTest instances: 1852
--------------- Explainer ----------------
For the evaluation number 0:
**Boosted Tree model**
NClasses: 2
nTrees: 100
nVariables: 42
--------------- Instances ----------------
number of instances selected: 1
----------------------------------------------
We compute a contrastive instance (with a time limit equal to 5 seconds). In order to compute contrastive reasons, it is better to activate the theory related to the type of features (see this page).
types = {
"numerical": ["Number_of_Priors"],
"categorical": {"Origin_*":['African_American', 'Asian', 'Hispanic', 'Native_American', 'Other'],
"Age_*": ["Above_FourtyFive", "Below_TwentyFive"]},
"binary": Learning.DEFAULT,
}
explainer = Explainer.initialize(model, instance, features_type=types)
contrastive_reason = explainer.minimal_contrastive_reason(time_limit=5)
print("instance: ", instance)
print("target_prediction:", explainer.target_prediction)
print("minimal contrastive reason:", explainer.to_features(contrastive_reason, contrastive=True))
print("is contrastive: ", explainer.is_contrastive_reason(contrastive_reason))
--------- Theory Feature Types -----------
Before the encoding (without one hot encoded features), we have:
Numerical features: 1
Categorical features: 2
Binary features: 3
Number of features: 6
Values of categorical features: {'Origin_African_American': ['Origin_', 'African_American', ['African_American', 'Asian', 'Hispanic', 'Native_American', 'Other']], 'Origin_Asian': ['Origin_', 'Asian', ['African_American', 'Asian', 'Hispanic', 'Native_American', 'Other']], 'Origin_Hispanic': ['Origin_', 'Hispanic', ['African_American', 'Asian', 'Hispanic', 'Native_American', 'Other']], 'Origin_Native_American': ['Origin_', 'Native_American', ['African_American', 'Asian', 'Hispanic', 'Native_American', 'Other']], 'Origin_Other': ['Origin_', 'Other', ['African_American', 'Asian', 'Hispanic', 'Native_American', 'Other']], 'Age_Above_FourtyFive': ['Age_', 'Above_FourtyFive', ['Above_FourtyFive', 'Below_TwentyFive']], 'Age_Below_TwentyFive': ['Age_', 'Below_TwentyFive', ['Above_FourtyFive', 'Below_TwentyFive']]}
Number of used features in the model (before the encoding): 6
Number of used features in the model (after the encoding): 11
----------------------------------------------
instance: [0 0 0 0 1 0 0 0 0 0 0]
target_prediction: 0
minimal contrastive reason: ('Number_of_Priors < 3.5', 'Origin_ = African_American')
is contrastive: True
If one wants to change the classification, one needs to change the origin and the number of priors (to at least 4).