Causal Effect on predicted variables

The following demonstrates a method [1] that analyzes the prediction mechanisms of constructed predictive models based on causality. This method estimates causal effects, i.e., intervention effects of features or explnatory variables used in constructed predictive models on the predicted variables. Users can use estimated causal structures, e.g., by a LiNGAM-type method or known causal structures based on domain knowledge.


  1. Blöbaum and S. Shimizu. Estimation of interventional effects of features on prediction.

In Proc. 2017 IEEE International Workshop on Machine Learning for Signal Processing (MLSP2017), pp. 1–6, Tokyo, Japan, 2017.

First, we use lingam package:

import lingam

Then, we create a DirectLiNGAM object and call the fit() method:

model = lingam.DirectLiNGAM()

Next, we create the prediction model. In the following example, linear regression model is created, but it is also possible to create logistic regression model or non-linear regression model.

from sklearn.linear_model import LinearRegression

target = 0
features = [i for i in range(X.shape[1]) if i != target]
reg = LinearRegression()[:, features], X.iloc[:, target])

Identification of Feature with Greatest Causal Influence on Prediction

We create a CausalEffect object and call the estimate_effects_on_prediction() method.

ce = lingam.CausalEffect(model)
effects = ce.estimate_effects_on_prediction(X, target, reg)

To identify of the feature having the greatest intervention effect on the prediction, we can get the feature that maximizes the value of the obtained list.


Estimation of Optimal Intervention

To estimate of the intervention such that the expectation of the prediction of the post-intervention observations is equal or close to a specified value, we use estimate_optimal_intervention() method of CausalEffect. In the following example, we estimate the intervention value at variable index 1 so that the predicted value is close to 15.

c = ce.estimate_optimal_intervention(X, target, reg, 1, 15)
print(f'Optimal intervention: {c:.3f}')
Optimal intervention: 7.871

Use a known causal model

When using a known causal model, we can specify the adjacency matrix when we create CausalEffect object.

m = np.array([[0.0, 0.0, 0.0, 3.0, 0.0, 0.0],
              [3.0, 0.0, 2.0, 0.0, 0.0, 0.0],
              [0.0, 0.0, 0.0, 6.0, 0.0, 0.0],
              [0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
              [8.0, 0.0,-1.0, 0.0, 0.0, 0.0],
              [4.0, 0.0, 0.0, 0.0, 0.0, 0.0]])

ce = lingam.CausalEffect(causal_model=m)
effects = ce.estimate_effects_on_prediction(X, target, reg)

For details, see also: