Abstract
In this paper we study the problem of making predictions using multiple structural causal models defined by different agents, under the constraint that the prediction satisfies the criterion of counterfactual fairness. Relying on the frameworks of causality, fairness and opinion pooling, we build upon and extend previous work focusing on the qualitative aggregation of causal Bayesian networks and causal models. In order to complement previous qualitative results, we devise a method based on Monte Carlo simulations. This method enables a decision-maker to aggregate the outputs of the causal models provided by different agents while guaranteeing the counterfactual fairness of the result. We demonstrate our approach on a simple, yet illustrative, toy case study.
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Notes
- 1.
A Bayesian network (BN)Â [10] is a structured representations of the joint probability distribution of a set of variables in the form of a directed acyclic graph with associated conditional probability distributions. A causal BN is a BN where all the edges represent causal relations between variables.
- 2.
- 3.
Notice that the decision of considering just the expected value of the pdfs may not be ideal in this case, given the multimodality of these pdfs, as shown in Fig. 5 in the appendix.
- 4.
This precision can be increased by incrementing the number of Monte Carlo samples collected.
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Appendices
Appendix A: Algorithms
Appendix B: Figures
Histogram and probability distribution function (computed via kernel density estimation) of \(P(\hat{Y})\) in the model provided by Alice and Bob. The x-axis reports the domain of the outcome of the predictor \(\hat{Y}\); the left y-axis reports the number of samples used to compute the histogram, while the right y-axis reports the normalized values used to compute the pdf.
Histogram and probability distribution function (computed via kernel density estimation) of \(P(\hat{Y}\vert Dpt= CS , Mrk=0.8, Cvr=0.4)\) in the model provided by Alice and Bob. The x-axis reports the domain of the outcome of the predictor \(\hat{Y}\); the left y-axis reports the number of samples used to compute the histogram, while the right y-axis reports the normalized values used to compute the pdf.
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Zennaro, F.M., Ivanovska, M. (2019). Counterfactually Fair Prediction Using Multiple Causal Models. In: Slavkovik, M. (eds) Multi-Agent Systems. EUMAS 2018. Lecture Notes in Computer Science(), vol 11450. Springer, Cham. https://doi.org/10.1007/978-3-030-14174-5_17
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DOI: https://doi.org/10.1007/978-3-030-14174-5_17
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