Artificial-intelligence systems are becoming ubiquitous in society, yet their predictions typically inherit biases with respect to protected attributes such as race, gender, or age. Classical fairness notions, most notably Statistical Parity (SP), demand that predictions be independent of the protected attributes, but are overly restrictive when these attributes influence mediating variables that are considered business necessities. Recent causal formulations relax SP by distinguishing allowed from not-allowed causal paths and by complementing SP with Predictive Parity (PP), requiring the predictor to replicate the legitimate influence of business-necessities. Existing path-based definitions are mainly practical when applied to categorical attributes. This paper introduces a new framework for fairness in structural causal models that is tailored to continuous protected attributes. We formalize SP and PP through path-specific partial derivatives, establish conditions under which these criteria coincide with prior causal definitions, and characterize when a fair predictor, one that satisfies SP along not-allowed paths while achieving PP along allowed paths, exists. Building on this theory, we propose a fair tuning algorithm that either constructs such a predictor or, when not possible, allows for a trade-off between SP and PP. We present experiments on simulated and real data to evaluate our proposal, compare it with previously proposed methods, and show that it performs better when PP is considered.

Combination therapy refers to the use of multiple treatments - such as surgery, medication, and behavioral therapy - to cure a single disease, and has become a cornerstone for treating various conditions including cancer, HIV, and depression. All possible combinations of treatments lead to a collection of treatment regimens (i.e., policies) with mixed scopes, or what physicians could observe and which actions they should take depending on the context. In this paper, we investigate the online reinforcement learning setting for optimizing the policy space with mixed scopes. In particular, we develop novel online algorithms that achieve sublinear regret compared to an optimal agent deployed in the environment. The regret bound has a dependency on the maximal cardinality of the induced state-action space associated with mixed scopes. We further introduce a canonical representation for an arbitrary subset of interventional distributions given a causal diagram, which leads to a non-trivial, minimal representation of the model parameters.

Most of the literature in fair machine learning focuses on defining and achieving fairness criteria in the context of prediction, while not explicitly focusing on how these predictions may be used later on in the pipeline.

The study of causal relations can be seen through the lens of learning andinference [16,21].

Based on the condition of alcohol dependant patients (S1), the physician may prescribe a medication or behavioral therapy (X1).

One of the most common mistakes made when performing data analysis is attributing causal meaning toregression coefficients.

In the causal inference literature, this generalization task has been formalized under the rubric oftransportability (Pearl and Bareinboim, 2011), where a number of criteria and algorithms have been developed forvarious settings.

Let G beacausalQ = Pr.