Federated discretization for supervised classification

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Several classifiers operate exclusively on discrete variables, requiring continuous attributes to be preprocessed through discretization. Supervised discretization addresses this need by partitioning the domain of continuous variables into intervals that define a discretization policy. Federated learning, in turn, enables the collaborative training of global models without sharing raw data: users train local models and communicate their parameters to a central server, which aggregates them into a global model. A key challenge in this setting is achieving performance comparable to centralized methods while minimizing communication overhead. In this work, we propose a federated discretization framework that computes a global discretization policy in a single communication round. Each user estimates Gaussian mixture models for the continuous variables and transmits their parameters-referred to as representatives-to the server. The server then applies a discretization algorithm to these representatives to derive a global policy, which is subsequently distributed back to the users. The proposed framework accommodates multiple discretization strategies; specifically, we present federated adaptations of equal-width, equal-frequency, entropy-based, and kernel density-based methods. Experiments conducted on ten benchmark datasets demonstrate that the proposed framework achieves performance comparable to centralized discretization approaches, with the kernel density-based and equal-frequency variants yielding the most competitive results.