Learning Fair Canonical Polyadical Decompositions using a Kernel Independence Criterion

TL;DR

This paper introduces a method to learn fair low-rank tensor decompositions by regularizing with the kernel Hilbert-Schmidt independence criterion, effectively balancing fairness and data fit.

Contribution

It presents a novel regularization approach using KHSIC for fair tensor decomposition, outperforming existing algorithms in fairness control.

Findings

KHSIC regularization guarantees approximate statistical parity.

The proposed algorithm outperforms FATR in fairness and residual fit.

Empirical results on synthetic and real data validate the method.

Abstract

This work proposes to learn fair low-rank tensor decompositions by regularizing the Canonical Polyadic Decomposition factorization with the kernel Hilbert-Schmidt independence criterion (KHSIC). It is shown, theoretically and empirically, that a small KHSIC between a latent factor and the sensitive features guarantees approximate statistical parity. The proposed algorithm surpasses the state-of-the-art algorithm, FATR (Zhu et al., 2018), in controlling the trade-off between fairness and residual fit on synthetic and real data sets.