Learning Fair Canonical Polyadical Decompositions using a Kernel Independence Criterion

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.