Fairness in Forecasting of Observations of Linear Dynamical Systems
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In machine learning, training data often capture the behaviour of multiple subgroups of some underlying human population. When the nature of training data for subgroups are not controlled carefully, under-representation bias arises. To counter this effect we introduce two natural notions of subgroup fairness and instantaneous fairness to address such under-representation bias in time-series forecasting problems. Here we show globally convergent methods for the fairness-constrained learning problems using hierarchies of convexifications of non-commutative polynomial optimisation problems. Our empirical results on a biased data set motivated by insurance applications and the well-known COMPAS data set demonstrate the efficacy of our methods. We also show that by exploiting sparsity in the convexifications, we can reduce the run time of our methods considerably.
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