Fairness in Forecasting of Observations of Linear Dynamical Systems

In machine learning, training data often capture the behaviour of multiple subgroups of some underlying human population. This behaviour can often be modelled as observations of an unknown dynamical system with an unobserved state. When the training data for the subgroups are not controlled carefully, however, under-representation bias arises. To counter under-representation bias, we introduce two natural notions of fairness in timeseries forecasting problems: subgroup fairness and instantaneous fairness. These notion extend predictive parity to the learning of dynamical systems. We also show globally convergent methods for the fairness-constrained learning problems using hierarchies of convexifications of non-commutative polynomial optimisation problems. We also show that by exploiting sparsity in the convexifications, we can reduce the run time of our methods considerably. 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.

Automated summary

In machine learning, the behaviour of multiple subgroups of an underlying human population can be captured through training data. However, under-representation bias arises when the training data for the subgroups are not carefully controlled. To address this, two notions of fairness are introduced for timeseries forecasting problems: subgroup fairness and instantaneous fairness. These notions extend predictive parity to the learning of dynamical systems. Globally convergent methods for the fairness-constrained learning problems are also demonstrated using hierarchies of convexifications of non-commutative polynomial optimization problems. The run time of these methods can be significantly reduced by exploiting sparsity in the convexifications, as demonstrated through empirical results on biased data sets.