Kernel dependence regularizers and Gaussian processes with applications to algorithmic fairness

•A general framework of empirical risk minimization with fairness regularizers and an analysis of its risk and fairness statistical consistency results are presented.•A Gaussian Process (GP) formulation of the fairness regularization framework is derived, which allows uncertainty quantification and principled hyperparameter selection.•A normalized version of the fairness regularizer which makes it less sensitive to the choice of kernel parameters is derived.