Fairness in machine learning seeks to mitigate model bias against individuals based on sensitive features such as sex or age, often caused by an uneven representation of the population in the training data due to selection bias. Notably, bias unascribed to sensitive features is challenging to identify and typically goes undiagnosed, despite its prominence in complex high-dimensional data from fields like computer vision and molecular biomedicine. Strategies to mitigate unidentified bias and evaluate mitigation methods are crucially needed, yet remain underexplored. We introduce: (i) Diverse Class-Aware Self-Training (DCAST), model-agnostic mitigation aware of class-specific bias, which promotes sample diversity to counter confirmation bias of conventional self-training while leveraging unlabeled samples for an improved representation of the underlying population; (ii) hierarchy bias, multivariate and class-aware bias induction without prior knowledge. Models learned with DCAST showed improved robustness to hierarchy and other biases across eleven datasets, against conventional self-training and six prominent domain adaptation techniques. Advantage was largest on multi-class classification, emphasizing DCAST as a promising strategy for fairer learning in different contexts.

The multivariate adaptive regression spline (MARS) is one of the popular estimation methods for nonparametric multivariate regressions. However, as MARS is based on marginal splines, to incorporate interactions of covariates, products of the marginal splines must be used, which leads to an unmanageable number of basis functions when the order of interaction is high and results in low estimation efficiency. In this paper, we improve the performance of MARS by using linear combinations of the covariates which achieve sufficient dimension reduction. The special basis functions of MARS facilitate calculation of gradients of the regression function, and estimation of the linear combinations is obtained via eigen-analysis of the outer-product of the gradients. Under some technical conditions, the asymptotic theory is established for the proposed estimation method. Numerical studies including both simulation and empirical applications show its effectiveness in dimension reduction and improvement over MARS and other commonly-used nonparametric methods in regression estimation and prediction.