  Nuclear norm maximization has shown the power to enhance the transferability
of unsupervised domain adaptation model (UDA) in an empirical scheme. In this
paper, we identify a new property termed equity, which indicates the balance
degree of predicted classes, to demystify the efficacy of nuclear norm
maximization for UDA theoretically. With this in mind, we offer a new
discriminability-and-equity maximization paradigm built on squares loss, such
that predictions are equalized explicitly. To verify its feasibility and
flexibility, two new losses termed Class Weighted Squares Maximization (CWSM)
and Normalized Squares Maximization (NSM), are proposed to maximize both
predictive discriminability and equity, from the class level and the sample
level, respectively. Importantly, we theoretically relate these two novel
losses (i.e., CWSM and NSM) to the equity maximization under mild conditions,
and empirically suggest the importance of the predictive equity in UDA.
Moreover, it is very efficient to realize the equity constraints in both
losses. Experiments of cross-domain image classification on three popular
benchmark datasets show that both CWSM and NSM contribute to outperforming the
corresponding counterparts.
