  Knowledge transfer from a source domain to a different but semantically
related target domain has long been an important topic in the context of
unsupervised domain adaptation (UDA). A key challenge in this field is
establishing a metric that can exactly measure the data distribution
discrepancy between two homogeneous domains and adopt it in distribution
alignment, especially in the matching of feature representations in the hidden
activation space. Existing distribution matching approaches can be interpreted
as failing to either explicitly orderwise align higher-order moments or satisfy
the prerequisite of certain assumptions in practical uses. We propose a novel
moment-based probability distribution metric termed dimensional weighted
orderwise moment discrepancy (DWMD) for feature representation matching in the
UDA scenario. Our metric function takes advantage of a series for high-order
moment alignment, and we theoretically prove that our DWMD metric function is
error-free, which means that it can strictly reflect the distribution
differences between domains and is valid without any feature distribution
assumption. In addition, since the discrepancies between probability
distributions in each feature dimension are different, dimensional weighting is
considered in our function. We further calculate the error bound of the
empirical estimate of the DWMD metric in practical applications. Comprehensive
experiments on benchmark datasets illustrate that our method yields
state-of-the-art distribution metrics.
