  Transfer learning enhances prediction accuracy on a target distribution by
leveraging data from a source distribution, demonstrating significant benefits
in various applications. This paper introduces a novel dissimilarity measure
that utilizes vicinity information, i.e., the local structure of data points,
to analyze the excess error in classification under covariate shift, a transfer
learning setting where marginal feature distributions differ but conditional
label distributions remain the same. We characterize the excess error using the
proposed measure and demonstrate faster or competitive convergence rates
compared to previous techniques. Notably, our approach is effective in
situations where the non-absolute continuousness assumption, which often
appears in real-world applications, holds. Our theoretical analysis bridges the
gap between current theoretical findings and empirical observations in transfer
learning, particularly in scenarios with significant differences between source
and target distributions.
