Preprint compares Banach, Hilbert and Euclidean domain adaptation
Original title: The comparison of density estimation for transfer learning in Banach, Hilbert, Euclidean spaces
An L1 density regularizer beats an identical L2 ablation on every reported task, including 92.44% versus 89.80% on USPS to MNIST.
A preprint summarizes Non-Hilbertian Domain Adaptation and proposes Banach Manifold Transfer Learning. Features are embedded on a geodesic manifold, and an L1 Banach density regularizer is used to contract total variation between domain densities rather than an L2 divergence. On MNIST-USPS, COIL20 and Office+Caltech10, the L1 variant beats an otherwise identical L2 ablation on every task and surpasses DMDA by 3.68 percentage points on average over twelve Office+Caltech transfers.
- BMTL uses a geodesic manifold rather than a flat Euclidean feature space.
- The L1 regularizer is tied to total variation through Scheffe's theorem.
- USPS to MNIST accuracy is 92.44% for L1 versus 89.80% for L2.
- The L1 variant beats DMDA by 3.68 points on average across twelve transfers.
From the original article
1 min read at arxiv.orgDomain adaptation or DA methods are indispensable when target labels or computational resources are scarce, yet the domain kernel density and subspace alignment approaches completely assume a Hilbertian geometry. They measure distributional discrepancy with symmetric L2 divergences over Euclidean feature spaces or reproducing kernel Hilbert spaces (RKHS).
By Maryam Alsadat Kazemian · arxiv.org
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