  Source-free domain adaptation (SFDA) aims to adapt a model trained on
labelled data in a source domain to unlabelled data in a target domain without
access to the source-domain data during adaptation. Existing methods for SFDA
leverage entropy-minimization techniques which: (i) apply only to
classification; (ii) destroy model calibration; and (iii) rely on the source
model achieving a good level of feature-space class-separation in the target
domain. We address these issues for a particularly pervasive type of domain
shift called measurement shift which can be resolved by restoring the source
features rather than extracting new ones. In particular, we propose Feature
Restoration (FR) wherein we: (i) store a lightweight and flexible approximation
of the feature distribution under the source data; and (ii) adapt the
feature-extractor such that the approximate feature distribution under the
target data realigns with that saved on the source. We additionally propose a
bottom-up training scheme which boosts performance, which we call Bottom-Up
Feature Restoration (BUFR). On real and synthetic data, we demonstrate that
BUFR outperforms existing SFDA methods in terms of accuracy, calibration, and
data efficiency, while being less reliant on the performance of the source
model in the target domain.
