We propose a unified framework for addressing three key challenges of distribution shift: (1) estimating a model's performance on an unlabeled target domain, (2) explaining the shift by identifying the features responsible, and (3) improving the target domain performance. Our method, Entropic Projection Alignment (EPA), aligns the source distribution to the target by matching carefully selected moments while simultaneously minimising the KL divergence from the source. This formulation yields a unique closed-form solution for importance weights, achieving robustness through implicit variance control. Drawing on domain adaptation theory, we establish that moment matching is sufficient for reliable estimation and adaptation, avoiding the need for full density ratio recovery. Extensive experiments, together with strong theoretical guarantees, demonstrate that EPA consistently outperforms state-of-the-art baselines while offering substantial computational efficiency.

翻译：我们提出一个统一框架，用于解决分布偏移的三大关键挑战：（1）在无标签目标域上评估模型性能，（2）通过识别导致偏移的特征来解释偏移，以及（3）提升目标域性能。我们的方法——熵投影对齐（EPA）——通过匹配精心选择的矩，同时最小化与源分布的KL散度，将源分布对齐至目标分布。该公式导出一个独特的闭式解用于重要性权重，并通过隐式方差控制实现鲁棒性。基于领域适配理论，我们证明了矩匹配足以实现可靠的估计与适配，从而避免了完全密度比恢复的需求。大量实验及强理论保证表明，EPA在提供显著计算效率的同时，始终优于最先进的基线方法。