Iterative Alignment Flows
Iterative Alignment Flows
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发表时间：
2021-04
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通讯作者：
Zeyu Zhou;Ziyu Gong;Pradeep Ravikumar;David I. Inouye
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作者：
Zeyu Zhou;Ziyu Gong;Pradeep Ravikumar;David I. Inouye
在共享潜在空间中对齐两个或多个分布的无监督任务具有许多应用，包括公平表示、批量效应缓解和无监督域适应。现有的基于流的方法独立地估计多个流，这相当于学习多个完整的生成模型。其他方法需要对抗性学习，这可能会导致计算成本高昂且难以优化。因此，我们的目标是联合对齐多个分布，同时避免对抗性学习。受单变量分布最优传输 (OT) 理论的高效对齐算法的启发，我们开发了一种简单的迭代方法来构建深度且富有表现力的流。我们的方法将每次迭代分解为两个子问题：1）形成分布散度的变分近似，2）通过基于已知 OT 结果的封闭形式可逆对齐图最小化这种变分近似。我们的实证结果证明，这种迭代算法以较低的计算成本实现了竞争性分布对齐，同时能够自然地处理两个以上的分布。
The unsupervised task of aligning two or more distributions in a shared latent space has many applications including fair representations, batch effect mitigation, and unsupervised domain adaptation. Existing flow-based approaches estimate multiple flows independently, which is equivalent to learning multiple full generative models. Other approaches require adversarial learning, which can be computationally expensive and challenging to optimize. Thus, we aim to jointly align multiple distributions while avoiding adversarial learning. Inspired by efficient alignment algorithms from optimal transport (OT) theory for univariate distributions, we develop a simple iterative method to build deep and expressive flows. Our method decouples each iteration into two subproblems: 1) form a variational approximation of a distribution divergence and 2) minimize this variational approximation via closed-form invertible alignment maps based on known OT results. Our empirical results give evidence that this iterative algorithm achieves competitive distribution alignment at low computational cost while being able to naturally handle more than two distributions.