On Scalable and Efficient Computation of Large Scale Optimal Transport
On Scalable and Efficient Computation of Large Scale Optimal Transport
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发表时间：
2019-03
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通讯作者：
Yujia Xie;Minshuo Chen;Haoming Jiang;T. Zhao;H. Zha
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作者：
Yujia Xie;Minshuo Chen;Haoming Jiang;T. Zhao;H. Zha
最优传输(OT)在许多机器学习应用中自然而然地出现，但其沉重的计算负担限制了它的广泛应用。为了解决可伸缩性问题，我们提出了一个基于隐式生成性学习的框架，称为SPOT(Scalable Push-Forward of Optimal Transport)。具体地说，我们通过推进参考分布来逼近最优运输计划，并将最优运输问题转化为极小极大问题。然后，我们可以使用原始的对偶随机梯度型算法来有效地解决OT问题。我们还证明了利用神经常微分方程组可以恢复最优运输计划的密度。在合成数据集和真实数据集上的数值实验表明，SPOT算法具有较好的稳健性和良好的收敛特性。Spot还允许我们有效地从最优传输计划中进行采样，这有利于下游应用，如域适应。
Optimal Transport (OT) naturally arises in many machine learning applications, yet the heavy computational burden limits its wide-spread uses. To address the scalability issue, we propose an implicit generative learning-based framework called SPOT (Scalable Push-forward of Optimal Transport). Specifically, we approximate the optimal transport plan by a pushforward of a reference distribution, and cast the optimal transport problem into a minimax problem. We then can solve OT problems efficiently using primal dual stochastic gradient-type algorithms. We also show that we can recover the density of the optimal transport plan using neural ordinary differential equations. Numerical experiments on both synthetic and real datasets illustrate that SPOT is robust and has favorable convergence behavior. SPOT also allows us to efficiently sample from the optimal transport plan, which benefits downstream applications such as domain adaptation.