提出可扩展的近似算法，解决带熵正则化OT的非负线性回归问题。
Scalable Approximate Algorithms for Optimal Transport Linear Models
- 基于类似Sinkhorn的迭代，设计可并行的乘法更新规则。
- 支持常见正则项与目标分布损失，适用于大规模数据。
- 适合需要高效处理高维分布数据的研究者，如光谱解混。
近年来，结合最优传输（OT）损失的线性回归模型被用于光谱监督解混、音乐转录和质谱分析等任务。然而，这些特定任务的方法难以推广到更广泛的线性模型。本文提出一种新颖的算法框架，用于求解一类带熵正则化OT数据拟合项的非负线性回归模型，基于类似Sinkhorn的缩放迭代。该框架支持权重上的凸惩罚函数（如平方ℓ₂和ℓ₁范数），并可加入运输后边际分布与目标分布之间的凸损失项（如平方误差或总变差）。我们推导了常见惩罚项和数据拟合项的简单乘法更新规则。由于实现简单且易于并行化，该方法适用于大规模问题。
原文摘要 · Abstract (English)
Recently, linear regression models incorporating an optimal transport (OT) loss have been explored for applications such as supervised unmixing of spectra, music transcription, and mass spectrometry. However, these task-specific approaches often do not generalize readily to a broader class of linear models. In this work, we propose a novel algorithmic framework for solving a general class of non-negative linear regression models with an entropy-regularized OT datafit term, based on Sinkhorn-like scaling iterations. Our framework accommodates convex penalty functions on the weights (e.g. squared-$\ell_2$ and $\ell_1$ norms), and admits additional convex loss terms between the transported marginal and target distribution (e.g. squared error or total variation). We derive simple multiplicative updates for common penalty and datafit terms. This method is suitable for large-scale problems due to its simplicity of implementation and straightforward parallelization.
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