Learning transport cost from subset correspondence
Learning to align multiple datasets is an important problem with many applications, and it is especially useful when we need to integrate multiple experiments or correct for confounding. Optimal transport (OT) is a principled approach to align datasets, but a key challenge in applying OT is that we need to specify a cost function that accurately captures how the two datasets are related. Reliable cost functions are typically not available and practitioners often resort to using hand-crafted or Euclidean cost even if it may not be appropriate. In this work, we investigate how to learn the cost function using a small amount of side information which is often available. The side information we consider captures subset correspondence---i.e. certain subsets of points in the two data sets are known to be related. For example, we may have some images labeled as cars in both datasets; or we may have a common annotated cell type in single-cell data from two batches. We develop an end-to-end optimizer (OT-SI) that differentiates through the Sinkhorn algorithm and effectively learns the suitable cost function from side information. On systematic experiments in images, marriage-matching and single-cell RNA-seq, our method substantially outperform state-of-the-art benchmarks.
# Summary This paper proposes a new way to learn the optimal transport (OT) cost between two datasets that can utilize subset correspondence information. The main idea is to use a neural network to define a transport cost between two examples instead of using the popular Euclidean distance and have a L2 regularizer that encourages the resulting transport plan to be small if two examples belong to the same subset. The results on synthetic datasets (2D, MNIST image) and real-world datasets (RNA sequence) show that the learned transport cost outperforms the Euclidean distance and Procrustes-based OT. # Originality - This paper considers a new problem which is to learn OT given *subset correspondence* information. The prior work does not have a mechanism to utilize such information or requires more side information such as pair-wise matching. # Quality - The idea of parameterizing the transport cost using a neural network is novel to my knowledge. The idea of regularizing the transport cost based on the subset correspondence information sounds sensible. - The empirical result is quite comprehensive and convincing in that it includes from illustrative examples to real-world datasets (RNAs) and includes many relevant baselines. # Clarity - The paper is well-organized and well-written. - Since this paper considers a new problem (learning OT with subset correspondence data), it would be great to motivate and explain the problem better in the introduction. RNA-seq examples in the introduction were not easy to parse as I do not have any background on biology. It would be better if the paper presented more illustrative/intuitive examples ideally with a figure that describes the problem. - *an principled* -> *a principled* # Significance - This paper seems to present a neat and sensible idea for learning OT with neural networks given subset correspondence information. The problem and method are new, and the empirical results look comprehensive. One minor issue is that it is unclear how significant this new problem setup is (learning OT cost with subset correspondence). Although the paper presents real-world examples (RNAs), the paper could be stronger if it presented more real-world examples/results and emphasized that this is an important problem to solve.
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
Learning transport cost from subset correspondence
Learning to align multiple datasets is an important problem with many applications, and it is especially useful when we need to integrate multiple experiments or correct for confounding. Optimal transport (OT) is a principled approach to align datasets, but a key challenge in applying OT is that we need to specify a cost function that accurately captures how the two datasets are related. Reliable cost functions are typically not available and practitioners often resort to using hand-crafted or Euclidean cost even if it may not be appropriate. In this work, we investigate how to learn the cost function using a small amount of side information which is often available. The side information we consider captures subset correspondence---i.e. certain subsets of points in the two data sets are known to be related. For example, we may have some images labeled as cars in both datasets; or we may have a common annotated cell type in single-cell data from two batches. We develop an end-to-end optimizer (OT-SI) that differentiates through the Sinkhorn algorithm and effectively learns the suitable cost function from side information. On systematic experiments in images, marriage-matching and single-cell RNA-seq, our method substantially outperform state-of-the-art benchmarks.
user
<think>Okay, to do a decent peer review, I should start with summarizing what the work is about. This includes novelty, contributions, clarity, and impact. I might include suggestions to issues that I find critical to the usefulness of the work. Starting with novelty, there are different types of novelty. The first aspect of novelty is scope and scale. Is the work covering a broader perspective than previous works? The second aspect is methodology. Is the proposed methodology novel compared to previous methods? Do they provide any significant advantage over previous methodologies? The third aspect is results. Are the results different compared previous work? Does this lead to any novel theories or an extension of current theories? Next is clarity, I will be reading the work in depth and analyze if any sentences can be potentially ambiguous or misleading. If any sentences are ambiguous, I will state them and give a suggestion on how to rephrase such sentence or how to make more clear to the audience. Lastly, impact is important. I will attempt to predict how such work will impact the scientific community. This might include the applications of such work and how the work might transform the way we study a certain topic. Finally, I will might only mention issues that are critical. This is to keep the review as concise and helpful as possible.</think>



# Summary This paper proposes a new way to learn the optimal transport (OT) cost between two datasets that can utilize subset correspondence information. The main idea is to use a neural network to define a transport cost between two examples instead of using the popular Euclidean distance and have a L2 regularizer that encourages the resulting transport plan to be small if two examples belong to the same subset. The results on synthetic datasets (2D, MNIST image) and real-world datasets (RNA sequence) show that the learned transport cost outperforms the Euclidean distance and Procrustes-based OT. # Originality - This paper considers a new problem which is to learn OT given *subset correspondence* information. The prior work does not have a mechanism to utilize such information or requires more side information such as pair-wise matching. # Quality - The idea of parameterizing the transport cost using a neural network is novel to my knowledge. The idea of regularizing the transport cost based on the subset correspondence information sounds sensible. - The empirical result is quite comprehensive and convincing in that it includes from illustrative examples to real-world datasets (RNAs) and includes many relevant baselines. # Clarity - The paper is well-organized and well-written. - Since this paper considers a new problem (learning OT with subset correspondence data), it would be great to motivate and explain the problem better in the introduction. RNA-seq examples in the introduction were not easy to parse as I do not have any background on biology. It would be better if the paper presented more illustrative/intuitive examples ideally with a figure that describes the problem. - *an principled* -> *a principled* # Significance - This paper seems to present a neat and sensible idea for learning OT with neural networks given subset correspondence information. The problem and method are new, and the empirical results look comprehensive. One minor issue is that it is unclear how significant this new problem setup is (learning OT cost with subset correspondence). Although the paper presents real-world examples (RNAs), the paper could be stronger if it presented more real-world examples/results and emphasized that this is an important problem to solve.
assistant
# Summary This paper proposes a new way to learn the optimal transport (OT) cost between two datasets that can utilize subset correspondence information. The main idea is to use a neural network to define a transport cost between two examples instead of using the popular Euclidean distance and have a L2 regularizer that encourages the resulting transport plan to be small if two examples belong to the same subset. The results on synthetic datasets (2D, MNIST image) and real-world datasets (RNA sequence) show that the learned transport cost outperforms the Euclidean distance and Procrustes-based OT. # Originality - This paper considers a new problem which is to learn OT given *subset correspondence* information. The prior work does not have a mechanism to utilize such information or requires more side information such as pair-wise matching. # Quality - The idea of parameterizing the transport cost using a neural network is novel to my knowledge. The idea of regularizing the transport cost based on the subset correspondence information sounds sensible. - The empirical result is quite comprehensive and convincing in that it includes from illustrative examples to real-world datasets (RNAs) and includes many relevant baselines. # Clarity - The paper is well-organized and well-written. - Since this paper considers a new problem (learning OT with subset correspondence data), it would be great to motivate and explain the problem better in the introduction. RNA-seq examples in the introduction were not easy to parse as I do not have any background on biology. It would be better if the paper presented more illustrative/intuitive examples ideally with a figure that describes the problem. - *an principled* -> *a principled* # Significance - This paper seems to present a neat and sensible idea for learning OT with neural networks given subset correspondence information. The problem and method are new, and the empirical results look comprehensive. One minor issue is that it is unclear how significant this new problem setup is (learning OT cost with subset correspondence). Although the paper presents real-world examples (RNAs), the paper could be stronger if it presented more real-world examples/results and emphasized that this is an important problem to solve.