Distribution Regression Network
We introduce our Distribution Regression Network (DRN) which performs regression from input probability distributions to output probability distributions. Compared to existing methods, DRN learns with fewer model parameters and easily extends to multiple input and multiple output distributions. On synthetic and real-world datasets, DRN performs similarly or better than the state-of-the-art. Furthermore, DRN generalizes the conventional multilayer perceptron (MLP). In the framework of MLP, each node encodes a real number, whereas in DRN, each node encodes a probability distribution.
 The paper considers distribution to distribution regression with MLPs. The authors use an energy function based approach. They test on a few problems, showing similar performance to other distribution to distribution alternatives, but requiring fewer parameters. This seems to be a nice treatment of distribution to distribution regression with neural networks. The approach is methodological similar to using expected likelihood kernels. While similar performance is achieved with fewer parameters, it would be more enlightening to consider accuracy vs runtime instead of accuracy vs parameters. That’s what we really care about. In a sense, because this problem has been considered several times in slightly different model classes, there really ought to be a pretty strong empirical investigation. In the discussion, it says “For future work, a possible study is to investigate what classes of problems DRN can solve.” It feels like in the present work there should have been an investigation about what classes of problems the DRN can solve. Its practical utility is questionable. It’s not clear how much value there is adding yet another distribution to distribution regression approach, this time with neural networks, without some pretty strong motivation (which seems to be lacking), as well as experiments. In the introduction, it would also improve the paper to outline clear points of methodological novelty.
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
Distribution Regression Network
We introduce our Distribution Regression Network (DRN) which performs regression from input probability distributions to output probability distributions. Compared to existing methods, DRN learns with fewer model parameters and easily extends to multiple input and multiple output distributions. On synthetic and real-world datasets, DRN performs similarly or better than the state-of-the-art. Furthermore, DRN generalizes the conventional multilayer perceptron (MLP). In the framework of MLP, each node encodes a real number, whereas in DRN, each node encodes a probability distribution.
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>



 The paper considers distribution to distribution regression with MLPs. The authors use an energy function based approach. They test on a few problems, showing similar performance to other distribution to distribution alternatives, but requiring fewer parameters. This seems to be a nice treatment of distribution to distribution regression with neural networks. The approach is methodological similar to using expected likelihood kernels. While similar performance is achieved with fewer parameters, it would be more enlightening to consider accuracy vs runtime instead of accuracy vs parameters. That’s what we really care about. In a sense, because this problem has been considered several times in slightly different model classes, there really ought to be a pretty strong empirical investigation. In the discussion, it says “For future work, a possible study is to investigate what classes of problems DRN can solve.” It feels like in the present work there should have been an investigation about what classes of problems the DRN can solve. Its practical utility is questionable. It’s not clear how much value there is adding yet another distribution to distribution regression approach, this time with neural networks, without some pretty strong motivation (which seems to be lacking), as well as experiments. In the introduction, it would also improve the paper to outline clear points of methodological novelty.
assistant
 The paper considers distribution to distribution regression with MLPs. The authors use an energy function based approach. They test on a few problems, showing similar performance to other distribution to distribution alternatives, but requiring fewer parameters. This seems to be a nice treatment of distribution to distribution regression with neural networks. The approach is methodological similar to using expected likelihood kernels. While similar performance is achieved with fewer parameters, it would be more enlightening to consider accuracy vs runtime instead of accuracy vs parameters. That’s what we really care about. In a sense, because this problem has been considered several times in slightly different model classes, there really ought to be a pretty strong empirical investigation. In the discussion, it says “For future work, a possible study is to investigate what classes of problems DRN can solve.” It feels like in the present work there should have been an investigation about what classes of problems the DRN can solve. Its practical utility is questionable. It’s not clear how much value there is adding yet another distribution to distribution regression approach, this time with neural networks, without some pretty strong motivation (which seems to be lacking), as well as experiments. In the introduction, it would also improve the paper to outline clear points of methodological novelty.