Individualized Dosing Dynamics via Neural Eigen Decomposition

Summary

This develops a robust SDE algorithm for medical forecasting. This is demonstrated on both synthetic and real data.

Strengths

The problem solved is clearly compelling and the performance is evaluated on a wide range of datasets, where it exhibits superior performance to reasonable alternatives. It would appear to be an overall robust method.

Weaknesses

It would be nice if some of the components of the model such as hypernet were defined here rather than briefly described, even though I understand the desire to save space. It makes it so that this paper is more difficult to understand/review.

Questions

SDEs are not my area of expertise. I expect the other reviewers will have more enlightening questions and suggestions.

Rating

6: Weak Accept: Technically solid, moderate-to-high impact paper, with no major concerns with respect to evaluation, resources, reproducibility, ethical considerations.

Confidence

3: You are fairly confident in your assessment. It is possible that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.

Soundness

3 good

Presentation

3 good

Contribution

3 good

Limitations

No societal ramifications, but no limitations mentioned as far as shortcomings of the model are concerned.

Summary

The paper presents a piece-wise linear neural SDE with control for biomedical forecasting. The key contribution is combining rigorous linear SDE solutions with hypernet parameterisation.

Strengths

The paper is fantastically written and very clear. The idea of linearising SDEs is relatively novel, and the overall model is sensible and principled. The results are good, and show that a relatively simple model construction is perhaps ideal for medical data.

Weaknesses

The method is somewhat incremental: it combines linear SDEs with hypernets.

Questions

The imaginary/cyclicity argument could have been elaborated more in experiments. Is medical data cyclical? I'm not sure. How come in fig3 we get same performance with 2 or 8 datapoints?

Rating

6: Weak Accept: Technically solid, moderate-to-high impact paper, with no major concerns with respect to evaluation, resources, reproducibility, ethical considerations.

Confidence

3: You are fairly confident in your assessment. It is possible that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.

Soundness

3 good

Presentation

4 excellent

Contribution

3 good

Limitations

No issues

Summary

This paper proposes a novel network approach, named Neural Eigen Stochastic Differential Equations (NESDE), to solve sequential prediction problems mainly in medical dosing control field of applications.

Strengths

$\mathbf{1}.$ The proposal of NESDE is novel, along with the hypernet that determines the subsequent model parameters. $\mathbf{2}.$ This paper is very well written. The motivation, i.e., to address challenges in sequential prediction of medical dosing control, and the limitation of current works, is very well explained. The related works and background fundamental theories are also very well stated with intuitive illustrations. $\mathbf{3}.$ The theoretical analysis is comprehensive and sound (also seen in $\mathbf{Appendix}$.) $\mathbf{4}.$ The empirical analysis is detailed and thorough. Author designed the experiments to validity the algorithmic merits and also real life application in the medical dosing field.

Weaknesses

$\mathbf{Note: }.$ It is a unfamiliar application field to me, and thus it is hard to determine whether or not the proposed method is indeed a significantly novel approach in the field. $\mathbf{1}.$ The major concern is whether or not the proposed method has a broader application. It seems that the direct counterpart is neural ordinary differential equations, and is it possible to discuss and compare the general applicabilities of NODEs versus NESDEs?

Questions

$\mathbf{1}.$ See $\mathbf{1}.$ in $\mathbf{Weakness}$. $\mathbf{2}.$ The experiment with synthetic data seems to support, e.g., the sample efficiency of the proposed method. However, it lacks training efficiency/computational complexity in the experiments. Is it possible to quantify the computational cost when comparing with other methods? $\mathbf{Trivial}.$ What is the point of comparison in Figure 1?

Rating

7: Accept: Technically solid paper, with high impact on at least one sub-area, or moderate-to-high impact on more than one areas, with good-to-excellent evaluation, resources, reproducibility, and no unaddressed ethical considerations.

Confidence

4: You are confident in your assessment, but not absolutely certain. It is unlikely, but not impossible, that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work.

Soundness

4 excellent

Presentation

4 excellent

Contribution

4 excellent

Limitations

This paper does not provide broader impact or limitation statements, but i do not have any concerns on potential negative societal impact.

Summary

This paper presents a method for predicting time series at irregular time points. Its approach systematically integrates control signals, a convenient attribute for modelling dosing regimes in medicine. The latent process follows a piecewise linear stochastic differential equation (SDE) with control. The SDE is parameterized using its spectral representation, allowing for effective and analytical propagation. The parameters of the SDE are learned by a Hypernet. Experimental validation of the method is conducted on artificial data and two medication dosing problems.

Strengths

- The paper introduces a method that effectively models control, with experimental results indicating an improvement over baseline models lacking explicit control. - The well-structured experimental study underscores the applicability and value of the method for two specific medical dosing scenarios. - The authors propose an efficient technique to compute dynamics by parameterizing the system's eigenfunction, thereby enabling fast and analytical computation. - This parameterization strategy not only facilitates the integration of prior knowledge on the dynamics, as evidenced in the dosing experiments, but also enhances interpretability—which is a useful attribute in practise

Weaknesses

- The related work sections seems comprehensive, though neural SDE approaches could also be discussed as the model is based on a SDE latent process. - Explicitly stating which equations represent ESDE() and Filter() in Algorithm 1 would enhance clarity. - Although the experimental study appears to be well-executed and thoughtfully designed, the paper could be enhanced by including more baseline comparisons. Specifically, a comparison with NeuralSDE models would be intriguing, as they also yield uncertainty estimates and aren't confined to the piece-wise linearity constraint. - Minor: My understanding is that the context does not change over time, though Figure 2 suggest this on the first sight.

Questions

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Rating

6: Weak Accept: Technically solid, moderate-to-high impact paper, with no major concerns with respect to evaluation, resources, reproducibility, ethical considerations.

Confidence

3: You are fairly confident in your assessment. It is possible that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.

Soundness

3 good

Presentation

3 good

Contribution

2 fair

Limitations

The piece-wise linear assumption on the observation sequence $Y(t)$ seems a restrictive assumption and limits the type of dynamics that can be modeled with the method. (From my understanding, the model learns a piece-wise linear SDE for $X(t)$ where the observations $Y(t)$ is simply a subset of the features of $X(t)$ , i.e. $Y(t)=X(t)_{1:m}$ . Therefore, the sole non-linearity allowed in the observation sequence come from the piece-wise linear formulation.) A discussion on when the piece-wise linear assumption fails compared to other (more expressive) models is encouraged.