Venue: ICLR 2021 Conference

Reviews:

final_score: rating: 7: Good paper, accept
review_content: The authors present the split Poisson Gamma (SPG) distribution, an extension of the Poisson-Gamma distribution, to model a discrete non-stationary stochastic process. SPG has an analytical posterior allowing accurate prediction after the model parameters have been inferred a single time. The authors apply the SPG to model tumor mutation rates and show that model parameters can be accurately inferred from high-dimensional epigenetic data. This is achieved through a combination of CNNs, GPs and MLE. The results are promising in detecting tumor drivers such as genes, regulatory structures and base-pairs.

The paper is well written, with motivation described and prior literature being discussed. Figure 1 is well laid out to drive home the point. 

Comments:

* Section 2: are all the distributions univariate? If not, a table giving dimensions will be helpful. What is the dimension of the covariates (eta_R)? It would also help if a plate diagram of the generative model is given. 

*  Why was CNN chosen for dimensionality reduction?

*  Were other non neural architectures used for dimensionality reduction?

*  What is the significance of ‘735’ epigenetic tracks? 

*  How valid is the assumption that events are distributed independently in the mutation space? I think this is too restrictive but at the same time simplifies the problem. A discussion of this simplification will be essential for the medical/biology audience.

*  Title of paper has 'causes'. Title on ICLR webpage has 'cusses'. Please correct if possible.



review_title: Split Poisson Gamma distribution to model a discrete stochastic process 

final_score: rating: 6: Marginally above acceptance threshold
review_content: Summary: The paper extends Poisson-Gamma models for non-stationary sequences, in a manner that allows partitioning the counts according to a binomial model to account for multiple resolutions. This generalisation is motivated well with a biological application of practical relevance, and the proposed method is particularly strong in enabling linear computational scaling required for analysis of large genome data.

Reasons for score: I am leaning towards rejection in the current form.  The contribution itself is worth publishing and the method is likely to be valuable for the application, but the presentation would need to be improved (especially regarding the GP+CNN part; see the detailed feedback) to better communicate the technical contributions for the ICLR audience. Conditional on improved presentation, I would be leaning towards acceptance.

Detailed feedback: The proposed split Poisson-Gamma (SPG) process seems reasonable, but in technical terms is a fairly straightforward hierarchical structure and can be constructed using standard properties of Poisson-Gamma. It is well motivated by the resulting efficient inference and this specific application, and may find uses in other applications as well, but does not provide a very clear theoretical contribution that would open immediate follow-up research directions for more general modelling questions.

My main problem with the paper concerns the structure of the presentation. While the authors motivate the model well and provide very clear illustrations for the application, the method sections are disconnected and I had trouble following the technical contributions. In particular, the connection between Section 2 (SPG) and the technical algorithm required for using it (Section 3.3) is unclear. To me it seems the GP+CNN part is an integral part of the overall solution and a contribution in itself (and, in fact, an important one -- the SPG alone is not quite sufficient as theoretical contribution). It provides a concrete algorithm using SPG and is general, but now the description is provided only after talking about specific data and looks more like a minor technical detail with no proper theoretical justification. For me, the paper would be more natural if Section 3.3 (and possibly some other parts of Section 3) would be described after Section 2 as description of how SPG is used in practice, and if they would use shared notation and terminology. This would make the practical approach easier to follow and the contributions more clear.

The empirical experiments and illustrations for the application are well carried out, and serve as good demonstration of the method. However, a reader uninterested or uneducated in this specific application will have some trouble figuring out how well the method works; this could be improved by complementing the results with clear artificial data of slightly simpler nature.

Modifications after discussion:
Increased score by one as the presentation in the revised version has clearly improved, along the lines requested in the original review.
review_title: Well motivated model for specific biological application, with confusing presentation of technical contributions

final_score: rating: 6: Marginally above acceptance threshold
review_content: Short summary: This paper introduces a split-Poisson-Gamma model to capture discrete-time, integer-valued stochastic processes at multiple scales. Although it seems to be simple and incremental compared with Poisson gamma models, this novel method may has some impacts in modeling mutation rates and identifying genomic elements that drive tumor emergence. Thus, I vote for weak acceptance.

-quality: the technique contribution appears to be simple, incremental but could be useful in real applications of detecting cancer-related mutations.

-clarity: the most parts of the paper is clearly written. Nonetheless, I find the paper is improvable by clearly describing the input data in Sec.2.

-originality: to my knowledge, it is the first attempt to develop split-Poisson gamma model for discrete-time, integer-valued stochastic processes at multiple scales. 

-significance: it appears to be an incremental contribution in the family of Poisson gamma models. I think the split-Poisson gamma model is a sensible and useful method in detecting cancer-related mutation rates.

Pros: a useful and very sensible model for detecting cancer related mutation rates.

Cons: A clear description of the input data is missing in the beginning of Sec.2. I think it could be better if the authors can position the split-Poisson gamma model among the closely related Poisson gamma models, to clearly distinguish the main differences and why the novel model outperforms the others. 

In addition to estimating mu_R and sigma_R^2, how to place hyper priors over these parameters , and perform MAP estimations?

I agree the detection of cancer-causing mutations is a significant application of the multi-resolution modeling of discrete stochastic processes. Nonetheless, I would suggest the authors to discuss the broad applications of the split-Poisson gamma (SPG) model for a venue like ICLR. 

comments:
-"NB" notations are used in eq.(6,7) but are not defined for negative binomial yet.
-you miss a "Pr" for lambda_R in Eq.(9).
-can you present the complete procedure  to perform parameter inference in the supplement?
-In C.1 of pp14, it should be NB(M_i;alpha_R, 1/(p_i \theta_R+1)).
review_title: I vote for weak acceptance as I find that this paper introduces a split-Poisson-Gamma model for discrete stochastic processes at multi-resolutions, that appears to be inremental but may have impacts for the task of the detection of cancer-causaing mutation rates.

Meta-review: Reviewers agree that the paper excels in providing a principle pipeline that combines CNNs and GPs with a Poisson-Gamma distribution to provide a generic approach for multiresolution modelling of tumour mutation rates. As a whole such combination of techniques addresses a key challenge in computational biology that also scales to large datasets. 
Decision: Accept (Poster)