Venue: NeurIPS 2021 Conference

Reviews:

final_score: rating: 7: Good paper, accept
review_content: summary: The paper suggests a modification of partial dependence plot for assessing the influence of hyperparameter on the fitting of the model in the context of Bayesian optimization. Bayesian optimization provides a surrogate function that describes the influence of hyperpatameter on the cost function with associated uncertainty. The surrogate function can be used as a proxy of the actual cost function to generate the partial dependence plot. However, this approach usually does not capture the associated uncertainty. Moreover, given Bayesian optimization explores the high-performing hyperparameter space more to find a suitable solution, it samples the hyperparameter space in a biased manner by design, and thus, it is more uncertain in region where less hyperparameters are sampled. Estimating the uncertainty of the partial dependence plot from these regions can bias the partial dependence plot. The authors resolve this issue by partitioning the hyperparameter space in regions based on the certainty of the surrogate function, and show that estimating partial dependence plot from region that has low uncertainty provides a better estimate, and the partial dependence plot becomes more interpretable.
main_review: - The paper tackles an interesting problem. Explaining the contribution of hyperparamter choices in complex machine learning models helps the end-users select a hyperparameter value more informatively. Partial dependence plot is an effective way of achieving this. The proposed approach additionally provides uncertainty around the partial dependence plot, and breaks the parameter space down to estimate this uncertainty better.
- The paper is well written and explores issues with directly estimating the partial dependence plot from surrogate function, and the proposed  modifications well.
- The paper demonstrates extensively using simulated and real data that the estimated confidence interval drops by a large margin when splitting the hyperparameter space in regions over using the global estimate. This along with graphical representation of the region splits provide additional information on the effect of hyperparameter.
- The authors mention that the real-world data were modelled with deep neural network but line 290 it is mentioned that they use random forest. Table 2 and Figure 7, howeve
r, discusses deep neural network.
limitations_and_societal_impact: The authors are clear about the limitations of their work, i.e., proposed heuristics. The work, to my understanding, does not have any negative societal impact.
review_title: null

final_score: rating: 6: Marginally above the acceptance threshold
review_content: summary: This paper focuses on the topic of explaining the hyperparameter optimization (HPO) process usually used in AutoML via partial dependence plots (PDP). In particular, the authors argue that naive methods suffer from sampling bias of HPO, and demonstrate how to quantify uncertainty in the resulting PDP and propose a further improvement by looking at PDP in sub-regions. 
main_review: Originality: As far as I know the method proposed is original. There are lots of work on interpretable machine learning directly applied on models, but explaining the process of hyperparameter optimization is a relatively less studies while important area.

Quality: The claims made in the paper are supported by the experiment studies. The authors are also honest about discussing both pros and cons of the proposed method.

Clarity: Overall it has good clarity. However I think the author needs more discussion in the motivation of the proposed method. See later comments. I do feel that the intro and background are a bit too long. The authors can consider moving the mathematical introduction of PDP to late sections.

Significance: I believe this topic is of importance to practitioners and data scientists.
limitations_and_societal_impact: 1. One major disadvantage of PDP is that it can provides misleading results for correlated features, which usually happen in practice including in HPO setting. It is definitely worth some discussion in the last section.

2. The proposed method can be applied to explain ml models directly. It's worth to see how it can interpret using one or two examples.
review_title: null

final_score: rating: 5: Marginally below the acceptance threshold
review_content: summary: The paper presents several ideas to help understand and interpret the effects of different hyperparameters on the model chosen by automated machine learning. 

The contributions include proposing an uncertainty measure for PDPs of probabilistic surrogate models including Bayesian optimization and others. To further increase interpretability, the paper suggests a procedure of dividing the hyperparameter space into subspaces/sub-regions, so that the hyperparameter effect of sub-regions can be analyzed individually. 

The experiment results of the d-dimensional Styblinski-Tang function show the PDPs for surrogate models trained on less biased data produces lower values of the NLL and MC. , as well as lower values for the MC. Splitting into sub-regions helps to reduce MC generally. For high sampling bias, MC seems decrease when splitting 1 or 3 times, however, NLL can become worse in some cases. 

In the other experiment, the paper studies HPO for 35 different OpenML classification tasks. The study found that the MC of the PDPs reduces significantly after 6 splits when comparing the PDP in sub-regions with the global PDP.
 
main_review: Using Partial Dependence Plots (PDPs) to interpret the effects of hyperparameters is not a new idea. The paper proposes a new uncertainty measure and also the idea of divide the hyperparameter space into sub-regions by constructing a tree structure. The difference with existing work is clear, and incremental, in my opinion. The paper cites many previous studies. 

The paper claims the new method produces "more confident and more reliable regional PDP estimates in the sub-region containing the optimal configuration compared to the global PDP ". The experiment results confirm that claim by testing on a Synthetic Function and a set of OpenML classification tasks. The baselines in the paper use the same method proposed by the paper. It will be interesting to have results of comparing with other methods, for instance,  Greenwell [2017] or Grömping [2020].  The paper lists the limitation of the proposed approach. 

The paper is well written, overall. In Algorithm 1: Tree-based Partitioning, it is not clear to me how to choose the split t. Hyperparameters can be categorical or continuous, so the optimization problem to computing t can be difficult.

I believe interpretability is an import topic for ML and AutoML. Being able to explain why a model is chosen by AutoML helps to convince people to adopt the model. The conclusion from the study is not surprising for BO based AutoML. I don't feel the proposed method produces significant results.  

limitations_and_societal_impact: Yes.
review_title: null

Meta-review: We thank the authors for the detailed clarifications they provided during the rebuttal. Model understanding is an important topic and understanding the impact/role of hyperparameters is still an open question. The reviewers all agreed that this paper makes interesting contributions even though the authors built on top of earlier work that uses partial dependency plots to interpret the role of hyperparameters. The reviewers found that the experiments supported the claims and that the discussion was balanced, covering both pros and cons of the proposed approach.
Decision: Accept (Poster)