A Path to Simpler Models Starts With Noise

Summary

The authors propose a possible explanation for the often large Rashomon ratios in tabular datasets (criminal justice, healthcare, etc.). The explanation involves both the dataset generation process and choices made by the practitioners who train the model. The main thesis is that label noise leads to the adoption of simpler models. The authors provide empirical and theoretical justifications to support this hypothesis. In addition, the authors propose a new Rashomon metric.

Strengths

1. The paper is well-written and well-organized. 1. The paper focus on an important topic with practical implications for critical domains like criminal justice, healthcare, etc. 1. The authors provide an in-depth theoretical and empirical analysis to support their claims. 1. The authors introduce a new Rashomon metric.

Weaknesses

1. It would be beneficial to give some definition/example of a “simple model” in the introduction. 1. In the definition of the true Rashomon set, did you actually mean to take $L(f)<L(f^*)+\gamma$ in the definition of $R_{set}$? Otherwise, we should take $\gamma>=1$. 1. It would be interesting to see if the results generalize to more complex datasets and models. 1. Could you provide references to support the claim that the assumptions in Prop. 6 generally holds in practice? 1. How does the choice of the Rashomon coefficient affect the analysis? For example, could you provide Figures similar to Fig. 1, but for different choices of the Rashomon coeff? 1. Could you please elaborate on the motivation for defining the pattern diversity and on the connection to larger Rashomon ratios? This is not clear from Sec 5. If I understand correctly, the relation is only established through the analysis which shows that both Rashomon ratios and pattern diversity increase with noise. 1. While the arguments in Sec 4 regarding the path taken by the practitioner appear plausible, I’m not entirely convinced. Minor: 1. Line 41: there’s a missing period before “Our”. 1. Line 88: “...that often there are often…” 1. Line 139: $p_f$ -> $p^f$.

Questions

1. Is there a way to define (an equivalent to) the Rashomon ratio for a continuous hypothesis class? 1. Does the provided analysis hold for a continuous hypothesis class?

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

Addressed

Summary

How does noise influence the set of models that have similar performance? This paper presents a study that decomposes the problem in three stages, first showing how noise in labels harms generalisation, second, lower generalisation capability leading to more restrictive model choices, and lastly showing that the restrictive model space has a larger Rashomon ratio (i.e. larger proportion of models in this space with similar performance). The main claim is in presenting a technical argument for use of simpler (interpretable) models in critical domains, as these tend to be noisy.

Strengths

- The central idea of promoting simpler models on account of noise in real-world datasets is noteworthy. The use of arguments, albeit limited, to demonstrate a plausible sequence of choices leading to simpler model specification is also interesting.

Weaknesses

- The presented results use a patchwork of assumptions, model classes and conditions to hold for each result. I appreciate a comprehensive evaluation is out of scope and this is intended to be a plausible mechanism. This implies that the overall conclusions are only weakly supported. - How does label noise influence the Rashomon ratio? Empirical evidence of this central point should be directly provided. Figure 2 breaks this down by tree depth, and Figure 3 offers characteristics of the set. The paper would benefit from a more direct noise-to-metric plot.

Questions

None.

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

- While there are some useful analytical results, the paper largely rests on empirical work. The authors have alluded to this in their limitations.

Summary

The Rashomon set is the collection of all models that perform almost equally well in a given dataset. The Rashomon ratio is the fraction of models that are members of a given hypothesis class and simultaneously are in the Rashomon set. The paper studies the relationship between noise in the data generation process and the Rashomon ratio. The authors also argue that noisier datasets lead to a larger Rashomon ratio. Finally, the authors also define a measure that captures the average difference in prediction across different classification patterns in the Rashomon set.

Strengths

* The paper is well-written, and the problem of studying how data noise affects the Rashomon set is interesting. * Proposition 6 is interesting and confirms (in a specific scenario) that more complex hypothesis classes would lead to smaller Rashomon ratios. The experiments in Figure 2 (a) and (b) help illustrate Proposition 6. * The idea of defining a pattern Rashomon set is interesting, and using it as a proxy for exploring the Rashomon set can be helpful in other applications.

Weaknesses

* Some of the provided bounds are non-computable. For example, the bounds in Theorem 4 (as the authors discussed in the paper) and Theorem 9 (the empirical risk minimizer is not always attainable) can not be computable. * The pattern diversity metric (listed in the Abstract as a contribution) is a slight modification of the pairwise disagreement metric -- specifically, it assumes that all patterns are equiprobable. The result of Proposition 16 shows that these metrics may have different values in a particular (and maybe unrealistic) scenario. I encourage the authors to explore the differences further. Moreover, the authors could discuss when pattern diversity is useful but pairwise disagreement is not. * The paper shows that when label noise is large enough, the loss variance is larger; hence, the Rashomon ratio may also be larger. With this chain of thought, one can conclude that simple models may exist. However, given a dataset, it needs to be clarified how to decide whether the label noise is high. Moreover, even assuming that there exists a black box that gives practitioners the level of label noise, it is necessary to answer the question: How large the noise needs to be for simpler models to exist? * Most of the results depend on the fact that the 0-1 loss is being used. However, other losses may be preferred in practice, and discussing how the results extend to other losses is necessary.

Questions

* How would the results change when other losses (beyond the 0-1 loss) are used? Is it expected that the same/similar results will hold? It might be interesting to illustrate the results using other losses experimentally. * How can we compute the pattern diversity metric when listing all models in the Rashomon set is impossible? For example, how to compute the pattern diversity metric for SVMs? * How does Theorem 11 relate to Theorem 10? What should a practitioner expect when there is noise in both the label and the features? * How tight is the upper bound in Theorem 9?

Rating

5: Borderline accept: Technically solid paper where reasons to accept outweigh reasons to reject, e.g., limited evaluation. Please use sparingly.

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

3 good

Presentation

3 good

Contribution

2 fair

Limitations

The authors discuss the limitations of the paper.

Summary

The authors explore how the Rashomon Ratio (the fraction of all models that are in the Rashomon set) changes in the presence of label noise. They show that increased label noise causes the expected variance of the ERM’s performance to increase. Then, they hypothesize that this increased variance leads practitioners to use simpler model classes, which are known to have higher Rashomon Ratios. They also introduce pattern diversity as a metric for how diverse the prediction patterns are across members of the Rashomon set. The authors provide empirical support across several datasets that (i) simpler models perform better when a dataset is noisy, (ii) simpler model classes have higher Rashomon ratios for decision trees and linear models, and (iii) Rashomon set size, number of Rashomon patterns, and diversity of these patterns tends to increase with label noise. The authors are also forthright about the limitations of their work, and provide a nice overview of open questions related to Rashomon Ratios in the presence of noise.

Strengths

* Provides one of the first theoretical studies on the Rashomon effect. As the users state, there are important policy implications of the Rashomon effect and understanding the phenomenon is important to being able to craft policy around it. * The theoretical results are also shown to hold empirically on real datasets. * The “limitations” section is very welcome, as it helps the reader to contextualize what this paper does and does not do. It also provides a good set of ideas for future research. * The paper is generally well-written. The "path" framework is not perfect (see weaknesses), but I appreciate that the authors try to account for how both theoretical properties of the data and human choices lead to large Rashomon sets.

Weaknesses

* Certain claims are not proven in a broad sense and this is not clearly delineated (or worse, the authors claim something more general than what they prove) * Uniform label noise vs real-world patterns of noise: Theorem 2 shows that variance of the loss increases with uniformly random label noise, however, in lines 167-168, the authors say that it “holds more generally,” which is not true * The paper is written in a way that assumes that ML practitioners are following the standard ML pipeline (e.g., switching to a simpler model class given poor test set performance) but these claims are not backed up by any data. I would encourage the authors to see if the HCI literature has studied ML practitioner behavior in this situation, and if not, to reframe the paper so that it doesn’t present the human behavior narrative as fact. * Presentation * Generalization is a key part of the argument in section 4, but the paper never defines generalization or generalization bounds. * The discussion of learning with noise in the related works section also seemed very brief given the amount of work that this topic has received. For example, there is work that aims to learn more stable models in the presence of label noise.

Questions

A couple of minor points: * In section 5.1, wouldn’t it make more sense to call $a_i$ the sample agreement? (Or otherwise, to change its definition to sum over the indicator function with $p_k^i \neq y_i$? ) * In the equation under line 166, should $p$ (with no subscript) appear at all? One bigger question: * Do the results hold empirically when labels are not randomly corrupted? E.g., label errors are more likely in some subset of the population.

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

* Soundness limitations — see weaknesses above * The paper only considers random, uniform label noise. This seems more acceptable as a first step for the theoretical contributions, but real-world label noise is often not random and can be correlated with protected demographic group attributes. Given that the Rashomon effect is of particular interest in social prediction tasks, I wish the authors had explored how their findings generalize to realistic noise settings.