Calibration is a well-studied property of predictors which guarantees meaningful uncertainty estimates. Multicalibration is a related notion -- originating in algorithmic fairness -- which requires predictors to be simultaneously calibrated over a potentially complex and overlapping collection of protected subpopulations (such as groups defined by ethnicity, race, or income). We conduct the first comprehensive study evaluating the usefulness of multicalibration post-processing across a broad set of tabular, image, and language datasets for models spanning from simple decision trees to 90 million parameter fine-tuned LLMs. Our findings can be summarized as follows: (1) models which are calibrated out of the box tend to be relatively multicalibrated without any additional post-processing; (2) multicalibration post-processing can help inherently uncalibrated models and large vision and language models; and (3) traditional calibration measures may sometimes provide multicalibration implicitly. More generally, we also distill many independent observations which may be useful for practical and effective applications of multicalibration post-processing in real-world contexts. We also release a python package implementing multicalibration algorithms, available via `pip install multicalibration'.
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Summary
The paper investigates the necessity and effectiveness of multicalibration post-processing across data of different modalities and machine learning models. It finds that models which are calibrated out of the box tend to be multicalibrated without further post-processing, while multicalibration can help inherently uncalibrated models. Traditional calibration methods, such as Platt scaling, sometimes achieve multicalibration implicitly. The study, conducted on a wide range of datasets (tabular, image, language) and models (from decision trees to large language models), reveals that empirical risk minimization (ERM) often achieves multicalibration. It also notes that multicalibration post-processing is sensitive to hyperparameters and works best with large datasets. Additionally, traditional calibration methods can sometimes match the performance of multicalibration algorithms.
Strengths
Writing is excellent and the paper is well organized, easy to read, and understandable without an effort. The message is clear and there are actionable recommendations. The topic is timely and the experiments done by the authors are fairly comprehensive; lots of models for tabular data, fewer for language and vision. This is one of the largest set of experiments I've seen in the literature. Overall, the work has the potential to have a meaningful impact on the community.
Weaknesses
Not all the conclusions from the authors are well supported by their empirical findings. More details below. Regarding observation 3: * The association between the accuracy and the calibration fraction is somewhat clear for HMDA but it’s definitely unclear of the other datasets (Appendix F.3). Accuracy seems to even increase as the calibration fraction increases on certain datasets. Thus, the authors conclusion in observation 3 is only based on HMDA. I suggest dropping it or providing more support for that. The current experimental results do not support it. * Max smECE of ERM is about twice as large as the max smECE after calibration in case of Naive Bayes, SVM, and decision trees. Then how do the authors justify their observation? * Along the same lines, observation 7 suggests that there is a substantial difference between the results for language/vision data and tabular data because in the latter we do not see such gains. As mentioned right above, Figure 2 shows such gains. It just depends on which algorithms we look at. Other comments: * Observation 5 about the robustness of HJZ to hyperparameter choices does not hold for language and vision data? How do the authors explain this finding? Minor details: * What are the error bars in Figure 3? Standard deviations? * Do the \pm values in Figure 3 represent standard error or deviation?
Questions
I hope that the authors can solve my concerns noted above.
Rating
6
Confidence
3
Soundness
2
Presentation
4
Contribution
3
Limitations
Limitations are discussed.
Summary
The authors provide a large and broad set of evaluations of how useful it is to supplement empirical risk minimization procedures with multicalibration (and/or calibration) post-processing. Their experiments span a wide variety of settings and datasets, broadly falling into the tabular data, image data, and language data category. For all these categories of tasks, they evaluate whether or not one/both/neither of two existing multicalibration post-processing methods (referred to as HKRR and HJZ) are useful to apply to an ERM-trained predictor in order to ensure the resulting predictor is calibrated over a pre-specified family of subgroups in the data; and they do the same with respect to post-processing by applying simpler, marginal calibration methods such as isotonic regression. They distill the findings into many practical insights that should be useful to future practitioners wishing to apply multicalibration in their settings. In broad strokes, it is found that in many cases, especially for tabular data, full multicalibration postprocessing may not make as much practical sense, as pure ERM (possibly with marginal calibration) may already get you close enough to calibration; but at the same time, in image/language processing settings, the usefulness of multicalibration post processing generally increases and may become worth it. Along with these general insights, the authors provide many other guidelines and observations on aspects such as hyperparameter tuning for multicalibration, the comparison in performance between HKRR and HJZ, and other empirical tradeoffs.
Strengths
In general, the multicalibration literature has suffered from a lack of well-concerted assessments of the empirical validity of its undisputably significant theoretical achievements (both when it comes to its “multigroup fairness” motivation and in other applications). Such assessments are even more needed given that known theoretical bounds on multicalibration’s sample complexity, as well as the overfitting effects observed in limited empirical assessments, point to potentially pessimistic empirical performance (especially compared to non-multigroup, classic calibration algorithms like Platt or temperature scaling or isotonic regression). So one important merit of this paper is that it can serve as a good starting point for further empirical evaluation of multicalibration methods. The setup itself, which is to examine how to partition available data into training and calibration sets (+ validation set as necessary to tune the multicalibration algorithms’ hyperparameters), and to ask whether or not the calibration data would be better used for the training / ERM step, is a clean and reasonable question to ask; especially so given the many hints found in recent prior work suggesting that ERM procedures may already encapsulate some (multi)calibration guarantees even without explicitly enforcing them. In all, the authors have indeed managed to execute, to a fair degree (and modulo some concerns below), on their promise of a first comprehensive evaluation of multicalibration post-processing. As listed in the summary section above, they have also provided various useful rules of thumb along the way, which should benefit practitioners and also serve as conversation starters, and in several cases as cautionary notes, when it comes to applying multicalibration in practice.
Weaknesses
The prior work results about ERM being sufficient for obtaining various guarantees are mentioned, but not discussed in enough depth to provide the full context for the question being asked in the present manuscript. For instance, an important thing that [Blasiok et al, 2023]’s note in their intro, before providing their result on NNs giving multicalibration, is that one might imagine that ERM-based solutions might a-priori need to rely not just on a larger-sized NN, but also on a certain larger family of subsets that encapsulate/imply the subgroups that the practitioner wants to calibrate their data on — and their results show that in fact, aside from increasing the size of the neural net, it is (in that setting) not necessary to design any special enlarged family of subsets. So, put simply, the current manuscript needs to note much more explicitly that designing an enlarged group family for the ERM could a-priori be an important design choice for practitioners, but may not be as important (as enlarging the size of the model), as hinted on by prior work. Furthermore, in the same vein as, and aside from, [Kirichenko et al, 2023], please also cite/mention [Rosenfeld et al, 2023] — and for both these works, please discuss the overlap between robustness/multigroup fairness considerations. Group families with respect to which to multicalibrate, especially for tabular datasets, are defined in various “intuitive” ways, such as demographic groups. In that way, consistent with observations from [Kirichenko et al] and [Rosenfeld et al], it appears that explicit multicalibration not being necessary may be due to the fact that the predictors already learn the requisite features that are both prediction-relevant and also significantly correlate with the chosen protected groups. The extent to which this is an important factor — and that multicalibration may indeed be necessary for more “unusual” groups (worst-case, one can almost always hand-craft groups that, at least on training data, show miscalibration) —is not studied in this manuscript. For instance, the worst-group calibration reported only ranges over chosen groups of interest, but of course other groups not considered may have much worse calibration guarantees. So I’m not convinced the results that say multicalibration may not be necessary are robust to defining groups that are somehow non-standard. Another example of potential discrepancy in what is being studied here is the smECE vs ECE distinction — to my knowledge, the HKRR and HJZ algorithms were developed prior to the smECE paper, and can in their various instantiations explicitly target metrics like ECE or L2 or L_infty calibration, rather than smECE. Thus, at least to a less-familiar reader, this must at least be clarified e.g. in the form of a statement that conclusions based on smECE performance are of a purely empirical character. There are other presentation issues from my perspective. Besides not enunciating group choices in the main part as just discussed, the algorithms that are actually used are not explained in any sort of pseudocode, nor are their objectives/claimed bounds ever stated. This is an important writing issue given that HKRR and HJZ are introduced in their respective papers using very different notation, with differing guarantees, and with finer distinctions, such as e.g. that HJZ can output both deterministic and non-deterministic recalibrated predictors.
Questions
Please see the “Weaknesses” section above; some concerns I listed there (notably as far as writing/presentation is concerned) could be resolved within a revision.
Rating
5
Confidence
4
Soundness
2
Presentation
2
Contribution
2
Limitations
N/A
Summary
This work presents an empirical analysis of multi-calibration post-processing applied to a variety of models for binary classification, ranging from decision trees to transformers. They perform experiments with tabular, image, and text data on datasets of varying sizes. They compare model group calibration to overall calibration after a) only ERM b) calibration and c) multicalbration. They observe that, while multicalibration postprocessing does improve multicalibration, in many cases, simple calibration improves it similarly. Additionally, they find that for models that are already calibrated after ERM, they are often multicalibrated as well. They observe differences in metrics used to calculate multicalibration, varying with dataset size that have implications for the situations in which ECE and smECE are appropriate to use. Finally, they find that for large datasets, such as those for vision and language, HJZ shows bigger improvements over HKRR.
Strengths
This is a very expansive and thorough empirical study that has lots of practical takeaways for the ML fairness community that could be very valuable. Particularly in the context of larger models, where post-processing can be very costly, knowing what methods are likely to work is very important. The paper's organization is clear, results are easy to understand, and relevant takeaways are clearly highlighted. The paper builds well on prior work while providing novel key insights about how different methods perform in different settings.
Weaknesses
The paper could be more self-contained. While it's understandable for some results to be in the appendix given the number of experiments run in this paper, I worry that too much may have been pushed to the appendix (though this may be unavoidable). Some details, such as how groups are chosen for language tasks, are also not clear when consulting the appendix, particularly for readers who are not familiar with how these groups are normally chosen. Details like this would help readers to better understand the contribution of the paper.
Questions
1. What are the groups for text experiments? 2. Figure 2 claims that MLPs are among the models that do not benefit from post-processing, however the table appears to show better multicalibration after post-processing. Is this claim correct?
Rating
8
Confidence
4
Soundness
4
Presentation
4
Contribution
4
Limitations
The limitations of the paper seemed well addressed to me.
Summary
The paper investigates the effectiveness of multicalibration post-processing across various datasets and machine learning models. The study finds that models which are inherently calibrated often exhibit multicalibration without post-processing, while uncalibrated models benefit from multicalibration techniques. Traditional heuristics calibration methods can sometimes achieve similar outcomes as multicalibration algorithms. The research provides empirical evidence and practical insights for applying multicalibration in real-world scenarios, emphasizing the sensitivity of multicalibration algorithms to hyperparameter choices and the varying necessity of multicalibration depending on the model and dataset.
Strengths
1. The writing is clear: The introduction effectively establishes the need for this empirical study, and the algorithms and results are presented clearly and concisely. 2. This is the first comprehensive study to evaluate different multicalibration methods. 3. The experimental results are thoroughly discussed, and the observations are detailedly listed.
Weaknesses
1. The paper does not introduce any new algorithms, datasets, or theoretical analysis, but instead focuses on evaluating existing algorithms. 2. The experimental results are primarily observations and lack a deeper discussion of the reasons behind the observed phenomena. 3. Including experiments for all datasets in the main paper would help readers better understand the common findings and differences.
Questions
1. For lines 179-181, in what sense is HKRR sample inefficient? I thought multicalibration for binary problems was known to be sample efficient. 2. Could you provide more reasons why HKRR outperforms HJZ in language and vision datasets? 3. What is the rationale behind choosing a large fraction of data for calibration? From my understanding, it should be about 10% or even smaller when the overall dataset is small. 4. How do the results differ across different datasets for tabular data? I noticed that in the HMDA dataset, the post-processing algorithms perform strictly better than ERM. Do MC algorithms work better for large datasets? Could you add more experiments if this hypothesis makes sense? 5. Did you try to create more complicated groups for the tabular experiments? It is possible that the groups are simple enough that even ERM works well. 6. For Figure 3, could you explain why the max group smECE increases when the calibration fraction gets larger?
Rating
5
Confidence
4
Soundness
2
Presentation
3
Contribution
3
Limitations
Yes, the authors adequately addressed the limitations.
Thanks for the reply. I still believe that the paper, in its current version, presents several takeaways about algorithms/procedures that "can"/"may" or "cannot"/"may not" be helpful. However, in most cases, it's unclear why and when these statements hold true. While I acknowledge that the authors have conducted extensive experiments, more are needed, and I am concerned that practitioners may misinterpret these takeaways. Therefore, I suggest the authors carefully reconsider how each statement is phrased. I also agree with the other reviewers' comments regarding the lack of discussion on the specific nature of the groups, which were chosen arbitrarily. Different groups might lead to different conclusions about multicalibration. Although I don't disagree with the authors' response on this topic, I believe more should be said, and other groups should be explored on the same datasets to check if the results are consistent. This further adds to my concerns about how readers might interpret the paper's takeaways. Regarding W1: I believe the finding is not significant and could mislead practitioners, who are likely to skip the Appendix and focus only on the main body of the paper—or worse, just the takeaway without noticing the "may." As I mentioned in my initial rebuttal, this takeaway seems to overfit a specific dataset. If the trade-off only exists for larger calibration fractions, as highlighted in the examples, this should be clearly discussed in the takeaway. If the takeaway remains (and I don't think it should), the authors should emphasize the "may" in bold and explicitly state that the findings are supported by just one dataset or larger calibration fractions. This concern applies to all other questions/answers as well. The statements need to be crystal clear. Regarding W5: The authors likely mean standard error, not standard deviation.
We sincerely thank the reviewer for their engagement and for acknowledging that we have conducted extensive experiments. You requested additional experiments with “more complex” groups, which we have been running since your last response, and hope to have uploaded by the end of today. You previously had some input for the phrasing of our Observations. We will modify them to make the takeaways clearer. In particular, you mentioned Observations 3, 5, and 7. Here are the old and newly proposed versions: >Observation 3: A practitioner utilizing multicalibration post-processing may have to trade off worst group calibration error and overall accuracy. New: A practitioner utilizing multicalibration post-processing could potentially be faced with a trade-off between worst group calibration error and overall accuracy. This is most salient in high calibration fraction regimes (40-80%). >Observation 5: There is no clearly dominant algorithm between HKRR and HJZ on tabular data but HJZ is more robust to choice of hyperparameters. New: When considering statistical significance, there is no clearly dominant algorithm between HKRR and HJZ on tabular data. However, HJZ is more robust to our hyperparameter sweep. This may allow practitioners to find good solutions faster than using HKRR when, for example, post-processing Naive Bayes or Decision Tree predictors. >Observation 7: Multicalibration post-processing can improve worst group smECE relative to an ERM baseline by 50% or more. New: On language and vision data, multicalibration post-processing can improve worst group calibration error relative to neural network ERM baselines by 50% or more. This stands in contrast to multicalibration post-processing for neural network ERM on tabular data, where we found no statistically significant improvements.
In addition, we will also add the following explicit discussion section to discuss groups. Note that although portions of this are taken from previous responses, there are new discussions sprinkled throughout. We would further like to highlight that the way we construct groups is standard, used by large production systems such as LinkedIn [4], in the measurement of bias in NLP systems [6], and in the auditing of deployed ML systems [2, 3]. **Group Design and Limitations of Findings** Multicalibration requires the selection of “groups” or subsets of the population of interest. In most practical applications, these subgroups are given by features of the input, or simple conjunctions of features. This way of constructing groups is standard, used by large production systems such as LinkedIn [4], in the measurement of bias in ML [7, 8] and NLP systems [1, 6], and in the auditing of deployed ML systems like Facebook and LinkedIn [2, 3]. Furthermore, this approach still takes advantage of the group intersectionality notions (Ovalle et al.) that multigroup fairness is known for (Hébert-Johnson et al.). For our tested tabular datasets, we determined groups by such “sensitive” attributes—individual characteristics against which practitioners would not want to discriminate. In many cases, such attributes naturally include race, gender, and age, and vary with available information. For example, on ACS Income, we include groups such as “Multiracial”, “American Indian”, and “Seniors”. We also include some groups which are conjunctions of two attributes, for example “Black Women” or “White Women”. On Credit Default, for example, we include groups such as “Education = High School, Age > 40”, or “Married, Age > 60”. Similar groups are used throughout all the tabular data, as well as CelebA. On datasets where samples are not in correspondence with individuals—Camelyon17, Amazon Polarity, and Civil Comments—we define groups based on available information that can be viewed as “sensitive” with respect to the underlying task. In other words, we define groups such that an individual or institution using a predictor which is miscalibrated on this group may be seen as discriminating against the group. Ideally, a social media service will not be underconfident when predicting the toxicity of posts mentioning a minority identity group; such predictions may allow hate speech to remain on the platform. Thinking along this vein, we include “Muslim”, “Black”, and various other phrases defining protected groups in the Civil Comments dataset. Similarly, one would want a shopping platform to promote product listings fairly: a predictor which outputs mis-multicalibrated product ratings may boost listings for technology products proportionally to their true ratings but unfairly ignore the positive reviews of book listings. Thus, some groups from the Amazon Polarity dataset we used are defined as reviews containing the phrases “book”, “food”, “exercise”, or “tech”. There are (at least) two important properties of groups: group size and group “complexity”. The minimum group size $\gamma \in [0,1]$ is a parameter which has implications for the overall sample complexity of multicalibration (in particular, it introduces a $1/\gamma$ factor into known sample complexity upper / lower bounds. $\gamma$ is the size --- as a fraction of the dataset — of the smallest group in the collection). For this reason, we restricted ourselves to groups which were >0.5% of the entire dataset: without enough samples from a particular group, known multicalibration algorithms are prone to overfitting the training set and not providing any generalization performance. The increasing complexity of intersectional groups is a known issue, even at the scale of companies like LinkedIn [4]. Note that we consider groups spanning 0.5% all the way to 70-80% of the data. We deem this variety (details in appendix C.4) sufficient to capture the varying sizes. Group “size” can also be thought of as somewhat correlated with group complexity: one can imagine that some (but not all) sufficiently small groups are defined by more complex (boolean) functions of the features. (... continued in next response ...)
(...continued from previous response...) More broadly, group “complexity” is more difficult to capture. For imperfect predictors, we can (nearly) always construct groups for which the predictor is not multicalibrated against. These groups may be as complex as the underlying predictor (since they can, for example, capture where the predictor misclassified test points). However, it is not clear whether this is a meaningful set of groups to multicalibrate against. To avoid such discussion, we intentionally determine groups by available features which we hypothesize practitioners may deem important or “sensitive” to the underlying prediction task. This is standard in the literature (see, e.g., [1,2,3,5]). As a consequence of these group selection criteria, our results only apply to these sensitive groups about which a practitioner would be concerned in practice. Theoretical analyses consider multicalibration on worst-case groups from an infinite set; in practice, this perspective is overly pessimistic. Observations of poor multicalibration with respect to our “simple” groups are not fruitless either; conditioned on such observations, multicalibration with respect to the more complex groups seems unlikely. If sample complexity is already an issue with simpler groups, it will only become more of a problem as group complexity increases (and group size shrinks even further). It is entirely possible that defining more complex, but perhaps less practically motivated, group collections — e.g., the collection of all halfspaces — would yield different results than ours, and this remains an interesting direction for future work. We do not believe, however, that such possibilities detract from our overall message meant for practitioners using finite collections of groups defined from potentially sensitive features. [1]: Baldini et al. Your fairness may vary: Pretrained language model fairness in toxic text classification. [2]: Ali et al. Discrimination through Optimization: How Facebook’s Ad Delivery Can Lead to Biased Outcomes. [3]: Imana et al. Auditing for Racial Discrimination in the Delivery of Education Ads. [4]: Quiñonero-Candela et al. Disentangling and Operationalizing AI Fairness at LinkedIn. [5]: Czarnowska et al. Quantifying Social Biases in NLP: A Generalization and Empirical Comparison of Extrinsic Fairness Metrics. [6]: Li et al. A Survey on Fairness in Large Language Models. [7]: Tifrea et al. FRAPPE: A Group Fairness Framework for Post-Processing Everything [8]: Atwood et al. Inducing Group Fairness in LLM-Based Decisions >W5: The authors likely mean standard error, not standard deviation. We explicitly compute standard deviation in line 191-201 of our attached supplemental code file scripts/results.py using the empirical standard deviation formula: for m in metric_suffixes: # mean s = sum([run[m] for run in metrics[cf][alg_type][param_idx]]) n = len(metrics[cf][alg_type][param_idx]) mean[m] = s / n # standard deviation sq_diff = sum([(run[m] - mean[m])**2 for run in metrics[cf][alg_type][param_idx]]) sd[m] = (sq_diff / n) ** 0.5 Further, we plot using matplotlib.axes.Axes.errorbar, using the (explicitly computed) standard deviation as the yerr parameter. To generate Figure 3, for example, please see the function `increasing_CF_helps_mcb_algs’ in generate_figures.py line 37. Here, we call the code from results.py to get the means and standard deviations, then use matplotlib.axes.Axes.errorbar to plot the error bars in lines 96 and 108. We really appreciate the reviewer taking time and engaging with our discussion, and believe that the paper will greatly benefit from their input. We can certainly incorporate any additional feedback if requested!
I appreciate the additional work the authors have done. The rephrasing and experiments on groups have resolved my concerns. I will raise my score.
We thank the reviewer for their continued engagement and input in our work!
Thank you for your detailed response! Regarding Q1: I believe it would be beneficial to make this point clear in the final version. Regarding Q3: Yes, I definitely think it would be useful to include this in the discussion. Regarding Q4: It's important to be careful when stating observations and to list results across all datasets in the main paper so that readers can easily verify them. I agree with reviewer rHYn’s point that "However, in most cases, it's unclear why and when these statements hold true," and "Therefore, I suggest the authors carefully reconsider how each statement is phrased." I'm glad to see the authors provided a detailed response to this. Overall, while some of the reasoning behind the observations remains unclear, given that this paper is the first comprehensive study to evaluate different multicalibration methods and includes a large number of experiments, and considering that the authors plan to include additional discussion based on feedback from the reviewers, I will raise my score to 5.
Thank you for your response and engagement! To address your Q4, we will better compress the results from all datasets in the main body as discussed in M2Di weakness 1. We appreciate the feedback and believe it will result in improvements to the presentation!
Additional Experiments with Different and More "Complex" Groups
As requested, we ran some additional experiments for MLPs on the tabular datasets with different --- and in some cases, more complex --- groups. We present a few of the experiments here, and echo takeaways relative to the old experiments (with different group definitions). Unfortunately, we can no longer submit a PDF anywhere, so have included the results as markdown tables. Due to character limits, these tables may have to be split among multiple respones. Overall, the takeaway for MLPs largely remains the same: it is difficult to find instances where multicalibration helps in a statistically significant way over ERM or some form of simple calibration (Observations 1 and 2). Further, where multicalibration does help, this help sometimes comes at a cost to accuracy (Observation 3). For each dataset, we include the "initial" results which are in our submitted draft, and new results which we ran at the reviewers requests. ## ACS Income ### Group definitions: initial | group name | n samples | fraction | y mean | |:----------------|------------:|-----------:|---------:| | Black Adults | 8508 | 0.0435 | 0.3461 | | Black Females | 4353 | 0.0222 | 0.3193 | | Women | 92354 | 0.472 | 0.3491 | | Never Married | 68408 | 0.3496 | 0.2344 | | American Indian | 1294 | 0.0066 | 0.2836 | | Seniors | 14476 | 0.074 | 0.541 | | White Women | 55856 | 0.2855 | 0.3729 | | Multiracial | 8206 | 0.0419 | 0.3572 | | Asian | 32709 | 0.1672 | 0.4805 | | Dataset | 195665 | 1 | 0.4106 | ### Group definitions: new | group name | n samples | fraction | y mean | |:-------------------------|------------:|-----------:|---------:| | associates degree male | 7331 | 0.0375 | 0.4957 | | associates degree female | 8372 | 0.0428 | 0.3186 | | divorced female | 10652 | 0.0544 | 0.4415 | | under part time | 16525 | 0.0845 | 0.1025 | | part time | 55269 | 0.2825 | 0.1408 | | full time | 135989 | 0.695 | 0.5214 | | over full time | 11471 | 0.0586 | 0.6441 | | not white | 74659 | 0.3816 | 0.3574 | | government employee | 29121 | 0.1488 | 0.5337 | | private employee | 166544 | 0.8512 | 0.389 | | under 21 | 10166 | 0.052 | 0.0106 | | middle aged | 81582 | 0.4169 | 0.5064 | | Dataset | 195665 | 1 | 0.4106 |
### ACSIncome Results: initial | Model | ECE | Max ECE | smECE | Max smECE | Acc | |:-------------|:------------------------------------------------|:-------------------------------------------------|:-------------------------------------------------|:-------------------------------------------------|:-------------------------------------------------| | MLP ERM | 0.01 ± 0.003 | 0.069 ± 0.011 | 0.012 ± 0.003 | 0.058 ± 0.005 | **0.812 ± 0.001** | | MLP HKRR | 0.023 ± 0.001 | **0.065 ± 0.004** | 0.023 ± 0.001 | 0.063 ± 0.002 | 0.615 ± 0.0 | | MLP HJZ | 0.01 ± 0.002 | 0.069 ± 0.008 | 0.013 ± 0.001 | **0.055 ± 0.004** | 0.81 ± 0.002 | | MLP Platt | 0.017 ± 0.009 | 0.076 ± 0.008 | 0.018 ± 0.008 | 0.064 ± 0.008 | 0.809 ± 0.003 | | MLP Temp | 0.011 ± 0.005 | 0.068 ± 0.01 | 0.013 ± 0.004 | 0.059 ± 0.007 | 0.811 ± 0.001 | | MLP Isotonic | **0.01 ± 0.001** | 0.067 ± 0.008 | **0.011 ± 0.001** | 0.057 ± 0.002 | 0.811 ± 0.001 | ### Results: new | Model | ECE | Max ECE | smECE | Max smECE | Acc | |:-------------|:-------------------------------------------------|:-------------------------------------------------|:-------------------------------------------------|:-------------------------------------------------|:-------------------------------------------------| | MLP ERM | 0.014 ± 0.005 | 0.059 ± 0.007 | 0.015 ± 0.004 | 0.059 ± 0.008 | 0.811 ± 0.002 | | MLP HKRR | **0.009 ± 0.003** | **0.037 ± 0.005** | **0.009 ± 0.003** | **0.035 ± 0.003** | 0.803 ± 0.001 | | MLP HJZ | 0.019 ± 0.003 | 0.053 ± 0.01 | 0.02 ± 0.002 | 0.051 ± 0.011 | 0.807 ± 0.004 | | MLP Platt | 0.012 ± 0.004 | 0.046 ± 0.008 | 0.014 ± 0.002 | 0.044 ± 0.007 | 0.811 ± 0.001 | | MLP Temp | 0.012 ± 0.005 | 0.056 ± 0.005 | 0.013 ± 0.004 | 0.056 ± 0.005 | 0.811 ± 0.001 | | MLP Isotonic | 0.012 ± 0.002 | 0.055 ± 0.005 | 0.013 ± 0.001 | 0.054 ± 0.006 | **0.811 ± 0.001** | ## Takeaways: Old groups: (Observation 1) Multicalibration does not improve upon ERM in a statistically significant way. Note here also the poor performance in accuracy of HKRR in the results included in the paper. This is because we selected the best performing hyperparameter based on worst group smECE, which does not prioritize accuracy. However, there is another choice of hyperparameters which performs slightly worse for worst group smECE on the validation (and test) set, but achieves competitive accuracy of around 0.80. Furthermore, this relates to tradeoffs discussed in Observation 3. We will note this in the next draft as well. New groups: Multicalibration does not improve upon ERM + Platt scaling in a statistically significant way (Observation 1 and 2).
Response to Authors
Thank you for your responses to me and to the other reviewers, as well as for the general response. There, you gave several more experiments that are good to see, and provided several detailed discussions of the various moving parts involved in evaluating the benefits of multicalibration on various kinds of data; I agree with most of your points there. One "fine-print" point that I would like to highlight is that when you say that you will clarify that your work focuses on feature-defined groups that would be useful to practitioners --- as opposed to various potentially more convoluted group families such as ones that might predict which region in the data the predictor might be miscalibrated on --- it is important to further stress that these two categories of group families are not entirely disconnected from each other. Indeed, for some less-fancy (and even some fancy) predictors that people may be using in practice, it could well be the case that one might be able to "eyeball" (or deduce on a small holdout set) some feature-defined groups that would also explicitly target the model's inaccurate predictions region --- e.g. one might suspect that the model mispredicts a lot on some unprotected but still natural demographic group, and include that group in the family. Such a scenario would fall squarely into the "practical" category of applications of multicalibration, and thus cannot be discounted. Therefore, I urge you to be careful in your formulation of what kinds of groups your paper considers --- given my above point, I would refrain from saying that your statements are made about the general class of intuitive feature-based groups that practitioners might use, and steer it more into the direction of saying that you consider group families that may seem inherently important to protect regardless of which predictor is used on the data. (Again, to reiterate, my point is: just like the groups you experiment with, groups that capture inefficiencies of the predictor don't have to be complex or unnatural; they may well be feature-defined and relatively natural, and practitioners may intentionally or unintentionally come across such groups.) Also, I would place extra emphasis in the revision on the fact that "practitioners" refers to something like "fairness practitioners"; indeed empirical research in other areas may lead to other groups being used, that this paper was not focusing on. Finally, regarding raising my score, as it stands, there are many key updates needed in terms of the phrasing of the paper's setting and of its takeaways and of its literature connections etc., and while I believe the authors are on the right track in terms of this, judging by the rebuttal discussions, but the result of incorporating so many of these updates will inherently be high-variance in terms of the ensuing readability, focus etc of the updated paper. In this way, I am feeling more positive about this paper now but I am still in the "borderline" region; so I hope this explains why I would prefer to keep my current score.
Thank you again for these points and all of your thoughtful feedback. They will certainly help improve the clarity of discussion and limitations in our next draft!
Apologies for the late reply. Thank you for these clarifying points! I'll be keeping my score, but believe that adding the additional experiments and improved group descriptions to the paper would greatly improve the clarity.
Decision
Accept (poster)