How Much Imprecision is Enough Imprecision in my Classifier? A Practical Elicitation Procedure

1 Introduction

• Uncertainty research includes set-valued predictions alongside uncertainty measures, evidential methods, and Bayesian deep learning.Set-valued approaches include conformal methods, utilities over sets, credal sets, and skeptical inference.Source: §1 · pp. 1–2
• Set-valued predictions must balance accuracy, which requires containing the true class, against informativeness, which favors smaller sets.The paper identifies valuation functions as necessary both to define an optimal classifier and to select promising prediction sets for users.Source: §1 · p. 2
• Parametric utility functions can set the trade-off between accuracy and informativeness, while proper scoring rules for convex probability sets address a distinct problem.Utilities for set-valued predictions may arise from credal sets or other approaches.Source: §1 · p. 2
• Existing approaches do not provide an operational way to choose the trade-off parameter, which depends on user attitude toward imprecision and the application context.The paper therefore seeks to elicit that value from end-users.Source: §1 · p. 2

2 Set-valued classifiers

• A set-valued classifier outputs a subset of the label space for each input instance.The framework assumes inputs and labels are drawn from a distribution over their product space.Source: §2 · p. 2
• The user’s unknown weak ordering expresses preferences among classifiers, which the paper aims to uncover through an operational elicitation procedure.In practice, elicitation uses finite observed data and trained models rather than access to the underlying distribution or an unlimited model space.Source: §2 · pp. 2–3
• A parametric utility represents preferences numerically: a classifier is preferred when its expected utility is higher, and elicitation seeks the utility’s form.The paper applies this approach to set-valued prediction.Source: §2 · p. 3
• The illustrated classifiers span informative but error-prone predictions and less informative predictions that capture the true class on displayed instances.Intermediate classifiers can be difficult to compare.Source: §2 · p. 3, Figure 1 · p. 3

3.1 Some instance-wise, qualitative aspects

• Instance-wise preferences are clear when one prediction is correct and the other wrong, or when both are correct and one prediction set is a strict subset of the other.When the predictions are harder to compare, the presented instances should cover varied situations; otherwise the selected subset can skew preferences toward one classifier.Source: §3.1 · pp. 4–5

3.2 Numerical elicitation

• Numerical elicitation seeks the user’s unknown preferred utility parameter θ* by presenting classifier comparisons that can narrow its possible range, typically by half.The procedure assumes a single-parameter utility and uses empirical utility comparisons on a subset of instances.Source: §3.2 · pp. 5–6

3.3 Batch approach

• To help users compare models’ general behavior and reveal decision-maker preferences, the method selects typical scenarios—predictions on subsets of instances—and represents each model by its confusion matrix on a hypothetical dataset D′.Source: §3.3 · p. 7
• The batch approach may lack a matching data subsample, requires choosing among infinitely many solutions, and can ask non-experts to compare proportions rather than instances.The study leaves open whether incorrect predictions should receive non-null utility, or correct predictions non-zero loss.Source: §3.3 · p. 8, §3.4 · p. 9

3.4 Iterative construction procedure

• The iterative procedure builds actual comparison examples, assuming the test set contains enough instances where the two classifiers differ.The procedure can be sped up by restricting the test set to instances on which their predictions differ; the classifiers should be reasonably good but not perfect.Source: §3.4 · pp. 9–10

4 Related works

• Metric elicitation addresses point-prediction classification, whereas this approach elicits preferences for set-valued predictions.The related work considers linear and linear-fractional metrics based on confusion-matrix values.Source: §4 · p. 10
• For catastrophic errors, decision makers may need to elicit utilities for specific cautious prediction sets, beyond identifying utility-function parameters [12].The paper describes this setting as more involved.Source: §4 · p. 11
• Credal proper-scoring work [18] [5] explores truthful probability sets, but the closest work [18] remains mainly theoretical and lacks a fully operational elicitation protocol.Unlike that work, this approach is agnostic to how set-valued predictions are produced.Source: §4 · p. 11

5 Experimental results

• The six datasets comprise four UCI tabular datasets and two image datasets, with XGBoost classifiers for tabular data and neural networks with NDC predictions for images.The tabular data use a 70/30 train-test split; image predictions vary the desired Recall–Precision trade-off.Source: §5 · pp. 11–12
• The interval size converges exponentially toward the target parameter; actual progress deviates slightly from ideal halving because of tolerance ϵ.Figure 3 plots interval size on a logarithmic scale across iterations for six datasets.Source: Figure 3 · p. 12, §5 · p. 13
• At most 12 examples were needed in the tested cases, and the procedure converged successfully across all six datasets.Table 1 reports sample counts by iteration and dataset.Source: §5 · pp. 12–13, Table 1 · p. 12
• Fashion-MNIST examples at α*=1.4 and α*=2.2 show paired predictions from precise and possibly imprecise classifiers for user preference elicitation.The examples illustrate accuracy–informativeness trade-offs presented to users.Source: §5 · p. 13, Figure 4 · p. 13

• The paper introduces ways to elicit users’ acceptable robustness and illustrates them with a commonly used utility function whose Δ(h, h′) = 0 can be solved efficiently.Source: §6 · p. 13
• Incremental elicitation presents the decision maker with a reasonable number of specific instances.Source: §6 · p. 14
• Experiments with actual users are a proposed follow-up; Table 1 indicates an acceptable burden for those users.Source: §6 · p. 14
• The discussion raises whether set-valued utility extensions of 0/1 utility should be null when the predicted set excludes the ground-truth class.Source: §6 · p. 14