Beyond Explaining Predictions: Logic-Based Explanations for Confidence in Machine Learning Models

Carlos Henrique Leit\~ao Cavalcante; Thiago Alves Rocha; Vin\'icius Peixoto Chagas

arxiv: 2606.10347 · v1 · pith:S2KHFUPLnew · submitted 2026-06-09 · 💻 cs.LG · cs.LO

Beyond Explaining Predictions: Logic-Based Explanations for Confidence in Machine Learning Models

Vin\'icius Peixoto Chagas , Carlos Henrique Leit\~ao Cavalcante , Thiago Alves Rocha This is my paper

Pith reviewed 2026-06-27 14:18 UTC · model grok-4.3

classification 💻 cs.LG cs.LO

keywords abductive explanationsminimum confidence thresholdlogic-based explanationsboosted treesmachine learning interpretabilitytrustworthy AIconfidence-aware explanations

0 comments

The pith

Abductive explanations can be made to preserve both the predicted class and a user-specified minimum confidence level.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper defines a Minimum Confidence Threshold (MCT) as the weakest confidence value guaranteed by any instance covered by a standard abductive explanation. It then constructs confidence-aware explanations that are minimal feature sets sufficient to keep both the class and a chosen confidence floor. For boosted trees the authors encode the search for such sets as an optimization problem and solve it with a dedicated algorithm. Experiments indicate that ordinary abductive explanations frequently guarantee far less confidence than the original instance, whereas the new explanations raise that floor while adding only modest extra features.

Core claim

The central claim is that abductive explanations can be extended, via the MCT concept, to guarantee not only correct classification but also a user-chosen lower bound on model confidence, and that this extension can be computed for boosted trees with only a modest increase in explanation size.

What carries the argument

Minimum Confidence Threshold (MCT), the lowest model confidence among all instances that satisfy a given abductive explanation; used to define and compute confidence-aware explanations as minimal feature subsets that meet both class and MCT constraints.

If this is right

Standard abductive explanations can cover instances whose model confidence is lower than the explained instance itself.
Confidence-aware explanations raise the minimum guaranteed confidence while remaining short.
The same formulation applies to any model that outputs calibrated confidence scores.
Such explanations become relevant when decisions require both class correctness and a stated confidence floor.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The approach could be tested on models beyond boosted trees once an efficient solver for the corresponding optimization problem is available.
In high-stakes settings the added confidence guarantee might reduce the need for separate uncertainty quantification steps.
If confidence scores are mis-calibrated, the MCT values would inherit that error and the explanations would lose their intended meaning.

Load-bearing premise

The optimization problem for finding minimal explanations that meet a chosen confidence threshold can be solved without prohibitive cost for the boosted-tree models under study.

What would settle it

A benchmark run on boosted trees in which every confidence-aware explanation either exceeds a modest length bound or fails to raise the guaranteed confidence above that of the corresponding standard abductive explanation.

Figures

Figures reproduced from arXiv: 2606.10347 by Carlos Henrique Leit\~ao Cavalcante, Thiago Alves Rocha, Vin\'icius Peixoto Chagas.

**Figure 1.** Figure 1: Example of a GBT composed of two trees using features from the Iris dataset. Left branches correspond to False outcomes and right branches correspond to True outcomes. First Author et al.: Preprint submitted to Elsevier Page 4 of 22 [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗

**Figure 2.** Figure 2: Example of a tree in a GBT model (left branches correspond to False outcomes, and right branches correspond to True outcomes). First Author et al.: Preprint submitted to Elsevier Page 7 of 22 [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗

**Figure 3.** Figure 3: Confidence gain versus relative explanation growth for instances predicted as class +1. The horizontal axis reports the increase in explanation length normalized by the total number of features in the dataset, while the vertical axis reports the corresponding increase in sigmoid-transformed MCT. Each curve corresponds to confidence thresholds of 25%, 50%, and 75% of the original prediction score and is mea… view at source ↗

**Figure 4.** Figure 4: Confidence gain versus relative explanation growth for instances predicted as class −1. The horizontal axis reports the increase in explanation length normalized by the total number of features in the dataset, while the vertical axis is computed as 𝜎(MCT(𝐶𝐴)) −𝜎(MCT(𝐴𝑋𝑝)). Since lower values indicate stronger confidence guarantees for class −1, more negative values correspond to larger confidence improve… view at source ↗

read the original abstract

Machine learning is increasingly used in critical domains, where both predictions and their associated confidence levels influence important decisions. To enhance transparency in such scenarios, it is important to understand why a model is confident or uncertain about its predictions. Recent logic-based approaches provide abductive explanations, minimal subsets of features sufficient to preserve the predicted class, with correctness guarantees. However, these methods focus solely on classification behavior and may produce explanations that cover instances with low predictive confidence. In this work, we introduce the concept of Minimum Confidence Threshold (MCT), which quantifies the weakest confidence guarantee provided by an abductive explanation. Building upon this concept, we propose confidence-aware abductive explanations, which preserve not only the predicted class but also a user-specified confidence guarantee. We formulate MCT computation as an optimization problem and introduce an algorithm for generating minimal explanations that satisfy a desired confidence threshold. We evaluate the proposed framework on boosted trees for binary classification, although the approach is applicable to other machine learning models that provide confidence scores. Experimental results show that traditional abductive explanations often provide substantially weaker confidence guarantees than the confidence associated with the explained instance itself. In contrast, confidence-aware explanations consistently improve the minimum confidence guaranteed by an explanation while requiring only a modest increase in explanation length. These properties make the proposed approach particularly suitable for applications where both predictive correctness and confidence are essential for trustworthy decision making.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper defines Minimum Confidence Threshold for abductive explanations on boosted trees and shows how to enforce a user threshold, but the practical value hinges on uncalibrated model scores.

read the letter

The new contribution is the Minimum Confidence Threshold concept plus the formulation of confidence-aware abductive explanations. Standard abductive explanations are shown to sometimes guarantee only low minimum confidence across the covered region, while the new variant adds a constraint to meet a chosen threshold and solves for minimal feature sets that satisfy it. The abstract reports that this comes at modest extra length on binary classification tasks with boosted trees.

The work is clear about the gap it targets: explanations that preserve the class label but ignore how confident the model actually is over the explanation region. Framing the task as an optimization problem over the model's output scores is a direct extension of existing abductive methods, and the claim that the approach applies to any model supplying scores is reasonable.

The main limitation is that the entire guarantee rests on the raw boosted-tree probabilities. Boosted trees frequently produce miscalibrated scores, so raising the minimum reported confidence does not automatically strengthen a reliability claim. The abstract gives no indication that calibration was checked or applied before computing the MCT values. Without that step, the experimental comparison between standard and confidence-aware explanations is harder to interpret as a real improvement in trustworthiness.

The paper is aimed at researchers already working on logic-based explanations for tree ensembles. It supplies a concrete new primitive that those readers can test or extend. The idea is coherent on its own terms and engages the prior abductive-explanation literature, so it clears the bar for peer review even if the calibration issue needs attention in revision.

Referee Report

1 major / 1 minor

Summary. The paper introduces the Minimum Confidence Threshold (MCT) to quantify the weakest model-provided confidence guarantee over the region covered by an abductive explanation. It proposes confidence-aware abductive explanations that preserve both the predicted class and a user-specified confidence threshold, formulates MCT computation as an optimization problem, and presents an algorithm for generating minimal such explanations. The approach is evaluated on boosted trees for binary classification; experiments claim that standard abductive explanations often yield substantially lower MCT than the explained instance's own confidence, while the proposed explanations raise the guaranteed MCT with only modest growth in explanation size.

Significance. If the central experimental claims survive scrutiny of the underlying scores, the work would usefully extend logic-based explanation methods to incorporate predictive confidence, addressing a practical need in high-stakes domains. The optimization framing and the reported trade-off between explanation size and MCT improvement are concrete contributions that could be adopted by practitioners working with tree ensembles.

major comments (1)

[Experimental evaluation] The experimental comparison of MCT values (and the claim that confidence-aware explanations 'consistently improve the minimum confidence guaranteed by an explanation') is performed directly on the raw output probabilities of boosted trees. No calibration diagnostics, reliability diagrams, or post-hoc recalibration are reported. Because boosted-tree probabilities are known to be miscalibrated, the observed MCT improvement does not establish a stronger actual reliability guarantee; this directly undercuts the paper's motivation that the method supplies trustworthy confidence assurances in critical domains.

minor comments (1)

The abstract states that the framework applies to 'other machine learning models that provide confidence scores,' yet all reported results are restricted to boosted trees; a short paragraph discussing the additional algorithmic or computational obstacles for other model classes (e.g., neural networks) would strengthen the generality claim.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive feedback on our manuscript. We address the major comment point-by-point below, providing an honest assessment of the concern raised.

read point-by-point responses

Referee: [Experimental evaluation] The experimental comparison of MCT values (and the claim that confidence-aware explanations 'consistently improve the minimum confidence guaranteed by an explanation') is performed directly on the raw output probabilities of boosted trees. No calibration diagnostics, reliability diagrams, or post-hoc recalibration are reported. Because boosted-tree probabilities are known to be miscalibrated, the observed MCT improvement does not establish a stronger actual reliability guarantee; this directly undercuts the paper's motivation that the method supplies trustworthy confidence assurances in critical domains.

Authors: We acknowledge that boosted-tree output probabilities are frequently miscalibrated and that the manuscript reports no calibration diagnostics or recalibration steps. However, the MCT is defined strictly with respect to the model's own provided confidence scores, not as an estimate of true posterior probability. The contribution is to produce explanations that guarantee a user-specified minimum level of the model's reported confidence over the covered region; this property holds regardless of calibration and remains useful for interpreting and constraining model behavior. The motivation in the paper centers on explanations for the confidence values that the model actually outputs, which is a distinct (and still practically relevant) goal from guaranteeing calibrated reliability. We agree that calibration would strengthen real-world trustworthiness and will add an explicit discussion of this limitation, along with suggestions for combining the approach with post-hoc calibration methods, in the revised manuscript. revision: partial

Circularity Check

0 steps flagged

No circularity; definitions and experiments are independent

full rationale

The paper defines MCT directly as the minimum model confidence over the region covered by an abductive explanation and defines confidence-aware explanations as those satisfying an explicit threshold on MCT. These are independent of the evaluation results. The central claims are empirical comparisons on boosted trees showing that enforcing the threshold yields higher MCT at modest length cost. No equations, self-citations, or derivations reduce any result to a fitted parameter or prior self-work by construction. The optimization formulation and experimental protocol stand on external model outputs without self-referential loops.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The central claim rests on the domain assumption that models output usable confidence scores and that an optimization formulation exists for the MCT constraint. No free parameters or invented physical entities are described.

axioms (1)

domain assumption Machine learning models under consideration provide well-defined confidence scores for their predictions.
Required to define and compute the Minimum Confidence Threshold.

invented entities (1)

Minimum Confidence Threshold (MCT) no independent evidence
purpose: Quantifies the weakest confidence guarantee provided by an abductive explanation.
Newly introduced metric to extend standard abductive explanations.

pith-pipeline@v0.9.1-grok · 5786 in / 1193 out tokens · 18068 ms · 2026-06-27T14:18:13.557579+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

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Computing abductive explanations for boosted trees, in: International Conference on Artificial Intelligence and Statistics, PMLR

Audemard, G., Lagniez, J.M., Marquis, P., Szczepanski, N., 2023. Computing abductive explanations for boosted trees, in: International Conference on Artificial Intelligence and Statistics, PMLR. pp. 4699–4711

2023

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Formal xai via syntax-guided synthesis, in: International Conference on Bridging the Gap between AI and Reality, Springer

Bjørner, K., Judson, S., Cano, F., Goldman, D., Shoemaker, N., Piskac, R., Könighofer, B., 2023. Formal xai via syntax-guided synthesis, in: International Conference on Bridging the Gap between AI and Reality, Springer. pp. 119–137

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Decision procedures

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Logic-based explanations of imbalance price forecasts using boosted trees

Lagniez, J., Marquis, P., Toubeau, J.F., 2024. Logic-based explanations of imbalance price forecasts using boosted trees. Electric Power Systems Research 235, 110699

2024

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Concerning uncertainty–a systematic survey of uncertainty-aware xai

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arXiv 2026

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Calibrated explanations: With uncertainty information and counterfactuals

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A unified approach to interpreting model predictions, in: 31st NeurIPS, p

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Randal Olson, William La Cava, Patryk Orzechowski, Ryan Urbanowicz, and Jason Moore

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why should I trust you?

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Pith/arXiv arXiv 2016

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Anchors: high-precision model-agnostic explanations, in: 32nd AAAI, pp

Ribeiro, M.T., Singh, S., Guestrin, C., 2018. Anchors: high-precision model-agnostic explanations, in: 32nd AAAI, pp. 1527 – 1535

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Generalizing logic-based explanations for machine learning classifiers via optimization

Rocha Filho, F.M., da Rocha Neto, A.R., Rocha, T.A., 2025. Generalizing logic-based explanations for machine learning classifiers via optimization. Expert Systems with Applications 289, 128313

2025

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Rudin, C., 2019. Stop explaining black box machine learning models for high stakes decisions and use interpretable models instead. arXiv:1811.10154

arXiv 2019

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Select wisely and explain: Active learning and probabilistic local post-hoc explainability, in: Proceedings of the 2022 AAAI/ACM Conference on AI, Ethics, and Society, pp

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