Dirichlet-Based Monte Carlo Dropout for Uncertainty Estimation in Neural Networks

Noura Dridi (FEMTO-ST); Noureddine Zerhouni (FEMTO-ST); Rouaa Hoblos (FEMTO-ST); Zeina Al Masry (FEMTO-ST)

arxiv: 2605.23635 · v1 · pith:ZK72IZVGnew · submitted 2026-05-22 · 📊 stat.ML · cs.LG

Dirichlet-Based Monte Carlo Dropout for Uncertainty Estimation in Neural Networks

Rouaa Hoblos (FEMTO-ST) , Noura Dridi (FEMTO-ST) , Noureddine Zerhouni (FEMTO-ST) , Zeina Al Masry (FEMTO-ST) This is my paper

Pith reviewed 2026-05-25 03:10 UTC · model grok-4.3

classification 📊 stat.ML cs.LG

keywords uncertainty estimationMonte Carlo DropoutDirichlet distributionneural networksmodel calibrationBayesian approximation

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The pith

Integrating Dirichlet distributions into Monte Carlo Dropout produces better calibrated uncertainty estimates without added computation.

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

The paper seeks to improve uncertainty quantification in neural networks by embedding a Dirichlet-based model of class probabilities inside the stochastic forward passes of MC Dropout. Standard MC Dropout approximates Bayesian inference at low cost but often yields poorly calibrated uncertainties. Modeling outputs via a Dirichlet distribution supplies a more informative representation of uncertainty while preserving the original computational profile. Comparisons with other quantification methods show the combined approach achieves better calibration on the tested tasks. A reader would care because many real-world applications need reliable confidence measures to decide when to trust a prediction.

Core claim

By replacing the usual softmax output with a Dirichlet distribution inside each MC Dropout forward pass, the method produces uncertainty estimates that are better calibrated than those obtained from vanilla MC Dropout or several competing techniques, all while retaining the same number of stochastic evaluations.

What carries the argument

The Dirichlet distribution over class probabilities, substituted for the point-estimate softmax inside each stochastic forward pass of MC Dropout.

If this is right

Uncertainty estimates remain computationally cheap because only the same number of forward passes is needed.
No extra training data or calibration dataset is required beyond what MC Dropout already uses.
The resulting probabilities are more suitable for downstream decisions that depend on reliable confidence scores.
The approach can be swapped into existing MC Dropout pipelines with only a change in the output distribution.

Where Pith is reading between the lines

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

The same substitution might be tried in regression settings if the Dirichlet construction is replaced by an appropriate distribution over continuous outputs.
Improved calibration could reduce false positives in out-of-distribution detection pipelines that rely on uncertainty thresholds.
Because the change is local to the output layer, it could be combined with other low-cost Bayesian approximations without redesigning the entire network.

Load-bearing premise

The Dirichlet formulation from prior work slots directly into MC Dropout's existing stochastic passes and improves calibration with no further data assumptions or post-processing required.

What would settle it

A side-by-side evaluation on standard classification benchmarks in which the proposed method shows no gain in calibration error metrics over ordinary MC Dropout would falsify the central claim.

Figures

Figures reproduced from arXiv: 2605.23635 by Noura Dridi (FEMTO-ST), Noureddine Zerhouni (FEMTO-ST), Rouaa Hoblos (FEMTO-ST), Zeina Al Masry (FEMTO-ST).

read the original abstract

Traditional neural networks provide deterministic predictions without inherent uncertainty estimates. While Bayesian Neural Networks (BNNs) offer a principled approach to uncertainty quantification, their computational complexity limits scalability. Monte Carlo (MC) Dropout, initially introduced as a regularization technique, has been shown to approximate Bayesian inference by enabling probabilistic modeling through multiple stochastic forward passes. In this work, we enhance uncertainty estimation in deep learning by integrating a Dirichlet-based framework within MC Dropout. Specifically, we leverage the formulation proposed by Sensoy et al. (2018), where class probabilities are modeled using a Dirichlet distribution, allowing for a more informative uncertainty representation. The proposed approach maintains the computational efficiency of MC Dropout while improving the quality of uncertainty estimates. We discuss the theoretical foundations of our method and compare it with existing uncertainty quantification techniques. The results highlight the effectiveness of the proposed method in producing well-calibrated uncertainty estimates, offering a practical solution for uncertainty-aware deep learning models.

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

This paper applies Sensoy et al.'s Dirichlet model to MC Dropout without new derivations or evidence.

read the letter

The main point to know is that this paper takes the Dirichlet-based uncertainty from Sensoy et al. 2018 and applies it inside MC Dropout stochastic forward passes. That's the extent of the novelty as described. What the work does reasonably is preserve the low computational cost of MC Dropout while aiming for better uncertainty quality. Mentioning the theoretical foundations and comparisons to other methods shows some engagement with the literature. The soft spots are the lack of any concrete evidence. The abstract states the effectiveness but gives no experimental details, no data on calibration metrics, no baselines, and no indication of how the Dirichlet parameters are handled during the multiple passes. Without those, the improvement claim can't be evaluated. The approach seems to inherit all its math from the 2018 paper, so the circularity is real and the contribution reduces to an integration exercise. The stress-test note says no internal inconsistency was found after reviewing the manuscript description, and that seems accurate based on the abstract. The method aligns with the claim without hidden contradictions. Still, alignment with its own terms is not the same as having substance or new insight. This kind of paper might appeal to engineers already running MC Dropout in production who want a drop-in way to get Dirichlet-style uncertainty. It won't move the needle for researchers focused on new theoretical developments or scalable Bayesian methods. I would not send this to peer review. The combination is straightforward and the supporting material is missing, so it doesn't meet the bar for referee attention.

Referee Report

2 major / 1 minor

Summary. The paper proposes integrating the Dirichlet distribution formulation from Sensoy et al. (2018) into the MC Dropout framework to model class probabilities and improve uncertainty calibration in neural networks, while preserving the computational efficiency of multiple stochastic forward passes. It claims to discuss theoretical foundations, compare with existing techniques, and demonstrate effectiveness via well-calibrated uncertainty estimates.

Significance. If the integration yields measurable improvements in calibration metrics without added cost or assumptions, the work could offer a practical extension for uncertainty-aware models in deep learning. However, the significance is limited by the direct reliance on the 2018 Dirichlet prior without apparent new derivations or parameter-free elements, and the absence of any reported experiments, baselines, or error analysis in the provided text makes it difficult to evaluate impact.

major comments (2)

[Abstract] Abstract: the central claim that the method produces 'well-calibrated uncertainty estimates' and 'improving the quality of uncertainty estimates' is unsupported, as no quantitative results, datasets, baselines (e.g., standard MC Dropout or evidential deep learning), calibration metrics (e.g., ECE), or experimental protocol are provided; this is load-bearing for the contribution.
[Abstract] Abstract: the description states that the approach 'leverages the formulation proposed by Sensoy et al. (2018)' but gives no indication of any modification to the Dirichlet parameters, the stochastic forward-pass procedure, or the loss; without this, it is unclear whether the method reduces to a direct re-application rather than a novel integration.

minor comments (1)

The manuscript should explicitly state any new assumptions required for the Dirichlet-MC Dropout combination (e.g., on the concentration parameters during sampling) and include at least one worked example or pseudocode for the modified forward pass.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for the detailed comments. We address each major point below and agree that the abstract requires revision to avoid unsupported claims and to clarify the integration details. The manuscript text provided to the referee consists of the abstract only, which references results without including supporting experiments.

read point-by-point responses

Referee: [Abstract] Abstract: the central claim that the method produces 'well-calibrated uncertainty estimates' and 'improving the quality of uncertainty estimates' is unsupported, as no quantitative results, datasets, baselines (e.g., standard MC Dropout or evidential deep learning), calibration metrics (e.g., ECE), or experimental protocol are provided; this is load-bearing for the contribution.

Authors: We agree that the abstract's claims about well-calibrated uncertainty estimates lack supporting quantitative evidence in the provided manuscript text. The abstract references results and comparisons with existing techniques, but no datasets, baselines, metrics such as ECE, or experimental protocol appear in the text. We will revise the abstract to remove or qualify these claims until the full experimental section can be included, and we will add a brief experimental summary if space permits in a revised version. revision: yes
Referee: [Abstract] Abstract: the description states that the approach 'leverages the formulation proposed by Sensoy et al. (2018)' but gives no indication of any modification to the Dirichlet parameters, the stochastic forward-pass procedure, or the loss; without this, it is unclear whether the method reduces to a direct re-application rather than a novel integration.

Authors: The proposed integration applies the Dirichlet modeling of class probabilities from Sensoy et al. (2018) inside the MC Dropout procedure by deriving concentration parameters from the distribution of outputs across multiple stochastic forward passes. This allows uncertainty to be represented via the Dirichlet rather than direct softmax outputs. However, the abstract provides no explicit description of how the parameters are estimated from the MC samples, whether the loss function is modified, or other procedural changes. We will revise the abstract and expand the methods section to detail these steps and highlight the specific combination with MC Dropout. revision: yes

standing simulated objections not resolved

Absence of any reported experiments, baselines, or error analysis in the provided manuscript text, which prevents empirical evaluation of the claimed improvements in calibration.

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The paper's central step is the integration of the Dirichlet distribution formulation from the external reference Sensoy et al. (2018) into standard MC Dropout stochastic forward passes. This is an application of a prior independent result rather than any self-definitional loop, fitted-input prediction, or load-bearing self-citation chain. No equation or claim in the provided abstract or description reduces the new method to a renaming or re-derivation of its own inputs; the efficiency and calibration claims remain externally falsifiable against standard benchmarks without requiring the paper's own fitted values.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only the abstract is available, so no free parameters, axioms, or invented entities can be identified from the provided text.

pith-pipeline@v0.9.0 · 5713 in / 977 out tokens · 27881 ms · 2026-05-25T03:10:21.591359+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

9 extracted references · 9 canonical work pages

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Radford M. Neal. Bayesian learning for neural networks. 1995

work page 1995

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Simple and scalable predictive uncertainty estimation using deep ensembles

Balaji Lakshminarayanan, Alexander Pritzel, and Charles Blundell. Simple and scalable predictive uncertainty estimation using deep ensembles. Advances in neural information processing systems, 30, 2017

work page 2017

[3] [3]

Predictive uncertainty estimation via prior networks

Andrey Malinin and Mark Gales. Predictive uncertainty estimation via prior networks. Advances in neural information processing systems , 31, 2018

work page 2018

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Dropout as a bayesian approximation: Representing model uncertainty in deep learning

Gal.Y and Ghahramani.Z. Dropout as a bayesian approximation: Representing model uncertainty in deep learning. 2016

work page 2016

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Evidential deep learning to quantify classification uncertainty

Murat Sensoy, Lance Kaplan, and Melih Kandemir. Evidential deep learning to quantify classification uncertainty. Advances in neural information processing systems , 31, 2018

work page 2018

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Information aware max-norm dirichlet networks for predictive uncertainty estimation

Theodoros Tsiligkaridis. Information aware max-norm dirichlet networks for predictive uncertainty estimation. Neural Networks, 135:105–114, 2021

work page 2021

[7] [7]

Estimating a dirichlet distribution, 2000

Thomas Minka. Estimating a dirichlet distribution, 2000

work page 2000

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Subjective Logic: A formalism for reasoning under uncertainty

Audun Jsang. Subjective Logic: A formalism for reasoning under uncertainty . Springer Publishing Company, Incorporated, 2018

work page 2018

[9] [9]

Springer, 1977

Michel Lo` eve and M Lo` eve.Elementary probability theory. Springer, 1977. JdS2025 6

work page 1977