Paper: Experimental methodology to evaluate the effectiveness of uncertainty disentanglement on regression models (ICLR-2024)

Reviewer comment (Writing):
There is a lack of clarity in the story of this paper, and what the authors consider their main contributions. In the introduction, they state that "In this article, we seek to bridge this gap by introducing a dUQ evaluation methodology providing a comprehensive benchmark of various typologies of UQ models." but later on, in section three, they state that "The experimental goal is to highlight an epistemic confidence gap in model predictions, between nominal and altered queries (i.e. affected by injections of epistemic uncertainty)."

Author response:
W1) Indeed, the link is not necessarily clear: starting from the assumption established in Section 4.1 that the 4 models produce a relevant uncertainty quantification, we then use "epistemic confidence gap" due to our epistemic uncertainty injection mechanism as an evaluation tool (dE-ind shift measure) to characterize the "UQ disentanglement relevance". Furthermore, we investigate whether the disentangled epistemic component makes sense.

Reviewer comment (Presentation):
The paper has an entire section dedicated to training epistemic injections, but this is never mentioned before as a part of their contribution or utility. The beginning of the paper makes it seem like they offer an evaluation of modern methods, but this along with the meta-model seem to be proposing training procedures?

Author response:
W3) There may be some confusion due to the use of the term "training epistemic injection", which simply refers to the step where the injection takes place. The training-step injection is a scheme of evaluation that requires alteration of a subpart of the dataset during training. In contrast to adversarial learning, at this time, we do not envisage a (meta)-model learning procedure incorporating epistemic injection mechanisms, even if the idea makes perfect sense and could arise in the close future.

Reviewer comment (Writing):
Why is the training set parameterized by theta? (above equation 1 on page 3)

Author response:
Q1) The notation is ambiguous: The training set is not “parameterized” but is related to theta. Rather, it should be understood as starting from the sub-set of data called $D_\theta$ according to a type of model $\hat{f}$ (with deterministic optimization procedure), we obtain a trained model $\hat{f}_{\theta}$.

Reviewer comment (Theory):
Is Θ related to all different partitions of a particular dataset, or from the true distribution of data?

Author response:
Q2) Indeed, $\Theta$ is related to all the different partitions of a particular dataset (which corresponds to the observed data used for model training). Moreover, it's the "meeting" between all different partitions and a type of model, which produces all reachable sets of parameters for this considered model in the scope defined by observed data. It is by analyzing the stability of responses on this set of virtual models (in an approximate way) that we can access a form of epistemic confidence measure.

Reviewer comment (Writing):
What is meant above Figure 1 with "the previous negligible terms can then induce blurs into the uncertainty decomposition."?

Author response:
Q3) Deriving equation 2 is made using several assumptions (strong independence and zero-mean), to neglect terms that complexity the decomposition. When these assumptions cease to be valid, the decomposition into epistemic and aleatoric components becomes less obvious in its mathematical form, and the clear line between the two components is blurred by interaction terms. Some additional intuition is provided in Appendix C3

Reviewer comment (Writing):
What is the mentioned variability infusion mechanism referring to?

Author response:
Q4) The variability infusion mechanism mentioned on page 4 is a generic term referring to the fact that uncertainty quantification requires a diversity of predictions to be performed. To do so, there exist several possible mechanisms aiming at "simulating" the variance of model predictions. The choice of mechanism depends on the UQ paradigm and this variability is at the heart of epistemic uncertainty quantification.

Reviewer comment (Writing):
When Meta-models are introduced they are not explained. I see that they are mentioned later in the results section, but at a high level are these supposed to be neural networks?

Author response:
Q5) On page 2, we state that a metamodel is a way to synthesize an ensemble of outputs produced by an ensemble of submodels. Thus, metamodels are not necessarily neural networks. Rather, "metamodel" is a generic term encompassing several ways to compute an epistemic confidence level by aggregating submodels outputs (note that submodels can be neural networks).

Reviewer comment (Presentation):
It's very difficult to parse the analysis for the results in Figure 4. What are the high level takeaways?

Author response:
Q8) Thank you for the feedback. This figure has to be reworked, its main lessons are :  
- a) Proof that experimental setup is coherent:  For an epistemic injection linked to an altered subset, we clearly show that the performances and UQ indicators values (Aleatoric and Epistemics) are close to the non-altered subset for both control and degraded models. In contrast, we observe an impact (performance loss) between the control and degraded model for the altered subset.  
- b) Proof that we can claim a dUQ effectiveness : The degraded model expresses a more significant rise (shift of confidence) of UQ epistemic measure than its aleatoric counterpart. The dE-indicator synthesizes both of these observations in one value.  
- c) Unlike the three other approaches, EDL does not show this expected behavior, which questions the effectiveness of its uncertainty decomposition.

Reviewer comment (Experiments):
In Table 3, what is meant by "no cross validation due to size of the dataset"?

Author response:
Q9) For the year prediction dataset, which is much larger than other public dataset, we did not reproduce the experiments four times for each of our four approaches, so there is no measure of performance deviation.

Reviewer comment (Novelty):
The authors missed a whole section of the literature on calibration for regression models, which covers a highly related task. In particular, [1] demonstrates how calibration quantifies a meaningful tradeoff between sharpness and coverage.

Author response:
W1) Thank you for the reference. We are familiar with the calibration curves and should have mentioned them along with the assessment of total uncertainty. We computed curves of this kind, but we considered that they didn't add any value here, as the question of assessing total uncertainty is secondary (our paper focuses on the epistemic part). However, we disagree in part. Calibration curves, which provide more information than simple X\% coverage, cannot totally replace a sharpness measure: the paper seems to mention that part  "3.1 Paragraph Calibration and Sharpness".

Reviewer comment (Experiments):
It's not clear how the choices of the type of "attack" in the inference step rejection influence the conclusion – surely the way outliers are sampled from the tail (how far) is relevant? Similarly, how altered is the altered dataset and how does this affect conclusions? To me the main contribution is the benchmark study and this would need a much more exhaustive and systematic set of experiments.

Author response:
W3) It is difficult and time-consuming to exploit and interpret the results one by one. But, the aggregation of results nevertheless provides good insight for the comparison between approaches, as it illustrates that the models do not have the same sensitivity to these different kinds of OOD queries. Based on your feedback, we will think about a modification in the choice and presentation of the combinatorial experiments linked to the injection parameters.