Distinguishing Two Dimensions of Uncertainty

Some time ago already, Gal & Ghahramani published their Dropout as Bayesian Approximation paper, and a few more follow-up papers by Gal and colleagues about epistemic vs. aleatoric risks etc. There they claim that test-time dropout can be seen as Bayesian approximation to a Gaussian process related to the original network. (I would not claim to understand the proof in all of its details.) So far so good, but at the Bayesian DL workshop at NIPS2016 Ian Osband of Google DeepMind published his note Risk versus Uncertainty in Deep Learning: Bayes, Bootstrap and the Dangers of Dropout, where he claims that even for absurdly simple networks you can analytically show that the 'posterior' you get using MC dropout doesn't concentrate asymptotically -- which I take as saying that there's no Bayesian approximation happening, since almost any reasonable prior on the weights should lead to a near-certain posterior in the limit of infinite data.
Alas, there are still papers popping up using the MC dropout approach, without even mentioning Osband's note. Did I miss something? Is there a follow-up to Osband's note? A rebuttal? I didn't attend NIPS2016, and I am thus not aware of any discussions that might have happened there, but would certainly appreciate any pointers (-- and given that Yarin Gal was co-organizing that workshop, I am pretty sure that he has seen Osband's note).
Edit: For completeness, here is Yarin Gal's thesis on this topic and the appendix to their 2015 paper containing the proof. Additionally, the supplementary material (section A) of Deep Exploration via Bootstrapped DQN contains some more of Ian's thoughts on this issue

aleatoric uncertainty vs epistemic uncertainty video

Aleatoric uncertainty is related to data and increases with the increase of noise in the observations, which can cause class overlap. On the other hand, epistemic uncertainty is related to the model and the knowledge that is given to it. This uncertainty increases with test samples inout-of-distribution (OOD)regions, and it captures the lack of Uncertainty can be separate into two parts: aleatoric uncertainty and epistemic uncertainty. We know that there are ongoing discussions about the definition of aleatoric and epistemic uncertainty on philosophy level. But today we are not going to debate about it and use those two terminologies following previous literature. Epistemic uncertainty focuses attention on a single case that may occur (or a single statement that may be true) whereas aleatory uncertainty focuses attention on classes of possible outcomes in repeated realizations of an experiment. "Aleatory" and "Epistemic" Uncertainties Terminology/concepts built into multiple documents, e.g., • ASME/ANS PRA Standard • Regulatory Guides 1 200 aleatory uncertainty: the uncertainty inherent in a nondeterministic (s tochastic, random) phenomenon… is reflected by modeling the – 1.200 phenomenon in terms of a probabilistic – 1.174 Age-related macular degeneration (AMD) is one of the leading causes of permanent vision loss in people aged over 60 years. Accurate segmentation of biomarkers such as drusen that points to the early stages of AMD is crucial in preventing further vision impairment. However, segmenting drusen is extremely challenging due to their varied sizes and appearances, low contrast and noise resemblance. These forms of uncertainty can have insidious consequences for modeling if not properly identified and accounted for. In particular, confusion between aleatoric and epistemic uncertainty can lead to a fundamentally incorrect model being inappropriately fit to data such that the model seems to be correct. 5 Aleatory Variability and Epistemic Uncertainty Aleatory variability and epistemic uncertainty are terms used in seismic hazard analysis that are not commonly used in other fields, but the concepts are well known. Aleatory variability is the natural randomness in a process. For discrete variables, the This is in comparison to epistemic uncertainty which is mostly explained away with the large amounts of data often available in machine vision. We further show that modeling aleatoric uncertainty alone comes at a cost. Out-of-data examples, which can be identiﬁed with epistemic uncertainty, cannot be identiﬁed with aleatoric uncertainty alone. Epistemic uncertainty derives from the lack of knowledge of a parameter, phenomenon or process, while aleatory uncertainty refers to uncertainty caused by probabilistic variations in a random event . Each of these two different types of uncertainty has its own unique set of characteristics that separate it from the other and can be quantified through different methods. epistemic uncertainty is inperfection of the model, which may be alleviated by improving process representation. aleatoric uncertainty is inperfection of the data to which we apply our model, so even a model with (hypothetical) zero epistemic uncertainty might still yield uncertain predictions due to aleatoric input uncertainty.

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aleatoric uncertainty vs epistemic uncertainty

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[D] What is the current state of dropout as Bayesian approximation?

aleatoric uncertainty vs epistemic uncertainty video

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