What classifiers know what they don't know?
Authors: Mohamed Ishmael Belghazi
David Lopez-Paz
Venue: ICLR 2022 Submitted (2022)
Keywords: Uncertainty quantification
neural networks
benchmark

Abstract: Being uncertain when facing the unknown is key to intelligent decision making. However, machine learning algorithms lack reliable estimates about their predictive uncertainty. This leads to wrong and overly-confident decisions when encountering classes unseen during training. Despite the importance of equipping classifiers with uncertainty estimates ready for the real world, prior work has focused on small datasets and little or no class discrepancy between training and testing data. To close this gap, we introduce UIMNET: a realistic, ImageNet-scale test-bed to evaluate predictive uncertainty estimates for deep image classifiers. Our benchmark provides implementations of eight state-of-the-art algorithms, six uncertainty measures, four in-domain metrics, three out-domain metrics, and a fully automated pipeline to train, calibrate, ensemble, select, and evaluate models. Our test-bed is open-source and all of our results are reproducible from a fixed commit in our repository. Adding new datasets, algorithms, measures, or metrics is a matter of a few lines of code-in so hoping that UIMNET becomes a stepping stone towards realistic, rigorous, and reproducible research in uncertainty estimation. Our results show that ensembles of ERM classifiers as well as single MIMO classifiers are the two best alternatives currently available to measure uncertainty about both in-domain and out-domain classe.

Under review conference paper ICLR 2022
WHAT CLASSIFIERS KNOW WHAT THEY DON'T T KNOW?
Anonymous authors Paper under double-blind review
ABSTRACT
Being uncertain when facing the unknown is key intelligent decision making. However, machine learning algorithms lack reliable estimates about their predictive uncertainty. This leads wrong and everly-confident decisions when encountering classes unseen during training. Despite the importance of equipping classifiers with uncertainty estimates ready for the real world, most prior work focuses on small datasets with little or no class discrepancy between training and lesting data. To close this gap, we introduce UIMNET: a realistic, ImageNet-scale test- bed to evaluate predictive uncertainty estimates for deep image classifiers. Our benchmark provides implementations of ten state-of-the-ar algorithms, six uncertainty measures, four in-domain metrics, three out-domain metrics, and fully automated pipeline train, calibrate, ensemble, select, and evaluate models. Our test-bed open-source and all of results are reproducible from a fixed commit in our repository. Adding new datasets, algorithms, measures, or metrics matter of a few lines of code-in so hoping that UIMNET becomes a stepping stone towards realistic, rigorous, and reproducible research in uncertainty estimation. Our experimental results reveal that, in order to obtain the best possible uncertainty estimates in large-scale image classification, the practitioner should favor large, calibrated models. We recommend the use of single ERM models, single MIMO models, or ensembles of ERM models, in order of increasing performance and required computational budget.
1 INTRODUCTION
I don't think I've ever seen anything quite like this before -HAL 9000 in 2001: A Space Odyasey
Deep image classifiers exceed at discriminating the set of in-domain classes observed during training. However, when confronting test examples from unseen out-domain classes, these classifiers can only predict in terms of known categories, leading wrong and overly-confident decisions (Hein et al., 2019; Ulmer& & Cinà, 2020). In short, machine learning systems unaware of their limits, since "they do not know what they do not know". Since out-dommin data cannot be safely identified and treated accordingly, is reasonable to fear that, when deployed in-the-wild the safety and performance of these classifiers crumbles by leaps and bounds (Ovadia et al., 2019). The inability of machine learning systems to estimate their uncertainty and abstaining to classify out- domain classes roadblocks their use in critical applications. These include self-driving (Michelmore et al., 2018), medicine (Begoli et al., 2019), and the analysis of satellite imagery (Wadoux, 2019). Good uncertainty estimates are also a key ingredient in anomaly detection (Chalapathy & Chawla, 2019). active learning (Settles, 2009), sufe reinforcement learning (Henaff al., 2019), defending against adversarial examples (Goodfellow al., 2014), and model interpretability (Alvarez-Melia & Jaakkola, 2017). For an extensive literature review uncertainty estimation and its applications, refer the curious reader the surveys of Abdar al. (2020) and Ruff research effort spanning multiple decades. machine learning systems still lack trustworthy estimates of their predictive uncertainty. In our view, one hindrance this research program is the absence of realistic benchmarking and evaluation protocols. More specifically, prior attempts are limited in two fundamenial ways. First, these experiment on small datasets such as SVHN and CIFAR-10 (van Amersfoort et al., 2021). Sccond, these do not provide a challenging set of out-domain data. Instead, they construct out-domain classes by using second dataset (e.g., using MNIST in-domain versus FashionMNIST out-domain, ef. Van Amersfoort et al. (2020)) by perturbing the in in-domain classes
(2021). Despite

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Datasets
Algorithms
Uncertainty measures
In-Domain
Out-Domain
Ablations
metries
metries
ImageNot
ERM
Largest
ACC@1 1
AUC
Calibration (y/n)
(new)
Mixup
Gap
ACC
InAsin
Spectral norm (y/n)
Soft-lbbller
Entropy
ECE
OutAsOut
Model size (RN18/ RN50)
RBF
Jacobian
NLL
RND
GMM
OCs
Native
DeepAF
MC-Dropout
MIMO
DUE
(+ Ensembles)
Table 1: The UIMNET test-bed suite for uncertainty estimation.
using handcrafted transformations (such as Gaussian noise or blur, see ImageNet-C Hendrycks & Dietterich (2019)). Both approaches result in simplistic henchmarking, and little is learned about uncertainty estimation for the real world. One exception is the ImageNet-O dataset (Hendrycks et al., 2021), where out-domain data is selected from ImageNct-22k classes not contained in ImageNet- 1k. However, the images in ImageNet-O OO are collected adversarially as to maximize the prediction confidence of ResNet50 ImageNet-1k 1 classifiers, creating what's possibly an unnecessarity difficult benchmark. The purpose of this work is to introduce end-to-end benehmark and evaluation protocol as realistic possible. At the time of writing. UIMNET the most exhaustive benchmark uncertainty cstimation in the litcrature.
Formal setup We learn classifiers using in-domain data from some distribution (i,(X, Y). After training, we endow the classifier with a real-valued uncertainty measure =(f Given test example (zl,9) yy) )²) ~ P with unobserved label y'. we declare x¹ in-domain (hypothesizing P = Pun) ffffar)) is small. whereas we declare out-domain thypothesizing P & Pin) if u(f. x!) large. Using these tools. our goal is to abstain from classifying out-domain test examples, and to classify with calibrated probabilities in-domain test examples. The sequel assumes that the difference between in- and out-domain resides in that the two groups of data concern disjoint classes.
Contributions We introduce UIMNET, a test-bed for large-scale, realistic evaluation of uncertainty estimates in deep image classifiers. We build UIMNET as follows (see also Table l).
(Sec. 2)
We construct ImageNot, a perceptual partition of ImageNet into in-domain and out- domain classes. Unlike most prior work focusing on small datasets like SVHN and CIFAR-10, ImageNot provides a benchmark for uncertainty estimators at much larger scale. Morsover, both in-domain and out-domain categories in ImageNot originate from the original ImageNet dataset. This provides realistic out-domain data, as opposed to prior work rolying on a second dataset (c.g.. MNIST as in-domain versus SVHN as out-domain), or handcrafted perturbations of in-domain classes (Gaussian noise or blur as out-domain).
(Sec. 3) We re-implement eight state-of-the-a algorithms from scratch, listed in Table 1. This allows a fair comparison under the exact same experimental conditions (training/validation splits,
search, ncural network architectures and random initializations). Furthermore, we also study ensembles of multiple training instances for each algorithm.
(Sec. 4) Each ulgorithm can be endowed with one out of six possible uncertainty measures. allowing an exhaustive study of what algorithms play well with what measures. Listed in Table 1. these are the largest softmax score, the gap between the two largest softmax scores, the softmax entropy, the norm of Jacobian, per-class Gaussian density model, and (for those available) an algorithm-specific measure.
(Sec. 5) For cach classificr-measure pair, we study four in-domain metrics (top-1 and top-5 classification accuracy, log-likelihood, expected calibration error) and three out-domain metries (the AUC at classifying in-domain versus out-domain samples using the selected
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uncertainty measure, as well the confusion matrix fixed uncertainty threshold computed over in-domain validation set).
(Sec. 6) We explore three popular ablations to understand the impact of model calibration by temperature scaling, model size, and the use of spectral normalization.
(Sec. 7) UIMNET is entirely hands-off, since the pipeline from zero 1AGX tables is fully automated: this includes hyper-paramcter search, model calibration, model ensembling. and the production of all the tables included in our experimental results.
(Sec. 8) Our experimental results reveal that, in order obtain the best possible uncertainty estimates in large-scale image classification, the practitioner should favor large, calibrated models. We recommend the use of single ERM models, single MIMO models, or ensembles of ERM models, order of incrcasing performance and required computational budget.
UIMNET open sourced at hitps: : /t/////tttttt thub. com ANONYMOUS, All of tables presented in this paper are reproducible by running the main script in the repository at commit OxANON.
2 CONSTRUCTING THE IMAGENOT BENCHMARK
The ImageNet dataset (Russakovsky et al., 2015) a gold standard to conduct rescarch in computer vision pertaining image data of 1000 different classes. Here we use the ImageNet dataset to derive ImageNot, large-scalc and realistic henchmark for uncortainty estimation. ImageNot partitions the 1000 classes of the original ImageNet dataset into in in-domain classes (used to train and evaluate algorithms in-distribution) and out-domain classes (used to evaluate algorithms out-of-distribution).
To partition ImageNet into in-domain and out-domain, we fcaturize the entire datasct to understand the perceptual similarity between classes. To this end, we use a pre- pre-trained ResNet- 18 (He et al., 2016) to compute the average last-layer representation for each of the classes. Next, we use agglomerative hierarchical clustering Ward Jr (1963) to construct tree describing the perceptual similarities between the 1000 average feature vectors. Such perceptual tree has 1000 leafs, each of them being cluster containing one the classes. During each step of the iterative agglomerative clustering algorithm the two closest clusters are merged. where the distance between two clusters is computed using the criterion of Ward Jr (1963). The algorithm halts when there are only two clusters left to merge, forming the root node of the tree.
At this point, we declare the 266 classes the left of the root as in-domain, and first 266 classes to the right of the ront as out-domainn In the sequel, we call "training set" and "validation set" to 90/10 random split from the original ImageNet "train" set. We call "testing set" to the original ImageNet "val" split. The exact in-fout-domain class partition as well as the considered train/validatio splits are specified in Appendix D. Our agglomcrative clustcring procedure ended-up congregating different types of objects in-domain classes, while grouping animals out-domain classes.
While inspired by the BREEDS ImageNct splits (Santurkar et al., 2020), our benehmark ImageNot is conceived to tackle different problem. The aim of the BREEDS dataset is to classify ImageNet into small number of super-classes, each of them containing number of perceptually- similar sub-classes. The BREEDS training and testing distributions differ the sub-class proportions contributing to their super-classes. Since the BREEDS task is to classify super-classes, the set of labels remains constant from training to testing conditions. This is in contrast to ImageNNo, where the algorithm observes only in-domain classes during training. but both in-domain and out-domain classes during evaluation. While BREEDS studies the important problem domain gencralization (Gulrajani & Lopez-Paz, 2020), where there is always a right prediction to make within the in-domain classes during evaluation, here we focus on measuring uncertainty and abstaining from predicting about those out out- do-mio classes unavailable during training.
ImageNot is also similar to the ImageNet-O dataset of (Hendrycks et al., 2021). However, their out- domain images are collected adversarially, that is, to maximize the prediction confidence of ResNet50 classificrs. We believe that this drastic change in selection bias from ImageNet to ImageNet-O) may result in an unnecessarily difficult uncertainty estimation benchmark. Thus, here we favor using only the original ImageNct data, as described above. In contrast, the starting point for both in-domain and
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out-domain classes of our ImageNot is the ImageNet dataset, and thus should maximally overlap in terms of image statistics, leading to challenging and realistic henchmark.
3 ALGORITHMS
We benchmark ten supervised learning algorithms commonly applied to tasks involving uncertainty estimation. Each algorithm consumes one in-domain training set of image-label pairs 9()),9))7 9:]]2_. and returns a predictor [(x)) = w(((x)), composed by a featurizer
_332244224 - I and
classifier w IR* -> R We consider predictors implemented using deep convolutional neural networks (LeCun et al., 2015). Given an input image æ!, all predictors return a softmax vector f(=)) (()=")))== over C' classes. The considered algorithms are:
Empirical Risk Minimization, ERM (Vapnik. 1992). vanilla training.
Mixup (Zhang et al., 2017) chooses a predictor minimizing the empirical risk on mixed examples
(A-2;; + (1 X) - 2z. A 3t + (1 X) Bj]. where A Beta( a). a a mixing parameter, and ((22, (15, My]) is random pair of training examples. Mixup improves generalization performance (Zhang et al., 2017) and calibration (Thulasidasan et al., 2019).
Random Network Distillation, or RND (Burda et al., 2018). finds an ERM predictor f(a) =
w(((z)), but simultaneously trains an auxiliary classifier Watden to minimize [Waddem (((x))
Wreccerr (2 where Wheaher is fixed classifier with random weights. RND has shown good
performance tool for exploration in reinforcement learning.
OC (Tagasovska & Lopez-Paz, 2018), is analogous to RND for ((ccs)r(((()) = 0. for all z. That is, the goal of Wgudent is to map all the in-domain training ex- amples to zero in k different ways (or certificates). To ensure diverse and non non-trivial certificates, we regularize each weight matrix W' of Wsullat to be orthogonal by adding regularization term [ W 1 OCs have shown good performance at the task of estimating uncertainty across variety of classification tasks. Autoencoder, DeepAE (Vincent al., 2010), is analogous RND for Wheccer ( (0(x)) o(x)
Orthogonal Certificates,
and a Wardem with a bottleneck.
MC-Dropout (Gal & Ghahramani, 2016) trains ERMs with one or more dropout layers (Sri- vastava et al., 2014). These stochastic dropout layers remain active at test time, allowing the predictor to produce multiple softmax vectors (f(zl, (tropout))]: for each test example x! Here, dropout, is a random dropout mask sampled anew. MCDropout is one of the most pupular baselines to estimate uncertainty.
MIMO (Havasi et al., 2021) is variant of ERM over predictors accepting T images and producing 7 softmax vectors. For example, MIMO with T = 3 is trained to predict jointly the label vector (3/. Vý. 9&) using a predictor hi(,,, 23: where ((I,, s1 ve)) is random triplet of training examples. Given a test point x!, we form predictions by replicating and averaging,
that is f(=1)= = ا. h(x _zf _zf,=!').
Radial Basis Function, or RBF (Broomhead & Lowe, 1988). a variant of ERM where we transform the logit vector + e== before passing them to the final softmax layer. In such a way, the logit norm ||=| + oc, the predicted softmax vector tends to the maximum entropy solution (b) signaling high uncertainty far away from the training data. RBFs have been proposed defense to adversarial examples (Gooddflloow et al., 2014), but they remain under-explored given the difficulties involved in their training.
Soft labeler (Hinton et al., 2015; Szegedy et al., 2016) a variant of ERM where the onc-hot vector labels ys are smoothed such that every zero becomes Enin > 0 and the solitary one becomes Emax < 1. Using soft labels, we can identify softmax vectors with entries exceeding fmux as "over-shoots", and regard them as uncertain predictions.
DUE (van Amersfoort et al., 2021) enforces the smoothness of the featurizer é using spectral normalization (Miyato et al., 2018), implements the classifier (Quinonero- Candela & Rasmussen, 2005). and trains the resulting predictor using variational inference (Titsias, 2009). Gaussian processes considered one of the main tools to estimate predictive uncertainty in machine leamnngg systems.
sparse Gaussian Process
Ensembles of predictors Wc also consider ensembles of predictors trained by cach of the algo- rithms above. Ensembles are commonly regarded as the state-of-the-art in uncertainty estimation (Lak- shminarayanan et al., 2016). In particular, and for each algorithm, we construct bagging ensembles
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by (i) selecting the best K {1,5) predictors {f from all considered random initializations and haperr-srameters, and (ii) returning the average function f(x1) == * 1 (x+).
4 UNCERTAINTY MEASURES
equip a trained predictor with six different uncertainty measures. An uncertainty measure is
real-valued function u(f, x!) designed to return small values for in-domain instances x', and large values for out-domain instances x!. To describe the different measures, let (a())-... ((C)) be the
softmax scores returned by f(x]) sorted in decreasing order.
Largest (Hendryckk & Cimpel, 2016) returns minus the largest softmax score, $(1)
Softmax gap (Tagasovska & Lopez-Pazz Paz, 2018) returns 8(2) 8(1)-
Entropy (Shannon, 1948) returns >> ((o) ((c) > (()) S(e)-
Norm of the Jacobian (Novak et al., 2018) returns [+z(
GMM (Mukhoti et al., 2021) estimates one Gaussian density (oo(z); pe. Ee) per-class, top of the feature vectors (bx) collected from in-domain validation set. Given test example zt, return Σ Àe -N(((x)) Me, Ec), where xe is the proportion of in-domain validation examples from class c.
Test-time augmentation (Ashukha al., 2020) returns max Σ f(xl))) This is measure "Largest" about the average prediction over A random data augmentations (=t aa of the test instance r!.
These uncertainty measures are upplicable to all the algorithms considered in Section 3. Additionally, some algorithms provide their Native uncertainty measures, outlined below.
For Mixup, we return I Σ IIX f(xt) (1 X) Us f(A.xt at I (1 ( Ex)12 where
À ~ Beta(o, a), and (2k, Vkk example saved from the training set. This measures if the example 2f violates the Mixup criterion wrt the training dataset average.
that is, consider a prediction uncertain the outputs of the student and teacher disagree.
For RND. OC, and DeepåE
return || Wsnuddem (o(x")) "baccer((((
expect this disagreement to be related predictive uncertainty, as the student did not observe the behaviour of the teacher at out-domain instances æ!
For Soft labeler we return ($(1) )= This measures the discrepancy between the largest softmax and the positive soft label target, able to signal overly-confident predictions.
For MC- MC-Dropout and Ensembles, and following (Lakshminarayanaa et al., 2016), we return the Sensen-Shamnee divergence between the K members (or stochastic forward passes) f ......:
of the ensemble, H 1 Σ ((()) æ ΣK_, (x*((=t))
For DUE, return the predictive variance of the Gaussian process classifier.
5 EVALUATION METRICS
For each algorithm-meast measure pair, we evaluate several metrics both in-domain and out out-domain.
Following (Havasi et al., 2021), we implement four in-domain metrics to assess the performance and calibration of predictors when facing in-domain test examples.
Top-1 and Top-5 classification accuracy (Russakovsky et al., 2015). Expected Calibration
al., 2017): B " (9g Jace(f. - conf(f. Ba)l, where B, contains the examples where the al- gorithm predicts softmax score of b. The functions acc and conf compute the average classification accuracy and largest softmax score of over B,, ECE is minimized when is calibrated, that is wrong 72 of the times it predicts a largest softmax score p. Following (Guo et al., 2017), discretize b [0, into 15 equally-spacee bins.
Error
ECE (Guo
Negative Log Likelihoud (NLL)) Also known as the cross-entropy loss, this the objective minimized during the training process of the algorithms.
We assess the uncertainty estimates of cach predictor-measum pair using three out-domain metries.
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Area Under the Curve, AUC (Tagasovska & Lopez-Paz. 2018), describes how well does the meaticttormmasueee pair distinguish between in-domain and out-domain examples over all thresholds of the uncertainty measure.
Confusion matrix at fixed threshold. 'To reject out-domain examples real scenarios, one must fix a threshold 0 for the selected uncertainty measure. We do so by computing the 95% quantile of the uncertainty measure, computed over an in-domain validation set. Then, at testing time, we declare one example out-domain if the uncertainty measure exceeds 0. To understand where does the uncertainty measure hit or miss, monitor the metrics InAsIn (percentage of in-domain examples classified as in-domain) and OutAsOut (pereentage of in-domain examples classified as out-domain).
6 ABLATIONS
We exccute our entire test-bed under three popular ablations.
study the effect calibration by temperature scaling (Platt et al., 1999). To this end, we introduce a temperature scaling 7 > before the softmax layer, resulting in predictions Softmax( {) about the logit vector z. We estimate the optimal temperature f by minimizing the NLL of the predictor across an in-domain validation sct. Wc cvaluate all metries for both the un un-calibrated (r 1) and calibrated (r f) predictors. According to previous literature (Guo al., 2017), calibrated models provide better in-domain uncertainty estimates.
We analyze the impact of spectral normalization to control the behavior of the featurizer d. More specifically. recent works (Liu al., 2020; Van Amersfoort et al., 2020; Amersfoort al., 2021; Mukhoti al., 2021) have highlighted the importance of controlling both the smoothness and sensitivity the feature extraction process to avoid feature collapse and achieve high-quality uncertainty estimates. On the one hand, enforcing smoothness upper bounds the Lipschitz constant of o. limiting its reaction to changes in the input. Smoothness is often enforced by normalizing each weight matrix in ø by its spectral norm (Miyato et al., 2018). On the other hand, enforcing sensitivity lower bounds the Lipschitz constant of o, ensuring that the feature space reacts in some amount when the input changes. Sensitivity is often enforced by the residual connections of the hereby used ResNet models (He et al., 2016). We apply one-sided spectral normalization, with target spectral norm of 5, to the weights and the batch normalization layers following Miyato al. (2018) and Gouk et al. (2021) respectively. We analyze the impact of model size (ResNet-18 versus ResNet-50).
7 EXPERIMENTAL PROTOCOL
We now conduct experiments on the ImageNot henchmark (Section 2) for all algorithms (Section 3) and measures (Section 4), all metries (Section 5) and ablations (Section 6). Empirical oracle upper bounds To have measure of the maximally achievable separation of the in-domain and out-of-domain partitions, we train a ResNet-18 classifier to discriminate between the In-domain classes and the oft-of-domain partition. The oracle performance 0.985 + 0.002, 0.944 01.01 and 0.947 + 0.0U2 for the AUC, InAsIn and OutAsOut metrics respectivcly.
apper-paraneter search. We train each algorithm using (i) ResNet-18 or ResNet-50 architectures (ii) spectral normalization or not, (iii) ten hhper--ppue pare--areetter trials, and (iv) three random train/validation splits of the in-domain data (data seeds). We opt for random parameerrrmeter search (Bergstra & Bengio, 2012), where the search grid for each algorithm is detailed in Appendix C. More specifically, while the first trial uses the default algorithm, the additional four trials explore random syper-parametens
configuration suggested by the authors of each
Model selection. After training all instances of a given ulgorithm, we report the test average and standard deviation (over data sceds) of all metries. We report these metries for (a) the hest model
This strategy equivalent the statistical hypothesis test with null "Hy: the observed example is in- domain".
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(A 1), and (b) the ensemble containing the best five models (A: in terms of the validation average (over data seeds) negative log-likelihood..
Optimization. We use PyTorch (Paszke al., 2019) and SGD (Bottou, 2012) for 100 epochs using mini-batches of 256 examples distributed over NVIDIA Tesla V100 GPUs, and learning rate decaying by a factor of 10 every epochs.
8
RESULTS
The full experimental results available in Appendix A (in-domain) and Appendix (out-domain). Below, we summarize findings.
From the in-domain results summarized in Table we identify the following key takeaways:
No single method out-performs ERM significantly on any in-domain metric, except MIMO on ECE (-30% ECE).
No ensemble method outperforms ensembles of ERMs in any in-domain metric. Increasing model size is the most effective strategy to improve in-domain metrics (45% ACC 1, +2% ACC@5, 5, -17% NLI., -13% ECE).
Ensembling is the second most effective strategy to improve in-domain metrics (+2.5%
ACC 1, +1% ACC@5, -8.5% NI.L, -8% ECH).
Calibration is effective strategy improve test negative log-likelihood and expected calibration error (-2% NI.I,, -45% HCE).
Spectral normalization has little effect improve in-domain metrics (<1%)
DUE has brittle hchavior, performing well only default hyper- hyper-paramenn parameters and 18 architectures.
From the out-domain results summarized in Table 3, corresponding the best performing uncertainty measure "Entropy", identify the following key takeaways:
No single method outperforms ERM significantly on any out-domain metric, except MIMO on OutAsOut (+5% OutAsOut).
No ensemble method outperforms ensembles of HRMs in any out-domain metric.
Increasing model size is the most effective strategy to improve out-domain metries (+4%
AUC, +35% OutAsOut).
Ensembling is the second most effective strategy improve out-domain metrics (+ (+1%
AUC, +4% OutAsOut).
Calibration has small negative effect on out-domain metrics (-1%).
Spectral normalization has a small positive effect on out-domain metrics (<1%).
All methods are able to upper-bound their type-I crrors the requested threshold 5%.
The best performing uncertainty measure is Entrupy; then Largest, and Gup follow. The worst performing measures are Augmentations, Jacobian, and Native (Appendix B).
Other results We were unable to obtain competitive performances for the algorithm RBF (Broom- head & Lowe, 1988) and the measure GMM (Mukhoti et al., 2021). We believe that training RBFs at this large scale are challenging optimization problems that deserve further study in community. Furthermore, the large number of classes in study (266 ImageNet classes instead of the 10 CIFAR-10 classes often considered) poses difficult problem for the density-bused measures GMM.
CONCLUSION
To obtain the best possible uncertainty estimates in large-scale image classification. we recom- mend the use of large and calibrated models. We favor single ERM models (low computational budget), single MIMO models (medium budget), ensembles of ERM models (high budget).
GGraphs showing the relationship between validation negative likelihood and out-of-domain measures the test set show in the appendix.
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algorithm
calibration
spectral
ACC@1
ACC65
NLL (U)
ECE (L)
False
False
0.767
0.002
U.930
= 0.000
U.933
0:00
0.153 = 0.001
True
False
0.767
0.002
0.930
0.000
0.918
0.005
0,031
0.000
True
0.706
0.003
0.927 0.000
0.47
0.008
0,055 0.002
True
0.003 0.766
0.001 0.927
0.924
0.008
0.031 1 0.002
ERM
False
0.007
0.005
True
Fabe
0.780
0.007
0.933
0.005
0.029 0,863
0.021 0.005
True
0.788
+00001
0.957
+ 0.000
0.821
0.003
0.019 0,002
True
0.001
0.000
0.003
0.003
Palse
False
0.768
0.001
0.929 0.000
0,925
2 0.003
0.035
0.001
False
0.768
0.001
0.929
0.000
0.923
0.003
0,030
0.002
True
0.706
0.003
0.927
0.001
0,922
- 0.005
0,021
0.004
True
0.003 0.766
0.001 0.927
0.004 0.940
0.029 0.001
Mixup
False
0.001
0.002
0.001
False True
False
0.777
0.000
0.933 0.001
0.857
0.002
0.017 0.001
True
0.789
0.000
0.910
0.000
0 + 0.000
0,051
0,002
True
0.000
0.000
0.002
0.019 0.002
Halse
Fulse
0.767
0.003
0.930
1: 0.001
0 2 0.009
0.032 1 0.001
False
0.767
0.003
0.93)
0.001
0.010
0.003
True
0.767
0.001
0.928
0.001
0,984
0.003
0.631 0.002
SoALabeler
Thue
0.767
+ 1-0001
0.001 0.928
0,006 0,968
0.045
0.002
False
False
0.006
0.073
0.030
True
False
0.782
+ 0.006
0.933
+ 0.003
0.861
0.025
0.033
True
0.790
0.000
0.910
+ 0.001
0,906
0.001
0,089
0,003
True
0.001 0.750
0.001 0.940
0.002
0.032
0.001
False
Fulse
0.765
0.001
0.928
1: 0.001
0,933 1 0.004
0.046 1: 0.003
False
0.763
0.000
True
0.765
0.001
0.928
0.001
0.534
0.003
0,046 0.003
DeepAE
Thme
0.765
+ 0.001
0.001 0.928
0.923 + 0.003
0.030 0.002
False Trme
False
0.008
0.009
False
0.778
+ 0.008
0.931 + 0.001
0.855 + 0.031
0.015 + 0.001
True
0.789
0.001
0.910
2 0.000
0,811 0.000
0,02 0,000
True
0.001
0.940
0.000
0.812+0.00)
0.002 0.015
False True
False
0.762
+ 0.001
0.927
+ 0.001
0.957 + 0.008
0.056
0.001
False
0.007
0.002
True
0.764
0.002
0.926
0.001
0.555 0.008
0.055 0.002
RND
True
0.761 1 0.002
0.001 0,925
0,833 0.007
0,029 0,001
Fabs
False
0.081
0.006
Trme
False
0.781
0.107
0.936
+ 0.001
0.816 + 0.027
0.016 = 0.001
True
0.001 0,788
0,938
1 0.001
0,821 0.002
0.019 0,002
True
0.001 0.788
0.938
0.001
0.825 0.002
0.019 0.001
False True
False
0.764 + 0.001
0.928 + 0.001
0.947 + 0.002
0.034 0.001
False
0.001
0.001
Tree
0.765
0.002
0.927
0.002
0.948
0.002
0.054 0.001
OC
True
0.765
0.002
0.927
0.002
0,927
0.002
0,029 0,002
False
False
0.006
False
0.782 : 0.008
0.935 2 0.005
0.813 = 0.031
0,016 = 0.002
True
Trie
0.788
0.004
0.937
0.000
0.824
0.002
0,020 0.002
True
0.004 0.788
0.937
0.000
0.825 0.002
0.019 0.002
False
False
0.768
0.002
0.929
+ 0.000
0.929
+
0.048 0.001
True
False
0.002
0.000
0.00
0.001
Thee
0.768
0.002
0.928
0.001
0.530
0.004
0.051 0.001
MIMO
False True
False
True
0.768
0.002
0.928
0.001
0.005
0.905
0..004
0.042
0.023 0.000
0.012
Fulse
0.769
: 0.008
0.928
2 0.005
0.905
2 0.083
0.015 0.001
Trie
0.779
0.001
0.934
0.000
0.858
0.000
0.032- 0.003
True
0.001 0.779
0.931 0.001
0.00 0.857
0.015
0.002
False
False
0.766
0.002
0.928
+ 0.001
0.914 + 0.002
0,054 0.001
True
False
0.766
0.002
0.001
0.923
0.001
Trie
0.765
0.002
0.927
0.001
0.550
0.003
0,055 0.002
MCDropout
True
0.765
0.002
0.927
1 0.001
0,927
0.002
0,031 1 0.001
False
False
0.777 + 0.005
0.831
0.00
0.867
0.022
0,224 0.007
True
Fulse
True
0.788
0.777 1 0.008
0.0022
0.931
0.001
1 0.001
0.865 1 0.030
0.001
0.015 1 0.003
0.001
True
0.002 0.768
0.001 0.938
0.001 0.623
0.018 0.001
False True
False
0,080
+ 0.002
0.218 0.005
1,511
0.006
0,032
0.003
DUE
False
Thie
0.653
+ 0.000
0.005
0.891
0.000
0.005
4.538
1.675
0.000
0.019
0.069
0.010
+ 0.000
0.002
True
0.654
0.000
0.530
1. 0.000
1.560 0.0.00
0.023 1 0.000
Table 2: In-domain results for ResNet50.
8

---

Under review conference paper at ICLR 2022
algorithm
k
calibration
spectral
AUC
INASIa (f)
OutAsOut (*)
False
0,805 0.003
0.942
0.0011
0.373
False True
False
0.871 1 1.0004
0.943 1 0.001
0.377
0.007
True
0.001
True
0.871 1: 0.003
0.911 2: 0.001
0.371
0.010
ERM
False
False
0.878 + 0.002
0.943 + 0.002
0.301
0.008
Time
False
0.943
0.397
True
0.878 +: 0.001
0.942 + 0.001
0.398
0.003
True
0.877
0.001
0.942 0.001
0.397
0.003
False True
False
0.859
0.0022
0.943
0.000
0.353
0.004
False
0,858
0.002
0.943 1 0.000
0.353 0.005
True
Mixup
True
0.854 1: 0.007
0.940 1: 0.001
0.330
0.017
False True
False
0.874 + 0.001
0,940 + 0.001
0.307
0.000
False
0.940
0.396
5
Trie
0.876 + 0.002
0,939
0.001
0,399
0.006
True
0.872
0.001
0.939
0.001
0.393
0.002
False True
Fabse
0,832
0.009
0.941
0.001
0.305
0.015
False
0,835
0.009
0.942 1 0.001
0.313
0.014
True
SoftLabeler
Thue
0.839 + 0.004
0.941 + 0.001
0,322
0..00
False True
Palse
0 + 0.003
0.933 0.001
0.348
-.008
False
0.940
0.355
5
True
0,861 1: 0.000
0.940 + 0.001
0.351
0.001
True
0,862
0.001
0,940
0.001
0.361
0.004
False
0,863
0.003
0.942
0.001
0.376
0.016
Falso True
False
0.004 0,867
0.942 1 0.001
0.379
0.015
0,865
0.913
0,000
DeepAFF
Thee
0.869
0.002
0.942 0.000
0.381
(1.009
False True
Palse
0,881
0.002
0.942 0.001
0.117
0001
False
0.875
0.941
0,406
5
True
0,882 1 0.001
0.941 1 0.002
0.115
0.001
True
0.879
0.001
0.940 0.002
0.410
0,001
False
0.859
0.001
0.942
0.001
0.354
0.008
Falso True
False
0.861
0.001
0.943 = 0.001
0.357
0.010
0,855
0.943
0.354
RND
Thee
0.860 + 0.004
0,942 + 0.001
0.359 - 0.012
False True
False
0.878
0.002
0,941 0.000
0,398
0.008
False
0.875
0.040 0.000
0.305 0,006
5
True
0,875
0.002
0.941 1 0.001
0.389 0.006
Thue
Falso True
False
0,861
0.001
0.933
0.001
0.371
0.011
False
0.867
0.001
0.939
0.001
0.373
0.013
0.944
0.361
OC
Thee
0.868 =: 0.003
0.943 = 0.001
0.361 = 0.011
False True
False
0.878
0.001
0.943 0.001
0.395 0.009
5
False
0.875
0.001
0.043
0.001
0.303 0.008
True
0.876
0.001
0.941 1 0.001
0.390 0.012
False True
False
0,868
0.003
0.942 +: 0.001
0.388
0.005
Fabso
0.874
0.003
0.941 1 0.001
0.397
0.005
Thee
0.807
0.003
0.941
0.001
0.302
0.009
MIMO
True
0.874 =: 0.002
0.942 = 0.001
0.398 = 0.010
False Time
False
0.870
0.003
0.939
0.001
0.371 0.014
5
Fabse
0,864 1. 0.004
0.939
0.001
0.366 0,013
True
0.872 1. 0.001
0.040 1 0.001
0.377
0.005
False
False
0,854 0.002
0.943
0.001
0.368
0.005
True
Falso
0.569 1 0.002
0.942 1 0.001
0.373
0.000
Thue
0,805
0LAKU5
0.942
0.002
0.380
0.010
MCDropout
True
0.871 :: 0.005
0.942 : 0.002
0.385 = 0.011
False
False
0.878 0.001
0.942
0.001
0.304
5
True
Fabse
Thue
0,879 1: 0.001
0,874 1. 0.003
0.941
0,942
1: 0.000
0.001
0.400 0.003
0,391
0.008
0.002
0.911
False True
False
0.553 0:000
0.951
:: (10011
0.038
0.002
False
0.553
0.008
0.950
0.001
0.038
0.002
True
0.810 =: 0.000
0.942
0.000
0.288 0.0000
Thue
0.636 :: 0.000
0.042 :: 0.000
0.285 0.000
Table Out-domain results for ResNet50 using measure "Entropy"
9

---

Under review conference paper at ICLR 2022
ETHICS STATEMENT
This work does not involve the release of any new data, or the development of any new algorithm. However, we believe that the development of better uncertainty estimates for predictive models is at the core of responsible, fair machine learning. As such, hope that the UIMNET baseline is stepping stone towards advancing the ability of our systems say "I don't know". Also, we hope that our manuscript and software aids future research to study uncertainty estimates components also vulnerable to attacks and with their own set of limitations.
REPRODUCIBILITY
main focus of this manuscript is reproducibility. To replicate of our experimental results, obtain our code from the Suppiementary Material and follow the instructions at README mci Upon publication, our code will be open-sourced in GitHub repository, and all of our experimental results will be replicable from fixed commit hash.
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12


Reviews:
[{"review_id": "lkgCvRmbDP", "reviewer": "Reviewer_R3aT", "summary": "", "questions": "", "limitations": "", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "Strengths:\n- The paper is well written.\n- The benchmarking is solid and very thorough. Many baselines and metrics have been implemented, and results are presented with confidence intervals.\n\nWeaknesses:\n- Overall, the major weakness is in the design of this benchmark. For a study claiming to be \"the most exhaustive uncertainty estimation benchmark,\" the only test-time distribution shift considered is the presentation of novel classes. The authors do not appear to justify this design decision anywhere in the paper. The authors make multiple appeals to \"providing realistic out-domain data,\" but there are many, many ways out-domain data can be presented in real world applications. This disjoint class assumption is very strong and is not clear why or when this is representative.\n- From reading about the construction of the benchmark, it's not entirely clear why BREEDS wasn't a suitable candidate and why something new had to be created. The authors state that the BREEDS task is to classify super-classes and so the label set remains fixed from train to test - that is true, but could the authors not have just used the same split and kept the leaf node original class labels instead of using the superclass labels?\n- The agglomerative clustering method used to construct the splits seems round-about. The ImageNet hierarchy contains a lot of metadata that could have been used to create the splits - do the authors have any comment on why this wasn't used? Also, the result of this split is that the train-test gap is over object classes to animal classes, which is perhaps (a priori) not as realistic of a setting as in the BREEDS dataset, where the train-test gap is between very similar class categories. This design decision was again never justified.", "summary_of_the_paper": "This paper proposes a new testbed to test the uncertainty of image classifiers based on a split of ImageNet.", "summary_of_the_review": "In summary, this study has a large number of design flaws. However, given the benchmark, the authors have done a great job in thoroughly benchmarking existing algorithms.", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "2: Several of the paper’s claims are incorrect or not well-supported.", "technical_novelty_and_significance": "1: The contributions are neither significant nor novel.", "empirical_novelty_and_significance": "2: The contributions are only marginally significant or novel."}, "extra_text": {}}, {"review_id": "cbYdUryViMv", "reviewer": "Reviewer_tta3", "summary": "", "questions": "", "limitations": "", "rating": 6, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "For Strengths, the paper provides a solid test-bed for evaluating the uncertainty estimation for deep image classifiers. Also, the paper is well-written and both the data construction and results part are clearly described.\nThe main weakness of the paper is that the uncertainty measurements in Section 4 lack the SOTA uncertainty estimation methods. For example, no method in Section 4 measures the epistemic uncertainty such as deep ensemble/dropout and aleatoric uncertainty [1] explicitly. Also, recent dirichlet-distribution-based approaches [2][3] are not included to measure the evidence-based uncertainty. \n\n[1] Kendall, Alex, and Yarin Gal. \"What uncertainties do we need in bayesian deep learning for computer vision?.\" arXiv preprint arXiv:1703.04977 (2017).\n[2] Sensoy, Murat, Lance Kaplan, and Melih Kandemir. \"Evidential deep learning to quantify classification uncertainty.\" arXiv preprint arXiv:1806.01768 (2018).\n[3] Charpentier, Bertrand, Daniel Zügner, and Stephan Günnemann. \"Posterior network: Uncertainty estimation without ood samples via density-based pseudo-counts.\" arXiv preprint arXiv:2006.09239 (2020).\n", "summary_of_the_paper": "The paper introduce a benchmark UIMNET to evaluate predictive uncertainty estimates for deep image clasifiers. The authors provides implements of ten state-of-the-art algorithms and six uncertainty measures with four in-domain metrics and three out-domain metrics.", "summary_of_the_review": "Overall, I think the paper is well-written and the benchmark is valuble as testbed for uncertainty estimation. But the uncertainty measurement part lacks some important uncertainty estimation methods, which are highly encouraged to be included in the paper.", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.", "technical_novelty_and_significance": "2: The contributions are only marginally significant or novel.", "empirical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work."}, "extra_text": {}}, {"review_id": "5u7dIsoVSbF", "reviewer": "Reviewer_tETq", "summary": "", "questions": "", "limitations": "", "rating": 3, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "##########################################################################\n\nPros: \n \n* Uncertainty estimation is an important topic.\n\n* I commend the authors for their efforts on reproducibility.\n\n##########################################################################\n\nCons: \n\n* The novelty of the research is low. The data source, algorithms, and metrics are all prior work. \n\n* What value will the community get from the release of ImageNot? The authors have already reported their results. Can the authors outline some additional use cases? Otherwise there is not much point in branding it as a \"new dataset\".\n\n##########################################################################\n\nQuestions during rebuttal period: \n\n\n* The authors claim in/out domain data should be defined from the same dataset, and that \"this provides realistic out-domain data\", as opposed to the alternatives (different datasets, augmentations). What is the justification for this claim of greater \"realism\"? \n \n* How extensible is the software framework to new datasets? What would I have to implement to run the framework on a new dataset?", "summary_of_the_paper": "This paper proposes the UIMNET benchmark for uncertainty estimation. This benchmark includes (1) \"ImageNot\", a remix of ImageNet using hierarchical clustering of pairwise distances between features (2) framework for evaluating uncertainty estimation, including a suite of algorithms, metrics, and ablations studies. The authors report empirical results on their dataset using their suite, and make a number of recommendations based on these findings. Reproducible software is also provided.", "summary_of_the_review": "New empirical benchmark with reproducible software but with unclear research novelty and value to community. ", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.", "technical_novelty_and_significance": "2: The contributions are only marginally significant or novel.", "empirical_novelty_and_significance": "2: The contributions are only marginally significant or novel."}, "extra_text": {}}]

Author rebuttal:

Meta-review: This paper introduces an ImageNet-scale benchmark UIMNET for uncertainty estimation of deep image classifiers and evaluates prior works under the proposed benchmark. Two reviewers suggest reject, and one reviewer does acceptance. In the discussion period, the authors did not provide any response for many concerns of reviewers, e.g., weak baselines, weak novelty, and lack of justification for the current design. Hence, given the current status, AC recommends reject.
Decision: Reject