Venue: NeurIPS 2021 Conference

Reviews:

final_score: rating: 5: Marginally below the acceptance threshold
review_content: summary: This paper considers the idea of generating pseudo-inputs (i.e. extra augmented samples) to improve OOD uncertainty estimates by training with an uncertainty-increasing ("dissipative") loss at these pseudo-inputs. The pseudo-inputs are generated by minimizing estimated density under the data distribution via a simple gradient algorithm. The idea is evaluated in supervised learning (regression) and generative modeling (VAE for images).
main_review: While the idea presented in this paper seems reasonable, the paper comes off as incomplete scientific work as it lacks comparisons against many related methods that have been developed in this area (all using pseudo-inputs for better uncertainty). Since the paper does not present strong theoretical or conceptual advantages of their proposed method, a reader must be convinced of its merits purely from the empirical comparisons, which are currently insufficient to convince me in this paper.

I find the related work too general and misleadingly presents the history as if nobody has already considered out-of-distribution pseudo-inputs training to improve uncertainty estimates.
When in fact there are tons of related works that have been overlooked such as:

Maximizing Overall Diversity for Improved Uncertainty Estimates in Deep Ensembles. 
Jain et al. 2020.
https://arxiv.org/abs/1906.07380

This paper also generates augmented data to improve uncertainty estimates by increasing their entropy at the augmented samples, and does not require a GAN. It even explicitly considered generating pseudo-inputs with low density as in your work. Should be conceptually and empirically compared against as it seems highly related.

Noise Contrastive Priors for Functional Uncertainty. 
Hafner et al. 2019
https://arxiv.org/abs/1807.09289

Also Lee et al. ("Confidence-calibrated...") should be contrasted against far more, currently the only clear difference I can understand from reading your paper is that you do not require a GAN while Lee et al do, but I'm sure there are other key differences that should be described. The authors write that Lee et al require an extra GAN as a downside, but do not acknowledge their method requires an extra density estimator. Furthermore there is no discussion in this paper of the finding by Lee et al that "boundary samples" correspond to the best pseudo-inputs, whereas how close to the "boundary" pseudo inputs from your method will lie is unclear and may arbitrarily depend on hyperparameter values.


Other related work includes:

Prediction-Based Regularization Using Data Augmented Regression. 
Hooker et al. 2012.
http://faculty.bscb.cornell.edu/~hooker/darpaper.pdf

Predictive Uncertainty Estimation via Prior Networks. 
Malinin et al. 2018
https://arxiv.org/abs/1802.10501

Uncertainty in Neural Networks: Approximately Bayesian Ensembling
Pierce et al. 2020.
https://arxiv.org/abs/1810.05546

Furthermore there are a suspicious number of nan reported results for baseline methods, for which it is unclear why this is the case (and again suggests the chosen baselines in this work are not properly intended for the tasks considered).

Also how did you choose hyperparameters for baselines and your model in each task? For example in the MNIST vs FashionMNIST experiment, it seems possible to tweak hyperparameters to obtain the favorable AUROC curve depicted in Fig 10. There should be many more pairs of image datasets evaluated in this experiment using the same hyperparameters to control for hyperparameter settings and more convincingly demonstrate the superiority of your proposed method.

Finally your method depends on a density estimator, so it would be good to show your chosen density estimator alone does not lead to good OOD detection and your improved VAE is truly needed. For example, perhaps a simple linear combination of density-estimate + standard VAE is just as good for OOD detection in which case your method would not really be necessary.

### Update after reading author response to my original review ###

I believe the paper will be much stronger after the inclusion of the additional baselines and major updates to the related work to properly reflect the historical context of this contribution. However I think this stronger paper should be submitted to the next conference for a proper review, as there are simply too many critical updates made in the revision for me to recommend acceptance based only on the brief descriptions of the changes through the comment system. In particular, the revision needs to be carefully written in such a way that precisely describes what previously existed before and what exactly is a new contribution in this paper, without over-claiming anything. 

limitations_and_societal_impact: I believe the authors have adequately addressed societal impact & limitations of their work.
review_title: null

final_score: rating: 6: Marginally above the acceptance threshold
review_content: summary: The authors propose an approach (called d-VV) for learning better uncertainty estimates for neural network models. The core idea is a variation (pun not intended) on the variational variance work by Stirn and Knowles (2020) where an additional "dissipative" term is added to ELBO, which enforces that the latent precision stay close to its prior outside the training distribution as well. This is done to ensure that the uncertainty estimates are accurate even on OOD inputs.

The authors go on to propose a method for emulating "informative" OOD samples to estimate this dissipative term. This is achieved by starting from data samples and taking negative gradient steps on some differentiable density estimate (which is presumed to be available).

main_review: The paper's writing is quite good, and it is apparent by the extensive background section that the authors have a good command of the topic at hand. d-VV is well motivated and clearly exposed, and there is a clear effort from the authors to conduct a thorough empirical evaluation on the benchmarks they chose (although the results are not always communicated in the clearest fashion).

To me what holds the paper back is the lack of experiments on more "realistic" benchmarks: the largest datasets are SVHN/CIFAR and the biggest model is a 5 layer CNN. It appears that the main drawback of d-VV is that it necessitates the introduction of auxiliary models to (1) compute the variance through the latent code and (2) yield density estimates for deriving OOD pseudo inputs. Whether the associated computational overhead precludes the use of the method in large scale settings is not apparent in the current version of the paper.

This is why I think the paper is borderline, although I am willing to change my score to a more positive evaluation if some of the cons below are addressed.

### Pros

- Well written, good background and principled approach
- Simple concept
- Good empirical results

### Cons

- Possibly lots of computational
- Only toy-ish experiments, would be interesting to test on more realistic settings with large models
- Visualizations are hit or miss: they rely too much on color. While the holistic evaluation in Table 1 (which is actually a figure and not a table) is interesting, I think this section is missing a "punchline table" with the key results (in numerical form rather than as a heatmap).

### Remarks

- Eq. 4 would be clearer with proper bracketing of the sum over D_train
- L567 in the appendix: "a single hidden layer with 50 hidden layers" (I assume you mean 50 hidden units)

 

limitations_and_societal_impact: The authors addressed these concerns appropriately.
review_title: null

final_score: rating: 6: Marginally above the acceptance threshold
review_content: summary: The authors propose using pseudo-inputs, drawn OOD, during training to address unwanted extrapolation properties.These pseudo-inputs encourage the model to remain close to its prior away from the training data. This algorithm is then evaluated on regression and generative modeling tasks.
main_review: Originality: To the best of my knowledge, the idea of combining neural networks and pseudo-inputs is novel. Section 1, which discusses related work, was especially well written. One suggestion is that the definition of OOD that is used in the paper given Algorithm 1, seems to be input points that have low density under the data distribution. It might be useful to mention this earlier in the paper, when OOD is introduced.

Quality: The regression experiments in 1D (Figs. 1, 2, and 4) are helpful to build intuition, but I did not find the argument in Sec. 2.2 that only some pseudo-inputs near the training data are needed to correctly extrapolate everywhere convincing in higher-dimensional input spaces.
 
I think an ablation study wrt. to Algorithm 1 or PIGs would improve the paper. There are many ways to generate OOD pseudo-inputs, and it’s not clear whether Algorithm 1 is crucial to the dissipative loss. Similarly the sensitivity to the number of pseudo-inputs is not explored.
Clarity: 
- I think the connection between pseudo-inputs and priors in Gaussian processes could be elaborated on to improve the motivation.
- What is the maximum in Algorithm 1 as this is over vectors? How sensitive is the output of the algorithm to the number of iterations and tolerance? 
- Table 1 is very difficult to read. It’s not clear which model performed best from the intensity of the coloring

Significance: I like how simple a prescription training on pseudo-inputs is, and the results presented are encouraging. I feel that they would be of interest to the NeurIPS and robust deep learning communities. The significance of the paper would be improved further by benchmarking the method on the OOD calibration tasks of Ovadia et al., but I understand this may be beyond the scope of this work.
limitations_and_societal_impact: Yes, the authors include two sections at the end of the paper to address this.
review_title: null

final_score: rating: 5: Marginally below the acceptance threshold
review_content: summary: The paper proposes a method for learnable uncertainty estimation using neural networks without an explicit requirement of known out-of-distribution data. Instead, the model is trained to maximize model fit where there is explicit training data and maximize uncertainty on estimated “pseudo-inputs”. A key contribution of the method is in how the “pseudo-inputs” are generated and crafted. The authors propose a “Pseudo-Input Generator (PIG)” which generates samples based on the training data density -- locations with lower data density will receive more pseudo-inputs. Results are demonstrated on a variety of tasks with increasing complexity ranging from UCI benchmarks to image generation tasks. 

main_review: **Positives**:

A. Empirical results are both comprehensive (in terms of the datasets and data modalities tested), but also demonstrate strong advances of the proposed method. The authors do a great job at capturing a diverse range of tests, from UCI benchmarks, to synthetic regression data, and higher-dimensional image generation tasks. 

B. The result on generative models presented an excellent application of the proposed method beyond only prediction but also towards density estimation. While generative models frequently model aleatoric uncertainty, the ability and demonstration of also epistemic uncertainty is a great contribution. 

C. The optimization of placement of pseudo-inputs is a clever approach and contribution. Performing this optimization prior to training is a great observation. Did you experiment with an adaptive approach (updating throughout training) which aims to focus on certain regions of the data space depending on the model’s performance during training. 

**Negatives:**
 
The main two contributions, as stated by the authors, are (1) on how to generate reasonable pseudo-inputs in low-density regions of the input space which neighbors training data and (2) a dissipative loss which can jointly fit the in-domain training data while simultaneously maximizing uncertainty on out-of-distribution extrapolated regions, as determined by the pseudo inputs. 

E. I believe contribution (1) is novel and original; however, I think some additional discussion to other works which leverage contrastive priors to emulate the pseudo-inputs would be helpful. An example of such a work is [D. Hafner et al. “Noise contrastive priors for functional uncertainty” UAI 2020]

F. Contribution (2) on the other hand, overlaps significantly with prior work which is not covered in the related work section (despite this section being otherwise very thorough and well written). Specifically I want to raise the author’s attention to the methods of prior networks ([A. Malinin et al. “Predictive Uncertainty Estimation via Prior Networks” NeurIPS 2019]) and evidential learning ([A. Amini et al. “Deep evidential regression” NeurIPS 2020] and [M. Sensoy et al. “Evidential deep learning for …” NeurIPS 2019]). Specifically, the proposed dissipative loss (Eq. 4) is extremely similar to the prior networks training objective which also aims to jointly fit in-domain data while inflating uncertainty on the OOD data. However, a key difference between the proposed method and prior network OOD objective is that prior networks assume the OOD data is given, whereas the proposed method provides an algorithm for generating these. Furthermore, evidential methods (cited above) also leverage in-domain data to “simulate” and act in place of explicit OOD data, but again follow a similar OOD objective to inflate uncertainty on the extrapolated regions. The novelty of the proposed method (and lack of comparisons to both evidential regression and prior networks) in light of these works is my main criticism of the work. Greater discussion explaining the relation to these works would help alleviate my concerns of the contribution. 

**Minor**: 

G. Figure 3 and 4 are out of order on the page. 

H. Add quantitative  x-tick values to Figure 2. The legend references quantitative x-domains but these are meaningless without proper labeling on the plot. 

limitations_and_societal_impact: Yes
review_title: null

Meta-review: The idea of the paper is interesting, however the submitted work fails to acknowledge a fair amount of related work, and the experimental evaluation fails to incorporate sufficient relevant baselines (of which there are many). Although the authors attempted to address this in rebuttal, incorporating this into the paper would require significant changes. The reviewers also noted a number of other concerns (more extensive experiments, clarity) that can be addressed at the same time. Thus I recommend the authors revise their manuscript and resubmit with these improvements.
Decision: Reject