Paper:
Semi-supervised Deep Kernel Learning: Regression with Unlabeled Data by Minimizing Predictive Variance
Large amounts of labeled data are typically required to train deep learning models. For many real-world problems, however, acquiring additional data can be expensive or even impossible. We present semi-supervised deep kernel learning (SSDKL), a semi-supervised regression model based on minimizing predictive variance in the posterior regularization framework. SSDKL combines the hierarchical representation learning of neural networks with the probabilistic modeling capabilities of Gaussian processes. By leveraging unlabeled data, we show improvements on a diverse set of real-world regression tasks over supervised deep kernel learning and semi-supervised methods such as VAT and mean teacher adapted for regression.

Review:
The paper paper applies Deep Kernel Learning [DKL, 1] to Semi-Supervised Regression. DKL is a combination of a Gaussian Process and a Deep Neural Network (DNN). The idea is to use DNN as a feature transformer inside the kernel of a Gaussian Process (GP). In other words, the the GP operates on the outputs of the DNN. Both the GP and the DNN can be trained using SGD in end-to-end fashion. This paper proposes to apply DKL to semi-supervised regression by minimizing the posterior predictive variance on the unlabeled data. Authors demonstrate improved performance on semi-supervised problems compared to conventional DKL (trained on labeled data only) as well as adapted versions of semi-supervised classification techniques such as VAT [2].  The paper is technically correct and well-written. I have the following questions and concerns: 1. Do I understand correctly that the idea of variance minimization is specific to DKL and would not work for GPs with conventional kernels? The variance of the predictive distribution serves as a proxy for how the unlabeled data points are close to labeled data in the output space of the DNN? While the paper spends several paragraphs on the motivation for minimizing the predictive variance I still find it somewhat unclear. In the rebuttal the authors confirmed my claim above. I encourage them to try to make the motivation more clear for the camera-ready version.  2. To the best of my knowledge this paper is the first to consider deep semi-supervised regression. Thus, there are no known reference results that could be used to compare against the proposed method. The authors adapt several SSL techniques such as VAT [2] to regression for the sake of comparison, but it is not clear if the baselines are tuned sufficiently. For this reason, it would be beneficial to evaluate the proposed technique on semi-supervised classification, where multiple baseline results are available. The authors leave semi-supervised classification for future work.  To address this issue the authors will publicly release their code according to the rebuttal.  3. The authors use cross-validation for tuning hyper-parameters. Is it possible to tune the hyper-parameters by maximizing the likelihood / evidence lower bound (ELBO)? As discussed in [3], only very small validation sets can be used in realistic applications of semi-supervised learning; using the bayesian model selection can be especially beneficial in this application, if it would allow to avoid using a validation set.  According to the rebuttal the authors tune some of the hyper-parameters with marginal likelihood optimization, and will make this point more clear in the camera-ready version.  The paper explores semi-supervised regression, an unexplored but potentially important area of machine learning. It proposes new interesting methodology for this problem and shows promising results. I recommend an accept for this paper.  I was satisfied with the author's feedback and the discussion phase didn't raise any important issues with this paper. I thus increase my score to 7.  [1] Deep Kernel Learning; Andrew Gordon Wilson, Zhiting Hu, Ruslan Salakhutdinov, Eric P. Xing [2] Virtual Adversarial Training: A Regularization Method for Supervised and Semi-Supervised Learning; Takeru Miyato, Shin-ichi Maeda, Masanori Koyama, Shin Ishii [3] Realistic Evaluation of Deep Semi-Supervised Learning Algorithms; Avital Oliver, Augustus Odena, Colin Raffel, Ekin D. Cubuk, Ian J. Goodfellow