Digital twins have been actively explored in many engineering applications, such as manufacturing and autonomous systems. However, model discrepancy is ubiquitous in most digital twin models and has significant impacts on the performance of using those models. In recent years, data-driven modeling techniques have been demonstrated promising in characterizing the model discrepancy in existing models, while the training data for the learning of model discrepancy is often obtained in an empirical way and an active approach of gathering informative data can potentially benefit the learning of model discrepancy. On the other hand, Bayesian experimental design (BED) provides a systematic approach to gathering the most informative data, but its performance is often negatively impacted by the model discrepancy. In this work, we build on sequential BED and propose an efficient approach to iteratively learn the model discrepancy based on the data from the BED. The performance of the proposed method is validated by a classical numerical example governed by a convection-diffusion equation, for which full BED is still feasible. The proposed method is then further studied in the same numerical example with a high-dimensional model discrepancy, which serves as a demonstration for the scenarios where full BED is not practical anymore. An ensemble-based approximation of information gain is further utilized to assess the data informativeness and to enhance learning model discrepancy. The results show that the proposed method is efficient and robust to the active learning of high-dimensional model discrepancy, using data suggested by the sequential BED. We also demonstrate that the proposed method is compatible with both classical numerical solvers and modern auto-differentiable solvers.

Rebuttal: thank you for your clarifications. I still think that learning kernel (parameters) from multiple realizations of a GP is not very novel in general, but sufficiently novel in your specific context to get discussed at NIPS. The authors use Gaussian processes to learn human function extrapolation behaviour from human sample data. After a comprehensive literature review, they introduce the main idea of the paper: learn the kernel parameters by maximizing the conditional probability of the extrapolation data given the training data. To allow for flexible kernel shapes, they use spectral mixture kernels.

Additional Feedback: This paper proposes to use Bayesian estimates of fairness metrics. It combines this with Bayesian calibration models (one for each protected attribute value in this particular case) in order to use unlabelled data. In light of existing work (Foulds et al 2019) on Bayesian modelling of fairness, the contribution is rather minor and is limited to the case where we have unlabelled data. The approach the authors use, as it is based on calibration, seems limited to rather specific notions of fairness where Bayesian calibration can be usefully applied. Although in l.64 the definition of calibration is correct, in l. 105-107 you write that s_j P_M(y_j 1 s_j) . Since j is a specific example, there should not be any randomness here.

This paper focuses on the problem of leveraging unlabelled data to generate better estimates of fairness metrics given limited labelled data. All three reviewers agree that the manuscript makes a valuable contribution and is conceptually and mathematically sound. The significance of the contribution (an auditor tool only, instead of an auditor plus a mitigation tool) is however at the low side.

Additional Feedback: Some minor suggestions and typos: -Line 21, missing an "and" -Line 33, "while other developed" - "while other authors developed" -Line 50, and elsewhere in the paper, it is stated that LDA/PLSI use a squared Euclidean loss/distance. This is untrue - both models use likelihood based inference with a multinomial model, and/or Bayesian inference. The older LSI model uses a squared loss, but even the PLSI paper argued that this is insufficient (the implicit Gaussian assumption from squared errors does not hold with small counts as in text data), which motivates the probabilistic modeling approach in PLSI and LDA. The other papers by Mikolov by 2013 are more fundamental references which are better here, especially: Mikolov, T., Sutskever, I., Chen, K., Corrado, G. S., & Dean, J. (2013). Distributed representations of words and phrases and their compositionality.

The paper presents a general method for non-conjugate variational inference based on proximal method and linearisation of the non-conjugate model. This is shown to reduce to natural gradient optimisation for conjugate exponential models. The method is shown to lead to slightly better predictive accuracy than standard approximate inference methods in a few selected problems and data sets. Quality The method relies on linearisation to handle non-conjugate models. The seems potentially problematic, as previous works have found linearisation to be unreliable in variational inference with non-conjugate models (see e.g.

The paper describes tricks to scale Bayesian network structure learning to thousands of variables. This is achieved by developing new heuristics for candidate parent set identification and the subsequent order based structure optimization. In general, the paper is clearly written and easy to read. There are issues in editing and style, but the problems do not affect readability (much). The suggested heuristics feel bit ad-hoc, thus the value of the work is eventually judged by empirical evaluation.

Summary and Contributions: The paper considers the problem of sampling from the posterior distribution in Bayesian inference. To be more precise, the paper approaches the question of stochastic sampling that relies only on minibatches of data at each iteration. To achieve rapid mixing between isolated modes, the authors consider parallel tempered chains and introduce replica-exchange steps into the stochastic Nose-Hoover Dynamics. The crux of this approach is the stochastic test for the replica-exchange step. To develop such a test, the authors follow the paper [An efficient minibatch acceptance test for metropolis-hastings], which introduces the concept of correction distribution.

The paper proposes a novel MCMC-type algorithm to perform Bayesian inference on large datasets. The paper is a mixture of replica exchange, Nose-Hoover dynamics and non-standard acceptance criterion to deal with mini-batches. All the reviewers participated actively to the discussion after the rebuttal was made available. Although all the ingredients of the proposed method do exist, their combination is original and potentially useful for the ML literature as pointed out by most reviewers. Theorem 2 is also neat and proposes a nice way to propose swaps between replicas using mini-batches.

I would just like to confirm my understanding of the algorithmic contributions of this work. As far as I understand, Jin et al [2019] propose a learning algorithm for the standard RL case with linear function approximation in linear MDPs. Then Jin et al [2020] propose a method for efficient exploration in the reward-free RL case. This is for normal MDPs but in the tabular setting. In that work, exploration is achieved by constructing a reward function where the reward is 1 for states that are "significant", and 0 otherwise, and then solving the resulting task with an efficient learning algorithm.