After much discussion and follow up questions to the authors, the reviewers converged towards recommending to accept this submission. The reviewers were satisfied with the authors' response, and have updated their reviews accordingly. There are some remaining points about claims made in the paper which need to be toned down (single layer vs deep models), and the conclusions from empirical validation only supporting claims with small low dim data (while the effect reverses with the full 11000 datapoints in AL). I recommend acceptance and trust that the authors will address these remaining points for the camera ready.

The authors propose a method to trade-off "computational costs" and "model fit" when learning a Sum-Product-Network (SPNs) represented as an Arithmetic Circuit. An SPN is a compact representation of a probabilistic model over discrete random variables with finite domain. The proposed method involves an SPN learner that is restricted to binary random variables. In practice, this requires to convert continuous variables into categoricals (e.g., using binning), and categoricals into binaries. While SPNs can handle missing data, they do are typically black-box models where the structure is learned.

The authors present an interesting contribution to sum-product networks and yet there are some concerns on its impact and significance, hence the mixed reviews.

Summary: Conditional Independence Testing is an important part of causal structure learning algorithms. However, in the most general case either one has to do a lot of conditional independence tests and/or test by conditioning on a very large number of variables. This work proposes using at most two CI tests per candidate parent involving exactly at most one conditioning variable to filter the real parents of a response variable under certain conditions. This work is interested in identifying direct causes of a Response variable from amongst a set of a candidate parent variables {M_i}. Response variable does not have any observed descendants.

In this paper, the authors describe a novel causal discovery method that performs a single conditional independence test per features, and is thus scalable to high dimensional data, along with a novel encelographic data application. The reviewers appreciated the novelty of the methods, and the chosen application.

Strengths: Soundness: The model formulation appears to be mathematically sound. As with several previous works, the authors utilize linear-Gaussian distributions for dynamics, which have the benefit of permitting exact computation of expectations, e.g. The authors propose two main improvements over related models: 1) the use of recurrent switch transitions through Gaussian switch variables, and 2) non-linear emission models through the use of an additional (auxiliary) latent variable, z. They train this model with a sequential Monte Carlo objective utilized in previous works. This paper builds off of many of the theoretical developments of previous works, adding a couple of useful techniques.

The paper considers a Bayesian decision theoretic formulation of the problem of minimizing the number of queries to identify the desired number of positive instances (instances with positive labels), given a probabilistic model of the labels in the dataset. This formulation is motivated by the material and drug discovery problems. The problem is properly formulated and contrasted with the recently suggested budgeted-learning setting, where the goal is to identify the largest number of positive instances given a fixed budget on queries. Further the authors show that the optimal Bayesian policy is hard to compute and hard to approximate. However, further assuming certain conditional independence the policy can be approximated efficiently using the negative-poisson-binomial distribution, for which the authors propose computationally-cheap expectation estimates.The resulting policy is compared to several other alternatives, and it is shown to obtain overall superior performance in both material discovery and drug discovery datasets.

Originality - this research is similar to prototype-based learning of neural networks, but it is the first to propose learning and detecting generic components that characterize object using three different types of reasoning (positive, negative and indefinite). Clarity - the paper is hard to read and follow. There are large chunks of text with no figures or equations to illustrate the concepts. In the supplementary material they provide a lot more information which was left out of the main paper. It does feel like the paper is not self-sufficient, as many important steps are only brushed over, such as the training procedure and how to generate the interpretations.

The paper proposes an interesting probabilistic reasoning process that considers the presence or absence of various components (that are indicative of several properties of an instance) and combines them together as (potentially interpretable) evidence for its final classification. The idea seems to us novel and interesting. Multiple experiments are provided to support the approach. The paper is also well-written and clear.

The paper proposes a novel and interesting GAN-based method for conditional independence test. While there is some concern on applying the black-box method to rigorous statistical tests, I still think the paper includes a new and significant idea to the important but difficult problem of conditional independence. I would like the authors to reflect the review comments in making the final version.