First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. This paper proposes the Latent Case Model (LCM), a Bayesian approach to clustering in which clusters are represented by a prototype (a specific sample from the data) and feature subspaces (a binary subset of the variables signifying those features that are relevant to the class). The approach is presented as being a Bayesian, trainable version of the Case-Based Reasoning approach popular in AI, and is motivated by the ways such models have proved highly effective in explaining human decision making. The generative model (Figure 1) represents each item as coming from a mixture of S clusters, where each cluster is represented by a prototype and subspace (as above) and a function \phi which generates features matching those of the prototype with high probability for features in the subspace, and uniform features outside it. The model is thus similar in functionality to LDA but quite different in terms of its representation.

Compared to previous score matching algorithms, our method is more scalable to high dimensional data and more stable to optimize.

Humans are able to rapidly learn new concepts and continuously integrate them among prior knowledge.

Policy evaluation with smooth and nonlinear function approximation has shown great potential for reinforcement learning. Compared to linear function approximation, it allows for using a richer class of approximation functions such as the neural networks. Traditional algorithms are based on two timescales stochastic approximation whose convergence rate is often slow.

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We thank all reviewers for thoughtful feedback! We reply separately to each reviewer. Reviewer #1: We would like to point out some of the paper's main contributions, not fully recognized in the review. Another example is our algorithm for sampling DAGs conditionally on a root-partition (Sections 3.4 Accordingly, our main innovations are algorithmic. We would like to correct that our algorithm for sampling DAGs is not "classical" (cf.

First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. Overview: The paper proposes a framework for enforcing structure in Bayesian models via structured prior selection based on the maximum entropy principle. Although the optimal prior may not be tractable, the authors developed an approximation method using submodule optimization. Contructing priors with structured variables is an important topic, so this method should be able to make good impact. Quality The paper is technically sound.