This paper proposes the permuton-induced Chinese restaurant process (PCRP), a stochastic process on rectangular partitioning of a matrix.

This paper proposes the permuton-induced Chinese restaurant process (PCRP), a stochastic process on rectangular partitioning of a matrix. This distribution is suitable for use as a prior distribution in Bayesian nonparametric relational model to find hidden clusters in matrices and network data. Our main contribution is to introduce the notion of permutons into the well-known Chinese restaurant process (CRP) for sequence partitioning: a permuton is a probability measure on $[0,1]\times [0,1]$ and can be regarded as a geometric interpretation of the scaling limit of permutations. Specifically, we extend the model that the table order of CRPs has a random geometric arrangement on $[0,1]\times [0,1]$ drawn from the permuton. By analogy with the relationship between the stick-breaking process (SBP) and CRP for the infinite mixture model of a sequence, this model can be regarded as a multi-dimensional extension of CRP paired with the block-breaking process (BBP), which has been recently proposed as a multi-dimensional extension of SBP. While BBP always has an infinite number of redundant intermediate variables, PCRP can be composed of varying size intermediate variables in a data-driven manner depending on the size and quality of the observation data. Experiments show that PCRP can improve the prediction performance in relational data analysis by reducing the local optima and slow mixing problems compared with the conventional BNP models because the local transitions of PCRP in Markov chain Monte Carlo inference are more flexible than the previous models.

First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. In their paper "Information-based learning by agents in unbounded state spaces" the authors extend a previous model of information-based exploration as described in reference [11] to unbounded state spaces by introducing a Chinese restaurant process to model transition probabilities. Previous studies have used the Chinese restaurant process for reinforcement learning--for example, reference [2] cited by the authors. It would therefore be good if the authors could clarify the differences to previous studies that have used Chinese restaurant processes in reinforcement learning to clarify originality. L 130: verb is missing in the second part of the sentence To compute the information gain the authors need to compute relative entropies between the true state transition distribution and the estimated state transition distribution.

This paper proposes the permuton-induced Chinese restaurant process (PCRP), a stochastic process on rectangular partitioning of a matrix.

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To master a discipline such as algebra or physics, students must acquire a set of cognitive skills. Traditionally, educators and domain experts use intuition to determine what these skills are and then select practice exercises to hone a particular skill. We propose a technique that uses student performance data to automatically discover the skills needed in a discipline. The technique assigns a latent skill to each exercise such that a student's expected accuracy on a sequence of same-skill exercises improves monotonically with practice. Rather than discarding the skills identified by experts, our technique incorporates a nonparametric prior over the exerciseskill assignments that is based on the expert-provided skills and a weighted Chinese restaurant process.

The idea that animals might use information-driven planning to explore an unknown environment and build an internal model of it has been proposed for quite some time. Recent work has demonstrated that agents using this principle can efficiently learn models of probabilistic environments with discrete, bounded state spaces. However, animals and robots are commonly confronted with unbounded environments. To address this more challenging situation, we study informationbased learning strategies of agents in unbounded state spaces using non-parametric Bayesian models. Specifically, we demonstrate that the Chinese Restaurant Process (CRP) model is able to solve this problem and that an Empirical Bayes version is able to efficiently explore bounded and unbounded worlds by relying on little prior information.

We introduce a model where the rate of an inhomogeneous Poisson process is modified by a Chinese restaurant process. Applying a MCMC sampler to this model allows us to do posterior Bayesian inference about the number of states in Poisson-like data. Our sampler is shown to get accurate results for synthetic data and we apply it to V1 neuron spike data to find discrete firing rate states depending on the orientation of a stimulus.

The distance dependent Chinese restaurant process (ddCRP) was recently introduced to accommodate random partitions of non-exchangeable data [1]. The dd-CRP clusters data in a biased way: each data point is more likely to be clustered with other data that are near it in an external sense. This paper examines the dd-CRP in a spatial setting with the goal of natural image segmentation. We explore the biases of the spatial ddCRP model and propose a novel hierarchical extension better suited for producing "human-like" segmentations. We then study the sensitivity of the models to various distance and appearance hyperparameters, and provide the first rigorous comparison of nonparametric Bayesian models in the image segmentation domain. On unsupervised image segmentation, we demonstrate that similar performance to existing nonparametric Bayesian models is possible with substantially simpler models and algorithms.