The count-min sketch is a time-and memory-efficient randomized data structure that provides a point estimate of the number of times an item has appeared in a data stream. The count-min sketch and related hash-based data structures are ubiquitous in systems that must track frequencies of data such as URLs, IP addresses, and language n-grams. We present a Bayesian view on the count-min sketch, using the same data structure, but providing a posterior distribution over the frequencies that characterizes the uncertainty arising from the hash-based approximation. In particular, we take a nonparametric approach and consider tokens generated from a Dirichlet process (DP) random measure, which allows for an unbounded number of unique tokens. Using properties of the DP, we show that it is possible to straightforwardly compute posterior marginals of the unknown true counts and that the modes of these marginals recover the count-min sketch estimator, inheriting the associated probabilistic guarantees. Using simulated data with known ground truth, we investigate the properties of these estimators. Lastly, we also study a modified problem in which the observation stream consists of collections of tokens (i.e., documents) arising from a random measure drawn from a stable beta process, which allows for power law scaling behavior in the number of unique tokens.

Here we describe CGS in more details. Eqn. 10 we obtain: null null Expression under the last integral in Eqn. 13 is tractable, thanks to the conjugacy of the Normal-inverse-Wishart prior to the Gaussian likelihood. Finally, posterior predictive density (10) can be written as a mixture of multivariate Student's CIFAR experiments used the standard train/test split. Results for architectures not included in Section 4 are summarized in Fig. C.1. Table C.1: CNN architectures used in experiments (Section 4).

The model is used to investigate the complexity of representations through the KL divergence between the max entropy reference and the model posterior. The reviewers generally felt the paper made a variety of interesting observations. In a final version, the authors are encouraged to read and account for updates to reviewer comments after the rebuttal, and to discuss https://arxiv.org/abs/2002.08791, which provides a complementary Bayesian nonparametric perspective on deep neural networks.

We investigate neural network representations from a probabilistic perspective. Specifically, we leverage Bayesian nonparametrics to construct models of neural activations in Convolutional Neural Networks (CNNs) and latent representations in Variational Autoencoders (VAEs). This allows us to formulate a tractable complexity measure for distributions of neural activations and to explore global structure of latent spaces learned by VAEs. We use this machinery to uncover how memorization and two common forms of regularization, i.e. dropout and input augmentation, influence representational complexity in CNNs. We demonstrate that networks that can exploit patterns in data learn vastly less complex representations than networks forced to memorize.

In tracking multiple objects, it is often assumed that each observation (measurement) is originated from one and only one object. However, we may encounter a situation that each measurement may or may not be associated with multiple objects at each time step --spawning. Therefore, the association of each measurement to multiple objects is a crucial task to perform in order to track multiple objects with birth and death. In this paper, we introduce a novel Bayesian nonparametric approach that models a scenario where each observation may be drawn from an unknown number of objects for which it provides a tractable Markov chain Monte Carlo (MCMC) approach to sample from the posterior distribution. The number of objects at each time step, itself, is also assumed to be unknown. We, then, show through experiments the advantage of nonparametric modeling to scenarios with spawning events. Our experiment results also demonstrate the advantages of our framework over the existing methods.

The count-min sketch is a time- and memory-efficient randomized data structure that provides a point estimate of the number of times an item has appeared in a data stream. The count-min sketch and related hash-based data structures are ubiquitous in systems that must track frequencies of data such as URLs, IP addresses, and language n-grams. We present a Bayesian view on the count-min sketch, using the same data structure, but providing a posterior distribution over the frequencies that characterizes the uncertainty arising from the hash-based approximation. In particular, we take a nonparametric approach and consider tokens generated from a Dirichlet process (DP) random measure, which allows for an unbounded number of unique tokens. Using properties of the DP, we show that it is possible to straightforwardly compute posterior marginals of the unknown true counts and that the modes of these marginals recover the count-min sketch estimator, inheriting the associated probabilistic guarantees.