Statistical network analysis primarily focuses on inferring the parameters of an observed network. In many applications, especially in the social sciences, the observed data is the groups formed by individual subjects. In these applications, the network is itself a parameter of a statistical model. Zhao and Weko (2019) propose a model-based approach, called the hub model, to infer implicit networks from grouping behavior. The hub model assumes that each member of the group is brought together by a member of the group called the hub. The hub model belongs to the family of Bernoulli mixture models. Identifiability of parameters is a notoriously difficult problem for Bernoulli mixture models. This paper proves identifiability of the hub model parameters and estimation consistency under mild conditions. Furthermore, this paper generalizes the hub model by introducing a model component that allows hubless groups in which individual nodes spontaneously appear independent of any other individual. We refer to this additional component as the null component. The new model bridges the gap between the hub model and the degenerate case of the mixture model -- the Bernoulli product. Identifiability and consistency are also proved for the new model. Numerical studies are provided to demonstrate the theoretical results.

ABSTRACT Motivated by the ever-increasing demands for limited communication bandwidth and low-power consumption, we propose a new methodology, named joint V ariational Autoen-coders with Bernoulli mixture models (V AB), for performing clustering in the compressed data domain. The idea is to reduce the data dimension by V ariational Autoencoders (V AEs) and group data representations by Bernoulli mixture models (BMMs). Once jointly trained for compression and clustering, the model can be decomposed into two parts: a data vendor that encodes the raw data into compressed data, and a data consumer that classifies the received (compressed) data. To enable training using the gradient descent algorithm, we propose to use the Gumbel-Softmax distribution to resolve the infeasibility of the back-propagation algorithm when assessing categorical samples. Index T erms -- Clustering, V ariational Autoencoder (V AE), Bernoulli Mixture Model (BMM) 1. INTRODUCTION Clustering is a fundamental task with applications in medical imaging, social network analysis, bioinformatics, computer graphics, etc. Applying classical clustering methods directly to high dimensional data may be computational inefficient and suffer from instability.

I'm following the book Pattern recognition and machine learning by Bishop on Bernoulli mixture model, and trying to code it. But I don't understand how to calculate the conditional probability (page 446 of the first edition) So in the E-step I'm supposed to calculate this. But it is said that we should use the log of the probability, so as to avoid numerical underflow. So how do i apply it here? I can't see any way to do it.

When software developers modify one or more files in a large code base, they must also identify and update other related files. Many file dependencies can be detected by mining the development history of the code base: in essence, groups of related files are revealed by the logs of previous workflows. From data of this form, we show how to detect dependent files by solving a problem in binary matrix completion. We explore different latent variable models (LVMs) for this problem, including Bernoulli mixture models, exponential family PCA, restricted Boltzmann machines, and fully Bayesian approaches. We evaluate these models on the development histories of three large, open-source software systems: Mozilla Firefox, Eclipse Subversive, and Gimp. In all of these applications, we find that LVMs improve the performance of related file prediction over current leading methods.