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Belief Propagation is a well-studied message-passing algorithm that runs over graphical models and can be used for approximate inference and approximation of local marginals. The resulting approximations are equivalent to the Bethe-Peierls…

In this paper, we investigate distributed inference schemes, over binary-valued Markov random fields, which are realized by the belief propagation (BP) algorithm. We first show that a decision variable obtained by the BP algorithm in a…

Networks are models representing relationships between entities. Often these relationships are explicitly given, or we must learn a representation which generalizes and predicts observed behavior in underlying individual data (e.g.…

Joint machine learning models that allow synthesizing and classifying data often offer uneven performance between those tasks or are unstable to train. In this work, we depart from a set of empirical observations that indicate the…

Compressed communication, in the form of sparsification or quantization of stochastic gradients, is employed to reduce communication costs in distributed data-parallel training of deep neural networks. However, there exists a discrepancy…

We propose to estimate the number of communities in degree-corrected stochastic block models based on a pseudo likelihood ratio statistic. To this end, we introduce a method that combines spectral clustering with binary segmentation. This…

Hidden Markov Models (HMMs) are learning methods for pattern recognition. The probabilistic HMMs have been one of the most used techniques based on the Bayesian model. First-order probabilistic HMMs were adapted to the theory of belief…

How can we tell when accounts are fake or real in a social network? And how can we tell which accounts belong to liberal, conservative or centrist users? Often, we can answer such questions and label nodes in a network based on the labels…

Affinity propagation is an exemplar-based clustering algorithm that finds a set of data-points that best exemplify the data, and associates each datapoint with one exemplar. We extend affinity propagation in a principled way to solve the…

Predictive Coding (PC) is an influential account of cortical learning. Much of recent work has focused on comparing PC to Backpropagation (BP) to find whether PC offers any advantages. Small scale experiments show that PC enables learning…

Bayesian hierarchical linear models provide a natural framework to analyze nested and clustered data. Classical estimation with Markov chain Monte Carlo produces well calibrated posterior distributions but becomes computationally expensive…

Transfer learning is a recent field of machine learning research that aims to resolve the challenge of dealing with insufficient training data in the domain of interest. This is a particular issue with traditional deep neural networks where…

Hidden Markov models (HMMs) are widely used statistical models for modeling sequential data. The parameter estimation for HMMs from time series data is an important learning problem. The predominant methods for parameter estimation are…

There is an increasing interest in scaling tensor network methods through belief propagation (BP), as well as increasing the accuracy of BP through tensor network methods. We develop a unification framework that takes an arbitrary graphical…

We develop a mean field theory for sigmoid belief networks based on ideas from statistical mechanics. Our mean field theory provides a tractable approximation to the true probability distribution in these networks; it also yields a lower…

Tensor network contraction is a fundamental computational challenge underlying quantum many-body physics, statistical mechanics, and machine learning. Belief propagation (BP) provides an efficient approximate solution, but introduces…

Network embedding methods aim at learning low-dimensional latent representation of nodes in a network. While achieving competitive performance on a variety of network inference tasks such as node classification and link prediction, these…

Community detection in multi-layer networks has emerged as a crucial area of modern network analysis. However, conventional approaches often assume that nodes belong exclusively to a single community, which fails to capture the complex…

Deep belief networks are used extensively for unsupervised stochastic learning on large datasets. Compared to other deep learning approaches their layer-by-layer learning makes them highly scalable. Unfortunately, the principles by which…

Generative foundation models like Stable Diffusion comprise a diverse spectrum of knowledge in computer vision with the potential for transfer learning, e.g., via generating data to train student models for downstream tasks. This could…