Related papers: A visual introduction to Gaussian Belief Propagati…
A new algorithm based on bayesian inference for learning local graph conductance based on Gaussian Process(GP) is given that uses advanced MCMC convergence ideas to create a scalable and fast algorithm for convergence to stationary…
Gaussian processes (GPs) are a good choice for function approximation as they are flexible, robust to over-fitting, and provide well-calibrated predictive uncertainty. Deep Gaussian processes (DGPs) are multi-layer generalisations of GPs,…
The accurate prediction of time-changing variances is an important task in the modeling of financial data. Standard econometric models are often limited as they assume rigid functional relationships for the variances. Moreover, function…
The Graph Burning Problem (GBP) is a combinatorial optimization problem that has gained relevance as a tool for quantifying a graph's vulnerability to contagion. Although it is based on a very simple propagation model, its decision version…
Sparse variational Gaussian processes (GPs) construct tractable posterior approximations to GP models. At the core of these methods is the assumption that the true posterior distribution over training function values ${\bf f}$ and inducing…
We formulate natural gradient variational inference (VI), expectation propagation (EP), and posterior linearisation (PL) as extensions of Newton's method for optimising the parameters of a Bayesian posterior distribution. This viewpoint…
We introduce stochastic variational inference for Gaussian process models. This enables the application of Gaussian process (GP) models to data sets containing millions of data points. We show how GPs can be vari- ationally decomposed to…
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…
Max-product Belief Propagation (BP) is a popular message-passing algorithm for computing a Maximum-A-Posteriori (MAP) assignment over a distribution represented by a Graphical Model (GM). It has been shown that BP can solve a number of…
Belief propagation is an algorithm that is known from statistical physics and computer science. It provides an efficient way of calculating marginals that involve large sums of products which are efficiently rearranged into nested products…
We present a differentiable approach to learn the probabilistic factors used for inference by a nonparametric belief propagation algorithm. Existing nonparametric belief propagation methods rely on domain-specific features encoded in the…
A neural network (NN) is a parameterised function that can be tuned via gradient descent to approximate a labelled collection of data with high precision. A Gaussian process (GP), on the other hand, is a probabilistic model that defines a…
We extend Gaussian networks - directed acyclic graphs that encode probabilistic relationships between variables - to its vector form. Vector Gaussian continuous networks consist of composite nodes representing multivariates, that take…
Many inferential tasks involve fitting models to observed data and predicting outcomes at new covariate values, requiring interpolation or extrapolation. Conventional methods select a single best-fitting model, discarding fits that were…
We present a differentiable approach to learn the probabilistic factors used for inference by a nonparametric belief propagation algorithm. Existing nonparametric belief propagation methods rely on domain-specific features encoded in the…
We often encounter probability distributions given as unnormalized products of non-negative functions. The factorization structures are represented by hypergraphs called factor graphs. Such distributions appear in various fields, including…
Approximate Bayesian inference methods provide a powerful suite of tools for finding approximations to intractable posterior distributions. However, machine learning applications typically involve selecting actions, which -- in a Bayesian…
We develop a fast variational approximation scheme for Gaussian process (GP) regression, where the spectrum of the covariance function is subjected to a sparse approximation. Our approach enables uncertainty in covariance function…
This paper introduces a new probabilistic model for online learning which dynamically incorporates information from stochastic gradients of an arbitrary loss function. Similar to probabilistic filtering, the model maintains a Gaussian…
Learning general latent-variable probabilistic graphical models is a key theoretical challenge in machine learning and artificial intelligence. All previous methods, including the EM algorithm and the spectral algorithms, face severe…