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Markov Chain Monte Carlo (MCMC) algorithms are commonly used for their versatility in sampling from complicated probability distributions. However, as the dimension of the distribution gets larger, the computational costs for a satisfactory…
Bayesian learning in undirected graphical models|computing posterior distributions over parameters and predictive quantities is exceptionally difficult. We conjecture that for general undirected models, there are no tractable MCMC (Markov…
We present a novel Bayesian inference tool that uses a neural network to parameterise efficient Markov Chain Monte-Carlo (MCMC) proposals. The target distribution is first transformed into a diagonal, unit variance Gaussian by a series of…
A key quantity of interest in Bayesian inference are expectations of functions with respect to a posterior distribution. Markov Chain Monte Carlo is a fundamental tool to consistently compute these expectations via averaging samples drawn…
The Markov chain Monte Carlo (MCMC) method is the computational workhorse for Bayesian inverse problems. However, MCMC struggles in high-dimensional parameter spaces, since its iterates must sequentially explore the high-dimensional space.…
Despite recent advances, sampling-based inference for Bayesian Neural Networks (BNNs) remains a significant challenge in probabilistic deep learning. While sampling-based approaches do not require a variational distribution assumption,…
Proximal Markov Chain Monte Carlo is a novel construct that lies at the intersection of Bayesian computation and convex optimization, which helped popularize the use of nondifferentiable priors in Bayesian statistics. Existing formulations…
Bayesian inference in deep neural networks is challenging due to the high-dimensional, strongly multi-modal parameter posterior density landscape. Markov chain Monte Carlo approaches asymptotically recover the true posterior but are…
Probabilistic models are conceptually powerful tools for finding structure in data, but their practical effectiveness is often limited by our ability to perform inference in them. Exact inference is frequently intractable, so approximate…
Uncertainty estimation in deep models is essential in many real-world applications and has benefited from developments over the last several years. Recent evidence suggests that existing solutions dependent on simple Gaussian formulations…
Bayesian models are a powerful tool for studying complex data, allowing the analyst to encode rich hierarchical dependencies and leverage prior information. Most importantly, they facilitate a complete characterization of uncertainty…
There has been considerable interest in making Bayesian inference more scalable. In big data settings, most literature focuses on reducing the computing time per iteration, with less focused on reducing the number of iterations needed in…
Decision tree learning is a popular approach for classification and regression in machine learning and statistics, and Bayesian formulations---which introduce a prior distribution over decision trees, and formulate learning as posterior…
MCMC methods for sampling from the space of DAGs can mix poorly due to the local nature of the proposals that are commonly used. It has been shown that sampling from the space of node orders yields better results [FK03, EW06]. Recently,…
We introduce a new Markov-Chain Monte Carlo (MCMC) approach designed for efficient sampling of highly correlated and multimodal posteriors. Parallel tempering, though effective, is a costly technique for sampling such posteriors. Our…
High-dimensional data are routinely collected in many areas. We are particularly interested in Bayesian classification models in which one or more variables are imbalanced. Current Markov chain Monte Carlo algorithms for posterior…
We apply Markov Chain Monte Carlo (MCMC) to the problem of parametric galaxy modeling, estimating posterior distributions of galaxy properties such as ellipticity and brightness for more than 100,000 images of galaxies taken from DC2, a…
Segmenting images of low quality or with missing data is a challenging problem. Integrating statistical prior information about the shapes to be segmented can improve the segmentation results significantly. Most shape-based segmentation…
For Bayesian computation in big data contexts, the divide-and-conquer MCMC concept splits the whole data set into batches, runs MCMC algorithms separately over each batch to produce samples of parameters, and combines them to produce an…
Autoencoders gained popularity in the deep learning revolution given their ability to compress data and provide dimensionality reduction. Although prominent deep learning methods have been used to enhance autoencoders, the need to provide…