Related papers: Revisiting Bayesian Autoencoders with MCMC
Deep learning models, such as convolutional neural networks, have long been applied to image and multi-media tasks, particularly those with structured data. More recently, there has been more attention to unstructured data that can be…
Bayesian inference provides a methodology for parameter estimation and uncertainty quantification in machine learning and deep learning methods. Variational inference and Markov Chain Monte-Carlo (MCMC) sampling methods are used to…
This paper introduces a Bayesian framework that combines Markov chain Monte Carlo (MCMC) sampling, dimensionality reduction, and neural density estimation to efficiently handle inverse problems that (i) must be solved multiple times, and…
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,…
Rich data generating mechanisms are ubiquitous in this age of information and require complex statistical models to draw meaningful inference. While Bayesian analysis has seen enormous development in the last 30 years, benefitting from the…
Markov Chain Monte Carlo (MCMC) is a well-established family of algorithms primarily used in Bayesian statistics to sample from a target distribution when direct sampling is challenging. Existing work on Bayesian decision trees uses MCMC.…
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…
The past decades have seen enormous improvements in computational inference based on statistical models, with continual enhancement in a wide range of computational tools, in competition. In Bayesian inference, first and foremost, MCMC…
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…
Bayesian inference promises to ground and improve the performance of deep neural networks. It promises to be robust to overfitting, to simplify the training procedure and the space of hyperparameters, and to provide a calibrated measure of…
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…
In conducting non-linear dimensionality reduction and feature learning, it is common to suppose that the data lie near a lower-dimensional manifold. A class of model-based approaches for such problems includes latent variables in an unknown…
Bayesian inference for Markov processes has become increasingly relevant in recent years. Problems of this type often have intractable likelihoods and prior knowledge about model rate parameters is often poor. Markov Chain Monte Carlo…
We focus on generative autoencoders, such as variational or adversarial autoencoders, which jointly learn a generative model alongside an inference model. Generative autoencoders are those which are trained to softly enforce a prior on the…
Due to the importance of uncertainty quantification (UQ), Bayesian approach to inverse problems has recently gained popularity in applied mathematics, physics, and engineering. However, traditional Bayesian inference methods based on Markov…
Bayesian models have become very popular over the last years in several fields such as signal processing, statistics, and machine learning. Bayesian inference requires the approximation of complicated integrals involving posterior…
Established methods for unsupervised representation learning such as variational autoencoders produce none or poorly calibrated uncertainty estimates making it difficult to evaluate if learned representations are stable and reliable. In…
Bayesian neural learning feature a rigorous approach to estimation and uncertainty quantification via the posterior distribution of weights that represent knowledge of the neural network. This not only provides point estimates of optimal…
This study uses a Variational Autoencoder method to enhance the efficiency and applicability of Markov Chain Monte Carlo (McMC) methods by generating broader-spectrum prior proposals. Traditional approaches, such as the Karhunen-Lo\`eve…
We propose a new computationally efficient sampling scheme for Bayesian inference involving high dimensional probability distributions. Our method maps the original parameter space into a low-dimensional latent space, explores the latent…