Related papers: The Bayesian Bridge
We propose a novel approach to perform approximate Bayesian inference in complex models such as Bayesian neural networks. The approach is more scalable to large data than Markov Chain Monte Carlo, it embraces more expressive models than…
The topic of robustness is experiencing a resurgence of interest in the statistical and machine learning communities. In particular, robust algorithms making use of the so-called median of means estimator were shown to satisfy strong…
Bayesian model averaging, model selection and its approximations such as BIC are generally statistically consistent, but sometimes achieve slower rates og convergence than other methods such as AIC and leave-one-out cross-validation. On the…
Which neural networks are similar is a fundamental question for both machine learning and neuroscience. Here, it is proposed to base comparisons on the predictive distributions of linear readouts from intermediate representations. In…
We propose an empirical Bayes estimator based on Dirichlet process mixture model for estimating the sparse normalized mean difference, which could be directly applied to the high dimensional linear classification. In theory, we build a…
Bayesian methods are often optimal, yet increasing pressure for fast computations, especially with streaming data, brings renewed interest in faster, possibly sub-optimal, solutions. The extent to which these algorithms approximate Bayesian…
This paper motivates the use of random-bridges -- stochastic processes conditioned to take target distributions at fixed timepoints -- in the realm of generative modelling. Herein, random-bridges can act as stochastic transports between two…
We develop two models for Bayesian estimation and selection in high-order, discrete-state Markov chains. Both are based on the mixture transition distribution, which constructs a transition probability tensor with additive mixing of…
Estimation of parameters of a diffusion based on discrete time observations poses a difficult problem due to the lack of a closed form expression for the likelihood. From a Bayesian computational perspective it can be casted as a missing…
We introduce new estimation methods for a sub-class of the Gaussian scale mixture models for wavelet trees by Wainwright, Simoncelli & Willsky that rely on modern results for composite likelihoods and approximate Bayesian inference. Our…
Because of their multimodality, mixture posterior distributions are difficult to sample with standard Markov chain Monte Carlo (MCMC) methods. We propose a strategy to enhance the sampling of MCMC in this context, using a biasing procedure…
We discuss an approach for deriving robust posterior distributions from $M$-estimating functions using Approximate Bayesian Computation (ABC) methods. In particular, we use $M$-estimating functions to construct suitable summary statistics…
Monte Carlo (MC) generators are crucial for analyzing data in particle collider experiments. However, often even a small mismatch between the MC simulations and the measurements can undermine the interpretation of the results. This is…
We introduce a novel combination of Bayesian Models (BMs) and Neural Networks (NNs) for making predictions with a minimum expected risk. Our approach combines the best of both worlds, the data efficiency and interpretability of a BM with…
Through examples of coordinate and probability transformation between different distributions, the basic principle of normalizing flow is introduced in a simple and concise manner. From the perspective of the distribution of random variable…
This paper studies the sparse normal mean models under the empirical Bayes framework. We focus on the mixture priors with an atom at zero and a density component centered at a data driven location determined by maximizing the marginal…
We propose sequential Monte Carlo (SMC) methods for sampling the posterior distribution of state-space models under highly informative observation regimes, a situation in which standard SMC methods can perform poorly. A special case is…
Bayesian models provide a framework for probabilistic modelling of complex datasets. However, many of such models are computationally demanding especially in the presence of large datasets. On the other hand, in sensor network applications,…
Bayesian hierarchical Poisson models are an essential tool for analyzing count data. However, designing efficient algorithms to sample from the posterior distribution of the target parameters remains a challenging task for this class of…
Background: We proposed approximate Bayesian computation with single distribution selection (ABC-SD) for estimating mean and standard deviation from other reported summary statistics. The ABC-SD generates pseudo data from a single…