Related papers: Bayesian posterior repartitioning for nested sampl…
Neural Networks (NNs) have been widely {used in supervised learning} due to their ability to model complex nonlinear patterns, often presented in high-dimensional data such as images and text. However, traditional NNs often lack the ability…
Nested sampling (NS) computes parameter posterior distributions and makes Bayesian model comparison computationally feasible. Its strengths are the unsupervised navigation of complex, potentially multi-modal posteriors until a well-defined…
Solving Bayesian inverse problems typically involves deriving a posterior distribution using Bayes' rule, followed by sampling from this posterior for analysis. Sampling methods, such as general-purpose Markov chain Monte Carlo (MCMC), are…
Using instruments comprising ordered responses to items are ubiquitous for studying many constructs of interest. However, using such an item response format may lead to items with response categories infrequently endorsed or unendorsed…
Bayesian methods are actively used for parameter identification and uncertainty quantification when solving nonlinear inverse problems with random noise. However, there are only few theoretical results justifying the Bayesian approach.…
Nested sampling is an important tool for conducting Bayesian analysis in Astronomy and other fields, both for sampling complicated posterior distributions for parameter inference, and for computing marginal likelihoods for model comparison.…
Many modern experiments, such as microarray gene expression and genome-wide association studies, present the problem of estimating a large number of parallel effects. Bayesian inference is a popular approach for analyzing such data by…
Sparse representations have proven their efficiency in solving a wide class of inverse problems encountered in signal and image processing. Conversely, enforcing the information to be spread uniformly over representation coefficients…
It is now widely accepted that the standard inferential toolkit used by the scientific research community -- null-hypothesis significance testing (NHST) -- is not fit for purpose. Yet despite the threat posed to the scientific enterprise,…
Adding domain knowledge to a learning system is known to improve results. In multi-parameter Bayesian frameworks, such knowledge is incorporated as a prior. On the other hand, various model parameters can have different learning rates in…
We consider a prior for nonparametric Bayesian estimation which uses finite random series with a random number of terms. The prior is constructed through distributions on the number of basis functions and the associated coefficients. We…
Optimization is widely used in statistics, and often efficiently delivers point estimates on useful spaces involving structural constraints or combinatorial structure. To quantify uncertainty, Gibbs posterior exponentiates the negative loss…
The prior distribution for the unknown model parameters plays a crucial role in the process of statistical inference based on Bayesian methods. However, specifying suitable priors is often difficult even when detailed prior knowledge is…
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…
In this work we explore a straightforward variational Bayes scheme for Recurrent Neural Networks. Firstly, we show that a simple adaptation of truncated backpropagation through time can yield good quality uncertainty estimates and superior…
Sparse modeling for signal processing and machine learning has been at the focus of scientific research for over two decades. Among others, supervised sparsity-aware learning comprises two major paths paved by: a) discriminative methods and…
Prior information often takes the form of parameter constraints. Bayesian methods include such information through prior distributions having constrained support. By using posterior sampling algorithms, one can quantify uncertainty without…
Bayesian neural networks attempt to combine the strong predictive performance of neural networks with formal quantification of uncertainty associated with the predictive output in the Bayesian framework. However, it remains unclear how to…
In variational inference, the benefits of Bayesian models rely on accurately capturing the true posterior distribution. We propose using neural samplers that specify implicit distributions, which are well-suited for approximating complex…
This work proposes a Bayesian inference method for the reduced-order modeling of time-dependent systems. Informed by the structure of the governing equations, the task of learning a reduced-order model from data is posed as a Bayesian…