Related papers: EP-GIG Priors and Applications in Bayesian Sparse …
We propose a general framework for obtaining probabilistic solutions to PDE-based inverse problems. Bayesian methods are attractive for uncertainty quantification but assume knowledge of the likelihood model or data generation process. This…
This paper addresses Bayesian inference related to partial differential equations (PDEs), particularly nonparametric regression constrained by PDEs. To effectively encode prior information, we propose a novel framework that learns a…
We consider a Gaussian process formulation of the multiple kernel learning problem. The goal is to select the convex combination of kernel matrices that best explains the data and by doing so improve the generalisation on unseen data.…
Predictive uncertainty quantification is crucial for reliable decision-making in various applied domains. Bayesian neural networks offer a powerful framework for this task. However, defining meaningful priors and ensuring computational…
Gaussian process (GP) priors are non-parametric generative models with appealing modelling properties for Bayesian inference: they can model non-linear relationships through noisy observations, have closed-form expressions for training and…
L1-ball-type priors are a recent generalization of the spike-and-slab priors. By transforming a continuous precursor distribution to the L1-ball boundary, it induces exact zeros with positive prior and posterior probabilities. With great…
This work introduces a novel probabilistic deep learning technique called deep Gaussian mixture ensembles (DGMEs), which enables accurate quantification of both epistemic and aleatoric uncertainty. By assuming the data generating process…
This work addresses the fundamental linear inverse problem in compressive sensing (CS) by introducing a new type of regularizing generative prior. Our proposed method utilizes ideas from classical dictionary-based CS and, in particular,…
Computing expected information gain (EIG) from prior to posterior (equivalently, mutual information between candidate observations and model parameters or other quantities of interest) is a fundamental challenge in Bayesian optimal…
In this paper, we focus on the inverse problem of reconstructing distributional brain activity with cortical and weakly detectable deep components in non-invasive Electroencephalography. In particular, we aim to generalize the previously…
Logistic Gaussian process (LGP) priors provide a flexible alternative for modelling unknown densities. The smoothness properties of the density estimates can be controlled through the prior covariance structure of the LGP, but the challenge…
Bayesian analysis of data from the general linear mixed model is challenging because any nontrivial prior leads to an intractable posterior density. However, if a conditionally conjugate prior density is adopted, then there is a simple…
In this contribution, we present new algorithms to source separation for the case of noisy instantaneous linear mixture, within the Bayesian statistical framework. The source distribution prior is modeled by a mixture of Gaussians…
We introduce probabilistic embeddings using Laplacian priors (PELP). The proposed model enables incorporating graph side-information into static word embeddings. We theoretically show that the model unifies several previously proposed…
It is well-known that the distribution over functions induced through a zero-mean iid prior distribution over the parameters of a multi-layer perceptron (MLP) converges to a Gaussian process (GP), under mild conditions. We extend this…
Multi-task learning models using Gaussian processes (GP) have been developed and successfully applied in various applications. The main difficulty with this approach is the computational cost of inference using the union of examples from…
This work studies the learning problem of the energy-based prior model and the multi-layer generator model. The multi-layer generator model, which contains multiple layers of latent variables organized in a top-down hierarchical structure,…
Diffusion models have recently gained prominence in offline reinforcement learning due to their ability to effectively learn high-performing, generalizable policies from static datasets. Diffusion-based planners facilitate long-horizon…
We study the well-known problem of estimating a sparse $n$-dimensional unknown mean vector $\theta = (\theta_1, ..., \theta_n)$ with entries corrupted by Gaussian white noise. In the Bayesian framework, continuous shrinkage priors which can…
Inference on high-dimensional parameters in structured linear models is an important statistical problem. This paper focuses on the case of a piecewise polynomial Gaussian sequence model, and we develop a new empirical Bayes solution that…