Related papers: Stochastic Variational Inference for Bayesian Spar…
The Gaussian process latent variable model (GP-LVM) provides a flexible approach for non-linear dimensionality reduction that has been widely applied. However, the current approach for training GP-LVMs is based on maximum likelihood, where…
Recently, 3D Gaussian Splatting has emerged as a promising approach for modeling 3D scenes using mixtures of Gaussians. The predominant optimization method for these models relies on backpropagating gradients through a differentiable…
Gaussian processes (GP) provide a prior over functions and allow finding complex regularities in data. Gaussian processes are successfully used for classification/regression problems and dimensionality reduction. In this work we consider…
In this work, we study scaling limits of shallow Bayesian neural networks (BNNs) via their connection to Gaussian processes (GPs), with an emphasis on statistical modeling, identifiability, and scalable inference. We first establish a…
Deep Gaussian process models typically employ discrete hierarchies, but recent advancements in differential Gaussian processes (DiffGPs) have extended these models to infinite depths. However, existing DiffGP approaches often overlook the…
We introduce a novel Bayesian approach for variable selection using Gaussian process regression, which is crucial for enhancing interpretability and model regularization. Our method employs nearest neighbor Gaussian processes, serving as…
In this work, we propose a Bayesian type sparse deep learning algorithm. The algorithm utilizes a set of spike-and-slab priors for the parameters in the deep neural network. The hierarchical Bayesian mixture will be trained using an…
We develop a scalable deep non-parametric generative model by augmenting deep Gaussian processes with a recognition model. Inference is performed in a novel scalable variational framework where the variational posterior distributions are…
In this work, we focus on variational Bayesian inference on the sparse Deep Neural Network (DNN) modeled under a class of spike-and-slab priors. Given a pre-specified sparse DNN structure, the corresponding variational posterior contraction…
How can we perform efficient inference and learning in directed probabilistic models, in the presence of continuous latent variables with intractable posterior distributions, and large datasets? We introduce a stochastic variational…
For predictive modeling relying on Bayesian inversion, fully independent, or ``mean-field'', Gaussian distributions are often used as approximate probability density functions in variational inference since the number of variational…
Gaussian variational approximation is a popular methodology to approximate posterior distributions in Bayesian inference especially in high dimensional and large data settings. To control the computational cost while being able to capture…
Gaussian process regression (GPR) is a powerful machine learning method which has recently enjoyed wider use, in particular in physical sciences. In its original formulation, GPR uses a square matrix of covariances among training data and…
We have utilized the non-conjugate Variational Bayesian (VB) method for the problem of the sparse Poisson regression model. To provide approximate conjugacy in the model, the likelihood is approximated by a quadratic function, yielding…
We introduce a new scalable approximation for Gaussian processes with provable guarantees which hold simultaneously over its entire parameter space. Our approximation is obtained from an improved sample complexity analysis for sparse…
We introduce a stochastic variational inference procedure for training scalable Gaussian process (GP) models whose per-iteration complexity is independent of both the number of training points, $n$, and the number basis functions used in…
We propose a lower bound on the log marginal likelihood of Gaussian process regression models that can be computed without matrix factorisation of the full kernel matrix. We show that approximate maximum likelihood learning of model…
We investigate the frequentist guarantees of the variational sparse Gaussian process regression model. In the theoretical analysis, we focus on the variational approach with spectral features as inducing variables. We derive guarantees and…
We present a novel formulation for motion planning under uncertainties based on variational inference where the optimal motion plan is modeled as a posterior distribution. We propose a Gaussian variational inference-based framework, termed…
Surrogate models provide a quick-to-evaluate approximation to complex computational models and are essential for multi-query problems like design optimisation. The inputs of current deterministic computational models are usually…