Related papers: B\'ezier Curve Gaussian Processes

Machine learning models perform well across domains such as diagnostics, weather forecasting, NLP, and autonomous driving, but their limited uncertainty handling restricts use in safety-critical settings. Traditional neural networks often…

Uncertainty estimation is essential for robust decision-making in the presence of ambiguous or out-of-distribution inputs. Gaussian Processes (GPs) are classical kernel-based models that offer principled uncertainty quantification and…

Many machine learning problems can be framed in the context of estimating functions, and often these are time-dependent functions that are estimated in real-time as observations arrive. Gaussian processes (GPs) are an attractive choice for…

Bayesian model updating based on Gaussian Process (GP) models has received attention in recent years, which incorporates kernel-based GPs to provide enhanced fidelity response predictions. Although most kernel functions provide high fitting…

A Bayesian network is a widely used probabilistic graphical model with applications in knowledge discovery and prediction. Learning a Bayesian network (BN) from data can be cast as an optimization problem using the well-known…

This research proposes a flexible Bayesian extension of the composite Gaussian process (CGP) model of Ba and Joseph (2012) for predicting (stationary or) non-stationary $y(\mathbf{x})$. The CGP generalizes the regression plus stationary…

Bayesian approaches for learning deep neural networks (BNN) have been received much attention and successfully applied to various applications. Particularly, BNNs have the merit of having better generalization ability as well as better…

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…

It has long been known that a single-layer fully-connected neural network with an i.i.d. prior over its parameters is equivalent to a Gaussian process (GP), in the limit of infinite network width. This correspondence enables exact Bayesian…

Understanding how stochastic gene expression is regulated in biological systems using snapshots of single-cell transcripts requires state-of-the-art methods of computational analysis and statistical inference. A Bayesian approach to…

Graph convolutional neural networks (GCNN) have numerous applications in different graph based learning tasks. Although the techniques obtain impressive results, they often fall short in accounting for the uncertainty associated with the…

Bayesian optimization is an effective methodology for the global optimization of functions with expensive evaluations. It relies on querying a distribution over functions defined by a relatively cheap surrogate model. An accurate model for…

The class of recurrent mixture density networks is an important class of probabilistic models used extensively in sequence modeling and sequence-to-sequence mapping applications. In this class of models, the density of a target sequence in…

Neural Ordinary Differential Equations (N-ODEs) are a powerful building block for learning systems, which extend residual networks to a continuous-time dynamical system. We propose a Bayesian version of N-ODEs that enables well-calibrated…

A Gaussian process (GP)-based methodology is proposed to emulate complex dynamical computer models (or simulators). The method relies on emulating the numerical flow map of the system over an initial (short) time step, where the flow map is…

As data size and computing power increase, the architectures of deep neural networks (DNNs) have been getting more complex and huge, and thus there is a growing need to simplify such complex and huge DNNs. In this paper, we propose a novel…

Mixture Density Networks are a tried and tested tool for modelling conditional probability distributions. As such, they constitute a great baseline for novel approaches to this problem. In the standard formulation, an MDN takes some input…

Bayesian computation of high dimensional linear regression models with a popular Gaussian scale mixture prior distribution using Markov Chain Monte Carlo (MCMC) or its variants can be extremely slow or completely prohibitive due to the…

We introduce a variational Bayesian neural network where the parameters are governed via a probability distribution on random matrices. Specifically, we employ a matrix variate Gaussian \cite{gupta1999matrix} parameter posterior…

Neural bandits have been shown to provide an efficient solution to practical sequential decision tasks that have nonlinear reward functions. The main contributor to that success is approximate Bayesian inference, which enables neural…