Related papers: Laplace Approximation for Bayesian Tensor Network …

Bayesian neural networks (BNNs) augment deep networks with uncertainty quantification by Bayesian treatment of the network weights. However, such models face the challenge of Bayesian inference in a high-dimensional and usually…

The growing demand for accurate, efficient, and scalable solutions in computational mechanics highlights the need for advanced operator learning algorithms that can efficiently handle large datasets while providing reliable uncertainty…

We propose a novel probabilistic framework, termed LVM-GP, for uncertainty quantification in solving forward and inverse partial differential equations (PDEs) with noisy data. The core idea is to construct a stochastic mapping from the…

In many real-world applications we are interested in approximating costly functions that are analytically unknown, e.g. complex computer codes. An emulator provides a fast approximation of such functions relying on a limited number of…

Kernel models of potential energy surfaces (PES) for polyatomic molecules are often restricted by a specific choice of the kernel function. This can be avoided by optimizing the complexity of the kernel function. For regression problems…

The usual figure of merit characterizing the performance of neural networks applied to problems in the quantum domain is their accuracy, being the probability of a correct answer on a previously unseen input. Here we append this parameter…

Bayesian Neural Networks (BNNs) offer a principled and natural framework for proper uncertainty quantification in the context of deep learning. They address the typical challenges associated with conventional deep learning methods, such as…

Bayesian inference on non-Gaussian data is often non-analytic and requires computationally expensive approximations such as sampling or variational inference. We propose an approximate inference framework primarily designed to be…

Estimating causal effects in quasi-experiments with spatio-temporal panel data often requires adjusting for unmeasured confounding that varies across space and time. Gaussian Processes (GPs) offer a flexible, nonparametric modeling approach…

Several machine learning problems arising in natural language processing can be modeled as a sequence labeling problem. We provide Gaussian process models based on pseudo-likelihood approximation to perform sequence labeling. Gaussian…

Deep neural networks are prone to overconfident predictions on outliers. Bayesian neural networks and deep ensembles have both been shown to mitigate this problem to some extent. In this work, we aim to combine the benefits of the two…

Mapping with uncertainty representation is required in many research domains, especially for localization. Although there are many investigations regarding the uncertainty of the pose estimation of an ego-robot with map information, the…

We propose the first Bayesian encoder for metric learning. Rather than relying on neural amortization as done in prior works, we learn a distribution over the network weights with the Laplace Approximation. We actualize this by first…

We investigate the capabilities and limitations of Gaussian process models by jointly exploring three complementary directions: (i) scalable and statistically efficient inference; (ii) flexible kernels; and (iii) objective functions for…

Bayesian neural networks (BNN) can estimate the uncertainty in predictions, as opposed to non-Bayesian neural networks (NNs). However, BNNs have been far less widely used than non-Bayesian NNs in practice since they need iterative NN…

Gaussian Process Regression is a well-known machine learning technique for which several quantum algorithms have been proposed. We show here that in a wide range of scenarios these algorithms show no exponential speedup. We achieve this by…

Gaussian processes (GPs) are widely used in nonparametric regression, classification and spatio-temporal modeling, motivated in part by a rich literature on theoretical properties. However, a well known drawback of GPs that limits their use…

Performing gradient descent in a wide neural network is equivalent to computing the posterior mean of a Gaussian Process with the Neural Tangent Kernel (NTK-GP), for a specific prior mean and with zero observation noise. However, existing…

As Deep Learning continues to yield successful applications in Computer Vision, the ability to quantify all forms of uncertainty is a paramount requirement for its safe and reliable deployment in the real-world. In this work, we leverage…

This paper is an attempt to bridge the conceptual gaps between researchers working on the two widely used approaches based on positive definite kernels: Bayesian learning or inference using Gaussian processes on the one side, and…