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We provide simple schemes to build Bayesian Neural Networks (BNNs), block by block, inspired by a recent idea of computation skeletons. We show how by adjusting the types of blocks that are used within the computation skeleton, we can…
Uncertainty quantification is an important task in machine learning - a task in which standardneural networks (NNs) have traditionally not excelled. This can be a limitation for safety-critical applications, where uncertainty-aware methods…
In engineering design, surrogate models are widely employed to replace computationally expensive simulations by leveraging design variables and geometric parameters from computer-aided design (CAD) models. However, these models often lose…
There has recently been much work on the "wide limit" of neural networks, where Bayesian neural networks (BNNs) are shown to converge to a Gaussian process (GP) as all hidden layers are sent to infinite width. However, these results do not…
Bayesian Neural Networks (BNNs) have been proposed to address the problem of model uncertainty in training and inference. By introducing weights associated with conditioned probability distributions, BNNs are capable of resolving the…
This paper deals with the identification of linear stochastic dynamical systems, where the unknowns include system coefficients and noise variances. Conventional approaches that rely on the maximum likelihood estimation (MLE) require…
Many functions have approximately-known upper and/or lower bounds, potentially aiding the modeling of such functions. In this paper, we introduce Gaussian process models for functions where such bounds are (approximately) known. More…
We introduce a novel adaptive Gaussian Process Regression (GPR) methodology for efficient construction of surrogate models for Bayesian inverse problems with expensive forward model evaluations. An adaptive design strategy focuses on…
Due to its causal semantics, Bayesian networks (BN) have been widely employed to discover the underlying data relationship in exploratory studies, such as brain research. Despite its success in modeling the probability distribution of…
Not being able to understand and predict the behavior of deep learning systems makes it hard to decide what architecture and algorithm to use for a given problem. In science and engineering, modeling is a methodology used to understand…
Graph neural networks (GNNs) have extended the success of deep neural networks (DNNs) to non-Euclidean graph data, achieving ground-breaking performance on various tasks such as node classification and graph property prediction.…
Bayesian neural Networks (BNNs) are a promising method of obtaining statistical uncertainties for neural network predictions but with a higher computational overhead which can limit their practical usage. This work explores the use of high…
While Bayesian neural networks (BNNs) have drawn increasing attention, their posterior inference remains challenging, due to the high-dimensional and over-parameterized nature. To address this issue, several highly flexible and scalable…
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…
Active learning optimizes the exploration of large parameter spaces by strategically selecting which experiments or simulations to conduct, thus reducing resource consumption and potentially accelerating scientific discovery. A key…
This paper studies optimization on networks modeled as metric graphs. Motivated by applications where the objective function is expensive to evaluate or only available as a black box, we develop Bayesian optimization algorithms that…
High-dimensional Bayesian optimization (BO) tasks such as molecular design often require 10,000 function evaluations before obtaining meaningful results. While methods like sparse variational Gaussian processes (SVGPs) reduce computational…
Bayesian Last Layers (BLLs) provide a convenient and computationally efficient way to estimate uncertainty in neural networks. However, they underestimate epistemic uncertainty because they apply a Bayesian treatment only to the final…
Bayesian Optimization using Gaussian Processes is a popular approach to deal with the optimization of expensive black-box functions. However, because of the a priori on the stationarity of the covariance matrix of classic Gaussian…
Learning controller parameters from closed-loop data has been shown to improve closed-loop performance. Bayesian optimization, a widely used black-box and sample-efficient learning method, constructs a probabilistic surrogate of the…