Related papers: Marginalising over Stationary Kernels with Bayesia…
Identification of model parameters in computer simulations is an important topic in computer experiments. We propose a new method, called the projected kernel calibration method, to estimate these model parameters. The proposed method is…
Bayesian optimization with Gaussian processes (GP) is commonly used to optimize black-box functions. The Mat\'ern and the Radial Basis Function (RBF) covariance functions are used frequently, but they do not make any assumptions about the…
We propose a graph spectrum-based Gaussian process for prediction of signals defined on nodes of the graph. The model is designed to capture various graph signal structures through a highly adaptive kernel that incorporates a flexible…
Radial Basis Function (RBF), or Gaussian, kernels are among the most widely used parametric kernels in machine learning, particularly in methods such as Support Vector Machines (SVM) and kernel-based subspace approaches. The kernel…
Folding uncertainty in theoretical models into Bayesian parameter estimation is necessary in order to make reliable inferences. A general means of achieving this is by marginalizing over model uncertainty using a prior distribution…
We extend kernelized matrix factorization with a fully Bayesian treatment and with an ability to work with multiple side information sources expressed as different kernels. Kernel functions have been introduced to matrix factorization to…
This paper addresses the scalability problem of Bayesian deep neural networks. The performance of deep neural networks is undermined by the fact that these algorithms have poorly calibrated measures of uncertainty. This restricts their…
Quantum computing, with its potential to enhance various machine learning tasks, allows significant advancements in kernel calculation and model precision. Utilizing the one-class Support Vector Machine alongside a quantum kernel, known for…
It was demonstrated in earlier work that, by approximating its range kernel using shiftable functions, the non-linear bilateral filter can be computed using a series of fast convolutions. Previous approaches based on shiftable approximation…
Despite the ubiquity of the Gaussian process regression model, few theoretical results are available that account for the fact that parameters of the covariance kernel typically need to be estimated from the dataset. This article provides…
In recent years, there has been a growing demand to discern clusters of subjects in datasets characterized by a large set of features. Often, these clusters may be highly variable in size and present partial hierarchical structures. In this…
We introduce a fast algorithm for Gaussian process regression in low dimensions, applicable to a widely-used family of non-stationary kernels. The non-stationarity of these kernels is induced by arbitrary spatially-varying vertical and…
The generalization properties of Gaussian processes depend heavily on the choice of kernel, and this choice remains a dark art. We present the Neural Kernel Network (NKN), a flexible family of kernels represented by a neural network. The…
Marginalization of latent variables or nuisance parameters is a fundamental aspect of Bayesian inference and uncertainty quantification. In this work, we focus on scalable marginalization of latent variables in modeling correlated data,…
Bayesian probabilistic numerical methods are a set of tools providing posterior distributions on the output of numerical methods. The use of these methods is usually motivated by the fact that they can represent our uncertainty due to…
Random Fourier Features (RFF) demonstrate wellappreciated performance in kernel approximation for largescale situations but restrict kernels to be stationary and positive definite. And for non-stationary kernels, the corresponding RFF could…
Generative modeling using samples drawn from the probability distribution constitutes a powerful approach for unsupervised machine learning. Quantum mechanical systems can produce probability distributions that exhibit quantum correlations…
This paper presents a distance-based discriminative framework for learning with probability distributions. Instead of using kernel mean embeddings or generalized radial basis kernels, we introduce embeddings based on dissimilarity of…
The kernel function and its hyperparameters are the central model selection choice in a Gaussian proces (Rasmussen and Williams, 2006). Typically, the hyperparameters of the kernel are chosen by maximising the marginal likelihood, an…
We introduce a Bayesian framework for inference with a supervised version of the Gaussian process latent variable model. The framework overcomes the high correlations between latent variables and hyperparameters by using an unbiased pseudo…