Related papers: Bayesian Learning of Kernel Embeddings
Despite recent advances in automated machine learning, model selection is still a complex and computationally intensive process. For Gaussian processes (GPs), selecting the kernel is a crucial task, often done manually by the expert.…
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…
Although Gaussian processes (GPs) with deep kernels have been successfully used for meta-learning in regression tasks, its uncertainty estimation performance can be poor. We propose a meta-learning method for calibrating deep kernel GPs for…
The problem of robust hypothesis testing is studied, where under the null and the alternative hypotheses, the data-generating distributions are assumed to be in some uncertainty sets, and the goal is to design a test that performs well…
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…
A Hilbert space embedding for probability measures has recently been proposed, with applications including dimensionality reduction, homogeneity testing, and independence testing. This embedding represents any probability measure as a mean…
For Bayesian optimization (BO) on high-dimensional data with complex structure, neural network-based kernels for Gaussian processes (GPs) have been used to learn flexible surrogate functions by the high representation power of deep…
Bayesian nonparametric models, such as Gaussian processes, provide a compelling framework for automatic statistical modelling: these models have a high degree of flexibility, and automatically calibrated complexity. However, automating…
We apply kernel mean embedding methods to sample-based stochastic optimization and control. Specifically, we use the reduced-set expansion method as a way to discard sampled scenarios. The effect of such constraint removal is improved…
A key task in the emerging field of materials informatics is to use machine learning to predict a material's properties and functions. A fast and accurate predictive model allows researchers to more efficiently identify or construct a…
In this paper, we propose a novel supervised learning method that is called Deep Embedding Kernel (DEK). DEK combines the advantages of deep learning and kernel methods in a unified framework. More specifically, DEK is a learnable kernel…
We present a new method to approximate posterior probabilities of Bayesian Network using Deep Neural Network. Experiment results on several public Bayesian Network datasets shows that Deep Neural Network is capable of learning joint…
This paper investigates the formulation and implementation of Bayesian inverse problems to learn input parameters of partial differential equations (PDEs) defined on manifolds. Specifically, we study the inverse problem of determining the…
Bayesian neural networks utilize probabilistic layers that capture uncertainty over weights and activations, and are trained using Bayesian inference. Since these probabilistic layers are designed to be drop-in replacement of their…
Kernels are efficient in representing nonlocal dependence and they are widely used to design operators between function spaces. Thus, learning kernels in operators from data is an inverse problem of general interest. Due to the nonlocal…
One major impediment to the wider use of deep learning for clinical decision making is the difficulty of assigning a level of confidence to model predictions. Currently, deep Bayesian neural networks and sparse Gaussian processes are the…
Kernel methods, being supported by a well-developed theory and coming with efficient algorithms, are among the most popular and successful machine learning techniques. From a mathematical point of view, these methods rest on the concept of…
This paper introduces the kernel mixture network, a new method for nonparametric estimation of conditional probability densities using neural networks. We model arbitrarily complex conditional densities as linear combinations of a family of…
This is a tutorial and survey paper on kernels, kernel methods, and related fields. We start with reviewing the history of kernels in functional analysis and machine learning. Then, Mercer kernel, Hilbert and Banach spaces, Reproducing…
In the realm of statistical learning, the increasing volume of accessible data and increasing model complexity necessitate robust methodologies. This paper explores two branches of robust Bayesian methods in response to this trend. The…