Related papers: Deep kernel processes
We propose a novel deep learning paradigm of differential flows that learn a stochastic differential equation transformations of inputs prior to a standard classification or regression function. The key property of differential Gaussian…
We study wide Bayesian neural networks focusing on the rare but statistically dominant fluctuations that govern posterior concentration, beyond Gaussian-process limits. Large-deviation theory provides explicit variational objectives-rate…
This paper investigates efficient deep neural networks (DNNs) to replace dense unstructured weight matrices with structured ones that possess desired properties. The challenge arises because the optimal weight matrix structure in popular…
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…
Deep Neural Networks are, from a physical perspective, graphs whose `links` and `vertices` iteratively process data and solve tasks sub-optimally. We use Complex Network Theory (CNT) to represents Deep Neural Networks (DNNs) as directed…
We propose a principled way to define Gaussian process priors on various sets of unweighted graphs: directed or undirected, with or without loops. We endow each of these sets with a geometric structure, inducing the notions of closeness and…
We explore the link between deep ensembles and Gaussian processes (GPs) through the lens of the Neural Tangent Kernel (NTK): a recent development in understanding the training dynamics of wide neural networks (NNs). Previous work has shown…
Recent work has shown that the prior over functions induced by a deep Bayesian neural network (BNN) behaves as a Gaussian process (GP) as the width of all layers becomes large. However, many BNN applications are concerned with the BNN…
Gaussian process (GP) regression is a powerful probabilistic modeling technique with built-in uncertainty quantification. When one has access to multiple correlated simulations (tasks), it is common to fit a multitask GP (MTGP) surrogate…
Gaussian processes (GPs) are Bayesian nonparametric models for function approximation with principled predictive uncertainty estimates. Deep Gaussian processes (DGPs) are multilayer generalizations of GPs that can represent complex marginal…
Gaussian Processes (GPs) provide a convenient framework for specifying function-space priors, making them a natural choice for modeling uncertainty. In contrast, Bayesian Neural Networks (BNNs) offer greater scalability and extendability…
Deep neural networks (DNNs) have excellent representative power and are state of the art classifiers on many tasks. However, they often do not capture their own uncertainties well making them less robust in the real world as they…
Parameter retrieval and model inversion are key problems in remote sensing and Earth observation. Currently, different approximations exist: a direct, yet costly, inversion of radiative transfer models (RTMs); the statistical inversion with…
Deep neural networks (DNNs) have demonstrated state-of-the-art results on many pattern recognition tasks, especially vision classification problems. Understanding the inner workings of such computational brains is both fascinating basic…
The scaling limit where both the size of the training set $P$ and the width $N$ of a deep neural network grow at the same rate, the so-called proportional-width regime, has been intensely studied for shallow, single-hidden-layer networks.…
There is a previously identified equivalence between wide fully connected neural networks (FCNs) and Gaussian processes (GPs). This equivalence enables, for instance, test set predictions that would have resulted from a fully Bayesian,…
Bayesian inference and kernel methods are well established in machine learning. The neural network Gaussian process in particular provides a concept to investigate neural networks in the limit of infinitely wide hidden layers by using…
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…
We consider a Gaussian process formulation of the multiple kernel learning problem. The goal is to select the convex combination of kernel matrices that best explains the data and by doing so improve the generalisation on unseen data.…
While deep learning has achieved remarkable success across a wide range of applications, its theoretical understanding of representation learning remains limited. Deep neural kernels provide a principled framework to interpret…