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We investigate iterated compositions of weighted sums of Gaussian kernels and provide an interpretation of the construction that shows some similarities with the architectures of deep neural networks. On the theoretical side, we show that…

Deep kernel processes are a recently introduced class of deep Bayesian models that have the flexibility of neural networks, but work entirely with Gram matrices. They operate by alternately sampling a Gram matrix from a distribution over…

A recent series of theoretical works showed that the dynamics of neural networks with a certain initialisation are well-captured by kernel methods. Concurrent empirical work demonstrated that kernel methods can come close to the performance…

This paper presents a new insight into improving the performance of Stochastic Neighbour Embedding (t-SNE) by using Isolation kernel instead of Gaussian kernel. Isolation kernel outperforms Gaussian kernel in two aspects. First, the use of…

Dual-tree wavelet decompositions have recently gained much popularity, mainly due to their ability to provide an accurate directional analysis of images combined with a reduced redundancy. When the decomposition of a random process is…

We consider the problem of learning regression functions from pairwise data when there exists prior knowledge that the relation to be learned is symmetric or anti-symmetric. Such prior knowledge is commonly enforced by symmetrizing or…

Bayesian analysis has become an indispensable tool across many different cosmological fields including the study of gravitational waves, the Cosmic Microwave Background and the 21-cm signal from the Cosmic Dawn among other phenomena. The…

A new image denoising algorithm to deal with the additive Gaussian white noise model is given. Like the non-local means method, the filter is based on the weighted average of the observations in a neighborhood, with weights depending on the…

Most graph kernels are an instance of the class of $\mathcal{R}$-Convolution kernels, which measure the similarity of objects by comparing their substructures. Despite their empirical success, most graph kernels use a naive aggregation of…

We propose a method for fusing stereo disparity estimation with movement-induced prior information. Instead of independent inference frame-by-frame, we formulate the problem as a non-parametric learning task in terms of a temporal Gaussian…

This note is devoted to an analysis of the so-called peeling algorithm in wavelet denoising. Assuming that the wavelet coefficients of the signal can be modeled by generalized Gaussian random variables, we compute a critical thresholding…

We propose a bilateral filter with a locally controlled domain kernel for directional edge-preserving smoothing. Traditional bilateral filters use a range kernel, which is responsible for edge preservation, and a fixed domain kernel that…

Dense pixelwise prediction such as semantic segmentation is an up-to-date challenge for deep convolutional neural networks (CNNs). Many state-of-the-art approaches either tackle the loss of high-resolution information due to pooling in the…

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.…

Most of the classical denoising methods restore clear results by selecting and averaging pixels in the noisy input. Instead of relying on hand-crafted selecting and averaging strategies, we propose to explicitly learn this process with deep…

Statistical physics approaches can be used to derive accurate predictions for the performance of inference methods learning from potentially noisy data, as quantified by the learning curve defined as the average error versus number of…

In this article we investigate the effects of conformal transformations on kernel functions used in Support Vector Machines. Our focus lies in the task of text document categorization, which involves assigning each document to a particular…

Data-driven discovery of "hidden physics" -- i.e., machine learning of differential equation models underlying observed data -- has recently been approached by embedding the discovery problem into a Gaussian Process regression of spatial…

We establish a general form of explicit, input-dependent, measure-valued warpings for learning nonstationary kernels. While stationary kernels are ubiquitous and simple to use, they struggle to adapt to functions that vary in smoothness…

This work studies the problem of estimating a two-dimensional superposition of point sources or spikes from samples of their convolution with a Gaussian kernel. Our results show that minimizing a continuous counterpart of the $\ell_1$ norm…