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Crosscorrelation structures in the Green function retrieval by crosscorrelating wavefields are revealed using rigorous mathematical theory on integral equations. The previous practice on extracting the Green function by crosscorrelating the…
Drifting models train one-step generators by optimizing a kernel-induced mean-shift discrepancy between the data and model distributions, with Laplace kernels used by default in practice. At each point, this discrepancy compares the…
A method to reconstruct fields, source strengths and physical parameters based on Gaussian process regression is presented for the case where data are known to fulfill a given linear differential equation with localized sources. The…
Gaussian processes offers a convenient way to perform nonparametric reconstructions of observational data assuming only a kernel which describes the covariance between neighbouring points in a data set. We approach the ambiguity in the…
Gaussian processes are flexible function approximators, with inductive biases controlled by a covariance kernel. Learning the kernel is the key to representation learning and strong predictive performance. In this paper, we develop…
We study non-linear data-dimension reduction. We are motivated by the classical linear framework of Principal Component Analysis. In nonlinear case, we introduce instead a new kernel-Principal Component Analysis, manifold and feature space…
Whilst deep neural networks have shown great empirical success, there is still much work to be done to understand their theoretical properties. In this paper, we study the relationship between random, wide, fully connected, feedforward…
There are schemes for realizing different types of kernels by quantum states of light. It is particularly interesting to realize the Gaussian kernel due to its wider applicability. A multimode coherent state can generate the Gaussian kernel…
We present a new smooth, Gaussian-like kernel that allows the kernel density estimate for an angular distribution to be exactly represented by a finite number of its Fourier series coefficients. Distributions of angular quantities, such as…
Marginalising over families of Gaussian Process kernels produces flexible model classes with well-calibrated uncertainty estimates. Existing approaches require likelihood evaluations of many kernels, rendering them prohibitively expensive…
In decision-making systems, it is important to have classifiers that have calibrated uncertainties, with an optimisation objective that can be used for automated model selection and training. Gaussian processes (GPs) provide uncertainty…
We consider a differential model describing neuro-physiological contrast perception phenomena induced by surrounding orientations. The mathematical formulation relies on a cortical-inspired modelling [10] largely used over the last years to…
Gaussian processes provide a flexible, non-parametric framework for the approximation of functions in high-dimensional spaces. The covariance kernel is the main engine of Gaussian processes, incorporating correlations that underpin the…
Gaussian processes are rich distributions over functions, which provide a Bayesian nonparametric approach to smoothing and interpolation. We introduce simple closed form kernels that can be used with Gaussian processes to discover patterns…
Adaptive filtering algorithms operating in reproducing kernel Hilbert spaces have demonstrated superiority over their linear counterpart for nonlinear system identification. Unfortunately, an undesirable characteristic of these methods is…
Convolutional Neural Networks (CNNs) are known to be significantly over-parametrized, and difficult to interpret, train and adapt. In this paper, we introduce a structural regularization across convolutional kernels in a CNN. In our…
Vanilla convolutional neural networks are known to provide superior performance not only in image recognition tasks but also in natural language processing and time series analysis. One of the strengths of convolutional layers is the…
In the classical bilateral filter, a fixed Gaussian range kernel is used along with a spatial kernel for edge-preserving smoothing. We consider a generalization of this filter, the so-called adaptive bilateral filter, where the center and…
We introduce a parametric nonlinear transformation that is well-suited for Gaussianizing data from natural images. The data are linearly transformed, and each component is then normalized by a pooled activity measure, computed by…
Internal noise in deep networks is usually inherited from heuristics such as dropout, hard masking, or additive perturbation. We ask two questions: what correlation geometry should internal noise have, and is the implemented perturbation…