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In this article, we establish novel decompositions of Gaussian fields taking values in suitable spaces of generalized functions, and then use these decompositions to prove results about Gaussian multiplicative chaos. We prove two decomposition theorems. Th ...
The necessary and sufficient conditions for existence of a generalized representer theorem are presented for learning Hilbert space - valued functions. Representer theorems involving explicit basis functions and Reproducing Kernels are a common occurrence ...
At initialization, artificial neural networks (ANNs) are equivalent to Gaussian processes in the infinite-width limit [12, 9], thus connecting them to kernel methods. We prove that the evolution of an ANN during training can also be described by a kernel: ...
We present the first accelerated randomized algorithm for solving linear systems in Euclidean spaces. One essential problem of this type is the matrix inversion problem. In particular, our algorithm can be specialized to invert positive definite matrices i ...
In this paper we revisit the kernel density estimation problem: given a kernel K(x, y) and a dataset of n points in high dimensional Euclidean space, prepare a data structure that can quickly output, given a query q, a (1 + epsilon)-approximation to mu := ...
Random binning features, introduced in the seminal paper of Rahimi and Recht '07, are an efficient method for approximating a kernel matrix using locality sensitive hashing. Random binning features provide a very simple and efficient way to approximate the ...
Deep convolutional neural networks (CNNs), trained on corresponding pairs of high- and low-resolution images, achieve state-of-the-art performance in single-image super- resolution and surpass previous signal-processing based approaches. However, their per ...
The Neural Tangent Kernel is a new way to understand the gradient descent in deep neural networks, connecting them with kernel methods. In this talk, I'll introduce this formalism and give a number of results on the Neural Tangent Kernel and explain how th ...
Kernel methods are fundamental tools in machine learning that allow detection of non-linear dependencies between data without explicitly constructing feature vectors in high dimensional spaces. A major disadvantage of kernel methods is their poor scalabili ...
The nonparametric learning of positive-valued functions appears widely in machine learning, especially in the context of estimating intensity functions of point processes. Yet, existing approaches either require computing expensive projections or semidefin ...
