Related papers: Borel Kernels and their Approximation, Categorical…

We develop a coordinate-free probabilistic framework for determinantal point processes associated with Bergman kernels on compact complex manifolds. The basic issue is that Bergman kernels are naturally line-bundle-valued:…

Computing low-rank approximations of kernel matrices is an important problem with many applications in scientific computing and data science. We propose methods to efficiently approximate and store low-rank approximations to kernel matrices…

Determinantal point processes are characterized by a special structural property of the correlation functions: they are given by minors of a correlation kernel. However, unlike the correlation functions themselves, this kernel is not…

We present an alternative way of solving the steerable kernel constraint that appears in the design of steerable equivariant convolutional neural networks. We find explicit real and complex bases which are ready to use, for different…

With the strengths of both deep learning and kernel methods like Gaussian Processes (GPs), Deep Kernel Learning (DKL) has gained considerable attention in recent years. From the computational perspective, however, DKL becomes challenging…

Driven by a large number of potential applications in areas like bioinformatics, information retrieval and social network analysis, the problem setting of inferring relations between pairs of data objects has recently been investigated…

This PHD thesis is concerned with uncertainty relations in quantum probability theory, state estimation in quantum stochastics, and natural bundles in differential geometry. After some comments on the nature and necessity of decoherence in…

Probability monads on categories of topological spaces are classical objects of study in the categorical approach to probability theory, with important applications in the semantics of probabilistic programming languages. We construct a…

This paper considers the approximation of spatial convolution with a given radial integral kernel. Previous studies have demonstrated that approximating spatial convolution using a system of partial differential equations (PDEs) can…

It is well-known that non-linear approximation has an advantage over linear schemes in the sense that it provides comparable approximation rates to those of the linear schemes, but to a larger class of approximands. This was established for…

This paper investigates the critical role of eigenalignments between the kernel matrix and learning targets in achieving robust generalization in learning problems. We establish a direct connection between generalization performance in…

We propose a hierarchy for approximate inference based on the Dobrushin, Lanford, Ruelle (DLR) equations. This hierarchy includes existing algorithms, such as belief propagation, and also motivates novel algorithms such as factorized…

Kernel ridge regression (KRR) is a widely used nonparametric method due to its strong theoretical guarantees and computational convenience. However, standard KRR does not distinguish between linear and nonlinear components in the signal,…

We study mapping properties of operators with kernels defined via a combination of continuous and discrete orthogonal polynomials, which provide an abstract formulation of quantum (q-) Fourier type systems. We prove Ismail conjecture…

Decision forests induce supervised similarities through the partition structure of their trees. Yet forest proximity computation is still often treated as a quadratic operation in the number of samples, which limits scalability and…

Kernel Bayesian inference is a principled approach to nonparametric inference in probabilistic graphical models, where probabilistic relationships between variables are learned from data in a nonparametric manner. Various algorithms of…

We examine a class of embeddings based on structured random matrices with orthogonal rows which can be applied in many machine learning applications including dimensionality reduction and kernel approximation. For both the…

Strictly proper kernel scores are well-known tool in probabilistic forecasting, while characteristic kernels have been extensively investigated in the machine learning literature. We first show that both notions coincide, so that insights…

The regular open subsets of a topological space form a Boolean algebra, where the `join' of two regular open sets is the interior of the closure of their union. A `credence' is a finitely additive probability measure on this Boolean…

Parametric models in vector spaces are shown to possess an associated linear map. This linear operator leads directly to reproducing kernel Hilbert spaces and affine- / linear- representations in terms of tensor products. From the…