arXiv research

Improved Gaussian Process regression using TQFF over RFF and Gaussian QFF.

New Fourier features improve high-precision approximation in large-scale problems.

SLEIPNIR improves Gaussian process regression with derivatives, scaling up efficiently and accurately.

A new method optimizes Fourier pricing for multi-asset options using adaptive quadrature.

A new method slices and sums radial kernels faster.

Paper proposes no-regret algorithms for private GP bandit optimization.

No-trick kernel adaptive filtering uses deterministic features for scalability and robustness.

Closed pricing formulas for Variance Gamma model payoffs.

We propose an offline-online procedure for Fourier transform based option pricing. The method supports the acceleration of such essential tasks of mathematical finance as model calibration, real-time pricing, and, more generally, risk assessment and parameter risk estimation. We adapt the empirical magic point interpol…

This work improves Fourier pricing for multi-asset options using RQMC with domain transformation.

New method for optimizing risk in financial models using Fourier transforms.

Unified quadrature framework for large-scale kernel machines.

Developed a monotone numerical method for MV portfolio optimization under jump-diffusion models.

Efficiently calculates privacy guarantees for 2020 Census data.

We show that kernel-based quadrature rules for computing integrals can be seen as a special case of random feature expansions for positive definite kernels, for a particular decomposition that always exists for such kernels. We provide a theoretical analysis of the number of required samples for a given approximation e…

Random Fourier features is one of the most popular techniques for scaling up kernel methods, such as kernel ridge regression. However, despite impressive empirical results, the statistical properties of random Fourier features are still not well understood. In this paper we take steps toward filling this gap. Specifica…

Random Fourier features classification achieves fast learning rates with fewer features.

This work proves convergence of adaptive resampling for random Fourier features.

Enhances DGPs with adaptive RKHS Fourier features for better non-stationary pattern modeling.

Improves sparse recovery with non-linear Fourier features.

An infinitely wide model is a weighted integration $\int \varphi(x,v) d μ(v)$ of feature maps. This model excels at handling an infinite number of features, and thus it has been adopted to the theoretical study of deep learning. Kernel quadrature is a kernel-based numerical integration scheme developed for fast approxi…

New method uses tensor decompositions to overcome the curse of dimensionality for large-scale learning.

Orthogonal random features approximate a Bessel kernel, offering sharper bounds than random Fourier features.

Random Fourier features model reconstructs wind fields from sparse measurements.

Multipath is among the major sources of errors in precise positioning using GPS and continues to be extensively studied. Two Fast Fourier Transform (FFT)-based detectors are presented in this paper as GPS multipath detection techniques. The detectors are formulated as binary hypothesis tests under the assumption that t…

Bayesian optimisation has been successfully applied to a variety of reinforcement learning problems. However, the traditional approach for learning optimal policies in simulators does not utilise the opportunity to improve learning by adjusting certain environment variables: state features that are unobservable and ran…

New quadrature method using randomly pivoted Cholesky outperforms existing techniques.

Two ANOVA-based algorithms boost random Fourier feature models for function approximation.

Devoted to multi-task learning and structured output learning, operator-valued kernels provide a flexible tool to build vector-valued functions in the context of Reproducing Kernel Hilbert Spaces. To scale up these methods, we extend the celebrated Random Fourier Feature methodology to get an approximation of operator-…

Bayesian quadrature uses probabilistic models for estimating intractable integrals.

A new method integrates Fourier basis expansion and mapping for improved time series forecasting.

Random Fourier features improve tabular deep learning convergence.

Integrates Fourier features for faster Gaussian process regression.

SOBER optimizes and quadrates efficiently in parallel for diverse tasks.

Proposes a Complex Transformer for complex-valued sequence modeling.

Problems of interpolation, classification, and clustering are considered. In the tenets of Radon--Nikodym approach $\langle f(\mathbf{x})ψ^2 \rangle / \langleψ^2\rangle$, where the $ψ(\mathbf{x})$ is a linear function on input attributes, all the answers are obtained from a generalized eigenproblem $|f|ψ^{[i]}\rangle =…

This paper presents a convergence analysis of kernel-based quadrature rules in misspecified settings, focusing on deterministic quadrature in Sobolev spaces. In particular, we deal with misspecified settings where a test integrand is less smooth than a Sobolev RKHS based on which a quadrature rule is constructed. We pr…

Kernel methods are powerful and flexible approach to solve many problems in machine learning. Due to the pairwise evaluations in kernel methods, the complexity of kernel computation grows as the data size increases; thus the applicability of kernel methods is limited for large scale datasets. Random Fourier Features (R…

We consider the problem of improving kernel approximation via randomized feature maps. These maps arise as Monte Carlo approximation to integral representations of kernel functions and scale up kernel methods for larger datasets. Based on an efficient numerical integration technique, we propose a unifying approach that…

We study quadrature rules for functions from an RKHS, using nodes sampled from a determinantal point process (DPP). DPPs are parametrized by a kernel, and we use a truncated and saturated version of the RKHS kernel. This link between the two kernels, along with DPP machinery, leads to relatively tight bounds on the qua…

We show that the error probability of reconstructing kernel matrices from Random Fourier Features for the Gaussian kernel function is at most $\mathcal{O}(R^{2/3} \exp(-D))$, where $D$ is the number of random features and $R$ is the diameter of the data domain. We also provide an information-theoretic method-independen…

Bayesian quadrature improves integration efficiency with invariant priors.

Lecture notes on kernel functions and Random Fourier Features.

Random Fourier features is a widely used, simple, and effective technique for scaling up kernel methods. The existing theoretical analysis of the approach, however, remains focused on specific learning tasks and typically gives pessimistic bounds which are at odds with the empirical results. We tackle these problems an…

Herding and kernel herding are deterministic methods of choosing samples which summarise a probability distribution. A related task is choosing samples for estimating integrals using Bayesian quadrature. We show that the criterion minimised when selecting samples in kernel herding is equivalent to the posterior varianc…

Herding and kernel herding are deterministic methods of choosing samples which summarise a probability distribution. A related task is choosing samples for estimating integrals using Bayesian quadrature. We show that the criterion minimised when selecting samples in kernel herding is equivalent to the posterior varianc…

Improved kernel quadrature with convex weights using subsampling.

New Fourier analysis method for non-uniform Boolean hypercube.