A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
We develop Fourier methods to expand translation-invariant kernels.
Kernel method estimates long-term effects from short-term data.
SimpleMKKM improves multi-kernel clustering efficiency.
New findings show a balance between data fit and complexity in kernel hyperparameters.
Kernel-based methods exhibit well-documented performance in various nonlinear learning tasks. Most of them rely on a preselected kernel, whose prudent choice presumes task-specific prior information. Especially when the latter is not available, multi-kernel learning has gained popularity thanks to its flexibility in ch…
Kernel method learns PDEs from noisy data.
This paper makes kernels interpretable for wide feature matrices.
Efficient kernel method learns differential equations with fewer data.
This paper constructs and studies the long-term factorization of affine pricing kernels into discounting at the rate of return on the long bond and the martingale component that accomplishes the change of probability measure to the long forward measure. The principal eigenfunction of the affine pricing kernel germane t…
Paper introduces new neural network models and theories.
Quantum models are rephrased as kernel methods, improving performance.
In this paper, we study the relations between the log term of the Szegö kernel of the unit circle bundle of the dual line bundle of an ample line bundle over a compact Kählermanifold. We proved a local rigidity theorem. The result is related to the classical Ramadanov Conjecture.
In this paper, we compare 5 different nonlinear kernels: min-max, RBF, fRBF (folded RBF), acos, and acos-, on a wide range of publicly available datasets. The proposed fRBF kernel performs very similarly to the RBF kernel. Both RBF and fRBF kernels require an important tuning parameter (). Interestingly, for a …
Study uses G-BSDEs to decompose pricing kernels under robust G-expectation.
The term "CoRE kernel" stands for correlation-resemblance kernel. In many applications (e.g., vision), the data are often high-dimensional, sparse, and non-binary. We propose two types of (nonlinear) CoRE kernels for non-binary sparse data and demonstrate the effectiveness of the new kernels through a classification ex…
In this note we give a heat kernel lower bound in term of integral Ricci curvature, extending Cheeger-Yau's estimate.
Needlets have been recognized as state-of-the-art tools to tackle spherical data, due to their excellent localization properties in both spacial and frequency domains. This paper considers developing kernel methods associated with the needlet kernel for nonparametric regression problems whose predictor variables are de…
We consider the heat equation associated with a class of second order hypoelliptic Hörmander operators with constant second order term and linear drift. We describe the possible small time heat kernel expansion on the diagonal giving a geometric characterization of the coefficients in terms of the divergence of the dri…
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 anti-symmetrizing pairwise kernel functions. Through spectral analysis, we show that …
In this article, we construct the canonical semipositive current or the canonical measure ( the potential of the canonical semipositive current) on a smooth projective variety of nonnegative Kodaira dimension in terms of a dynamical system of Bergman kernels. This current is considered to be a generalization of a Kä…
Deep convolutional networks can be understood through kernel methods, providing insights into their inductive bias.
We compute the leading and sub-leading terms in the asymptotic expansion of the Szegö kernel on the diagonal of a class of pseudoconvex Reinhardt domains whose boundaries are endowed with a general class of smooth measures. We do so by relating it to a Bergman kernel over projective space.
The generalization performance of kernel methods is largely determined by the kernel, but common kernels are stationary thus input-independent and output-independent, that limits their applications on complicated tasks. In this paper, we propose a powerful and efficient spectral kernel learning framework and learned ke…
Physics-informed kernel learning integrates physical priors into machine learning models.
Multiple Kernel Learning (MKL) is used to replicate the signal combination process that trading rules embody when they aggregate multiple sources of financial information when predicting an asset's price movements. A set of financially motivated kernels is constructed for the EURUSD currency pair and is used to predict…
Kernel adaptive filters, a class of adaptive nonlinear time-series models, are known by their ability to learn expressive autoregressive patterns from sequential data. However, for trivial monotonic signals, they struggle to perform accurate predictions and at the same time keep computational complexity within desired …
New framework explains neural network bias in solving differential equations.
Inspired by Berndtsson's work on the subharmonicity property of the Bergman kernel, we give a local variation formula of the full Bergman kernels associated to deformations of complex manifolds. In compact case, it follows from the reproducing property of the Bergman kernel and the curvature formula of the 0-th direct …
This papers introduces an algorithm for the solution of multiple kernel learning (MKL) problems with elastic-net constraints on the kernel weights. The algorithm compares very favourably in terms of time and space complexity to existing approaches and can be implemented with simple code that does not rely on external l…
Kernel adaptive filters (KAF) are a class of powerful nonlinear filters developed in Reproducing Kernel Hilbert Space (RKHS). The Gaussian kernel is usually the default kernel in KAF algorithms, but selecting the proper kernel size (bandwidth) is still an open important issue especially for learning with small sample s…
Accelerates signature kernel computation for sequences.
Kernel methods improve geophysical forecasting accuracy and efficiency.
New algorithm speeds up polynomial kernel approximations.
Improved guarantees for misspecified kernelized bandit optimization.
Study guarantees convergence of mean shift mode estimation.
Kernel based methods have shown effective performance in many remote sensing classification tasks. However their performance significantly depend on its hyper-parameters. The conventional technique to estimate the parameter comes with high computational complexity. Thus, the objective of this letter is to propose an fa…
Paper improves generalization bounds for multi-kernel learning with mixed datasets.
Study examines boundedness of oscillating singular integrals on specific Lie groups.
We establish the cancellation of the first terms in the diagonal asymptotic expansion of the restriction to the -forms of the Bergman kernel associated to the spin Dirac operator on high tensor powers of a positive line bundle twisted by a (non necessarily holomorphic) complex vector bundle, over a c…
We prove that the trace of the logarithmic term of the Toeplitz kernel on a contact manifold is a contact invariant, generalizing K. Hirachi's invariant for the Szego kernel on a CR manifold. When the base manifold is the three-sphere, this vanishes identically.
Enhances KLR for indefinite kernels with -norm regularization.
The paper calculates heat kernel and closed geodesic asymptotics for nilpotent coverings.
Develops a new method for learning ODEs from sparse data.
Neural networks can learn kernel machines with a data-dependent kernel.
New method for spectral and Bergman kernels under local spectral gap condition.
A simple, flexible approach to creating expressive priors in Gaussian process (GP) models makes new kernels from a combination of basic kernels, e.g. summing a periodic and linear kernel can capture seasonal variation with a long term trend. Despite a well-studied link between GPs and Bayesian neural networks (BNNs), t…
Alzheimer's disease is a major cause of dementia. Its diagnosis requires accurate biomarkers that are sensitive to disease stages. In this respect, we regard probabilistic classification as a method of designing a probabilistic biomarker for disease staging. Probabilistic biomarkers naturally support the interpretation…
Proposes DP-MERF for privacy-preserving synthetic data generation.