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.
result The exponential kernel function optimally recovers clusters in high-dimensional data, matching information-theoretic limits up to a factor of √2.
Deep generative models can learn to generate realistic-looking images, but many of the most effective methods are adversarial and involve a saddlepoint optimization, which requires a careful balancing of training between a generator network and a critic network. Maximum mean discrepancy networks (MMD-nets) avoid this i…
Develops kernels for matchings, overcoming computational challenges.
problem Challenges in applying kernel methods to matchings due to their discrete, non-Euclidean nature.
method Characterizes stationary kernels, introduces heat and Matérn kernel families, and develops a sub-exponential algorithm for efficient evaluation.
result Establishes novel negative results and identifies an open problem in transferring the framework to trees.
The ratio of two probability densities can be used for solving various machine learning tasks such as covariate shift adaptation (importance sampling), outlier detection (likelihood-ratio test), and feature selection (mutual information). Recently, several methods of directly estimating the density ratio have been deve…
We propose graph kernels based on subgraph matchings, i.e. structure-preserving bijections between subgraphs. While recently proposed kernels based on common subgraphs (Wale et al., 2008; Shervashidze et al., 2009) in general can not be applied to attributed graphs, our approach allows to rate mappings of subgraphs by …
Unified approach to graph matching using Hilbert spaces and entropy-regularized Frank-Wolfe algorithm.
problem Graph matching problems in computer vision, pattern recognition, and bioinformatics.
method Unified view of Koopmans-Beckmann's QAP and Lawler's QAP, introducing new rules for array operations in Hilbert spaces. Entropy-regularized Frank-Wolfe (EnFW) algorithm for QAP optimization.
result Our approach significantly outperforms state-of-the-art in matching accuracy and scalability.
We develop an encompassing framework for matching, covariate balancing, and doubly-robust methods for causal inference from observational data called generalized optimal matching (GOM). The framework is given by generalizing a new functional-analytical formulation of optimal matching, giving rise to the class of GOM me…
We prove rates of convergence in the statistical sense for kernel-based least squares regression using a conjugate gradient algorithm, where regularization against overfitting is obtained by early stopping. This method is directly related to Kernel Partial Least Squares, a regression method that combines supervised dim…
Stein variational gradient descent (SVGD) is a non-parametric inference algorithm that evolves a set of particles to fit a given distribution of interest. We analyze the non-asymptotic properties of SVGD, showing that there exists a set of functions, which we call the Stein matching set, whose expectations are exactly …
We construct near-optimal coresets for kernel density estimates for points in Rd when the kernel is positive definite. Specifically we show a polynomial time construction for a coreset of size O(d/ε⋅log1/ε), and we show a near-matching lower bound of size $Ω(\min\…
This work studies low-rank approximation of a positive semidefinite matrix from partial entries via nonconvex optimization. We characterized how well local-minimum based low-rank factorization approximates a fixed positive semidefinite matrix without any assumptions on the rank-matching, the condition number or eigensp…
New algorithm optimizes Hölder smooth functions in RKHS with tighter regret bounds.
problem Optimizing Hölder smooth functions in RKHS with bounded norm.
method Proposes a new algorithm ( exttt{LP-GP-UCB}) using Local Polynomial (LP) estimators and multi-scale UCB.
result Derives high probability bounds on simple and cumulative regret, matching optimal performance for SE kernel and uniformly tighter bounds for Matérn kernels.
This study examines the practical equivalence of Laplace and neural tangent kernels.
problem Understanding the practical equivalence of Laplace and neural tangent kernels.
method The study matches the kernels exactly and by matching posteriors of a Gaussian process. It also analyzes the kernels in R^d and experiments with them in regression tasks.
result The Laplace and neural tangent kernels are practically equivalent.
In real supervised learning scenarios, it is not uncommon that the training and test sample follow different probability distributions, thus rendering the necessity to correct the sampling bias. Focusing on a particular covariate shift problem, we derive high probability confidence bounds for the kernel mean matching (…
Background: The problem of predicting whether a drug combination of arbitrary orders is likely to induce adverse drug reactions is considered in this manuscript. Methods: Novel kernels over drug combinations of arbitrary orders are developed within support vector machines for the prediction. Graph matching methods are …
The computational complexity of kernel methods has often been a major barrier for applying them to large-scale learning problems. We argue that this barrier can be effectively overcome. In particular, we develop methods to scale up kernel models to successfully tackle large-scale learning problems that are so far only …