arXiv research

Estimates spatio-temporal Hawkes processes using tensor recovery.

Advances in deep learning for spatio-temporal event modeling.

RKUM is an R package for robust kernel-based unsupervised methods.

Paper introduces AIF to analyze robust optimization effects.

Paper presents a new way to estimate model changes without full model evaluation.

We introduce kernel nonparametric tests for Lancaster three-variable interaction and for total independence, using embeddings of signed measures into a reproducing kernel Hilbert space. The resulting test statistics are straightforward to compute, and are used in powerful interaction tests, which are consistent against…

Paper shows robustness of kernel-based pairwise learning without strict assumptions.

Paper introduces a novel point process model for graph data using GNNs.

Develops a deep non-stationary kernel for non-stationary spatio-temporal point processes.

To the best of our knowledge, there are no general well-founded robust methods for statistical unsupervised learning. Most of the unsupervised methods explicitly or implicitly depend on the kernel covariance operator (kernel CO) or kernel cross-covariance operator (kernel CCO). They are sensitive to contaminated data, …

Efficient estimators for smooth Hilbert-valued parameters with theoretical guarantees.

ULFS-KDPE estimates parameters efficiently without influence functions.

Paper introduces a neural network-based non-stationary influence kernel for complex event data.

Imaging genetic research has essentially focused on discovering unique and co-association effects, but typically ignoring to identify outliers or atypical objects in genetic as well as non-genetics variables. Identifying significant outliers is an essential and challenging issue for imaging genetics and multiple source…

Many unsupervised kernel methods rely on the estimation of the kernel covariance operator (kernel CO) or kernel cross-covariance operator (kernel CCO). Both kernel CO and kernel CCO are sensitive to contaminated data, even when bounded positive definite kernels are used. To the best of our knowledge, there are few well…

Calibrates Hawkes models for market events, revealing power-law feedback kernels.

Identifying significant subsets of the genes, gene shaving is an essential and challenging issue for biomedical research for a huge number of genes and the complex nature of biological networks,. Since positive definite kernel based methods on genomic information can improve the prediction of diseases, in this paper we…

Study provides bounds for estimating intrinsic dimension using Gaussian kernels.

A new method debiases multiple target parameters without IFs.

Linearized attention fails to converge to NTK limit even at large widths.

Proposes a new estimator for causal mediation with continuous treatments.

We propose a method for nonparametric density estimation that exhibits robustness to contamination of the training sample. This method achieves robustness by combining a traditional kernel density estimator (KDE) with ideas from classical $M$-estimation. We interpret the KDE based on a radial, positive semi-definite ke…

This paper reviews the checkered history of predictive distributions in statistics and discusses two developments, one from recent literature and the other new. The first development is bringing predictive distributions into machine learning, whose early development was so deeply influenced by two remarkable groups at …

Kernels are powerful and versatile tools in machine learning and statistics. Although the notion of universal kernels and characteristic kernels has been studied, kernel selection still greatly influences the empirical performance. While learning the kernel in a data driven way has been investigated, in this paper we e…

Regularized empirical risk minimization using kernels and their corresponding reproducing kernel Hilbert spaces (RKHSs) plays an important role in machine learning. However, the actually used kernel often depends on one or on a few hyperparameters or the kernel is even data dependent in a much more complicated manner. …

We analyze double descent in finite-width neural networks using influence functions.

New findings show a balance between data fit and complexity in kernel hyperparameters.

We consider online learning for minimizing regret in unknown, episodic Markov decision processes (MDPs) with continuous states and actions. We develop variants of the UCRL and posterior sampling algorithms that employ nonparametric Gaussian process priors to generalize across the state and action spaces. When the trans…

Many real-world optimization problems require significant resources for objective function evaluations. This is a challenge to evolutionary algorithms, as it limits the number of available evaluations. One solution are surrogate models, which replace the expensive objective. A particular issue in this context are hiera…

DKLM learns adaptive kernels for robust nonlinear subspace clustering.

Paper establishes a generalization bound for gradient flow using a data-dependent kernel.

The study explains how neural networks align their kernels to target functions during training.

The paper establishes a central limit theorem for estimating the influence parameter in a partially observed Hawkes process system.

Develops robust persistence diagrams using kernel methods.

Ad-SVGD optimizes kernel parameters for SVGD, improving inference performance.

Since their emergence in the 1990's, the support vector machine and the AdaBoost algorithm have spawned a wave of research in statistical machine learning. Much of this new research falls into one of two broad categories: kernel methods and ensemble methods. In this expository article, I discuss the main ideas behind t…

RFFNet scales kernel methods to large datasets by learning kernel relevance.

Unified framework interprets SSL models, revealing biases.

Kernel functions in support vector machines (SVM) are needed to assess the similarity of input samples in order to classify these samples, for instance. Besides standard kernels such as Gaussian (i.e., radial basis function, RBF) or polynomial kernels, there are also specific kernels tailored to consider structure in t…

In genome-wide interaction studies, to detect gene-gene interactions, most methods are divided into two folds: single nucleotide polymorphisms (SNP) based and gene-based methods. Basically, the methods based on the gene are more effective than the methods based on a single SNP. Recent years, while the kernel canonical …

The Tick library simulates and learns Hawkes processes with latency effects.

In machine learning or statistics, it is often desirable to reduce the dimensionality of a sample of data points in a high dimensional space $\mathbb{R}^d$. This paper introduces a dimensionality reduction method where the embedding coordinates are the eigenvectors of a positive semi-definite kernel obtained as the sol…

Although the convolutional neural networks (CNNs) have become popular for various image processing and computer vision task recently, it remains a challenging problem to reduce the storage cost of the parameters for resource-limited platforms. In the previous studies, tensor decomposition (TD) has achieved promising co…

Recent developments in system identification have brought attention to regularized kernel-based methods, where, adopting the recently introduced stable spline kernel, prior information on the unknown process is enforced. This reduces the variance of the estimates and thus makes kernel-based methods particularly attract…

Volterra series are especially useful for nonlinear system identification, also thanks to their capability to approximate a broad range of input-output maps. However, their identification from a finite set of data is hard, due to the curse of dimensionality. Recent approaches have shown how regularized kernel-based met…

Large learning rates improve kernel method performance.

The paper analyzes how Gaussian kernel parameters affect posterior covariance in Gaussian processes.

Selecting diverse and important items, called landmarks, from a large set is a problem of interest in machine learning. As a specific example, in order to deal with large training sets, kernel methods often rely on low rank matrix Nyström approximations based on the selection or sampling of landmarks. In this context, …