Related papers: Dynamics-Adapted Cone Kernels
Using analytical calculations and computer simulations we consider both the lateral diffusion of a membrane protein and the fluctuation spectrum of the membrane in which the protein is embedded. The membrane protein interacts with the…
We consider hypo-elliptic diffusion and convection-diffusion on $\mathbb{R}^3 \rtimes S^2$, the quotient of the Lie group of rigid body motions SE(3) in which group elements are equivalent if they are equal up to a rotation around the…
In this paper, we extend the class of kernel methods, the so-called diffusion maps (DM) and ghost point diffusion maps (GPDM), to solve the time-dependent advection-diffusion PDE on unknown smooth manifolds without and with boundaries. The…
We consider a class of constant-coefficient partial differential operators on a finite-dimensional real vector space which exhibit a natural dilation invariance. Typically, these operators are anisotropic, allowing for different degrees in…
The goal of motion tomography is to recover a description of a vector flow field using information on the trajectory of a sensing unit. In this paper, we develop a predictor corrector algorithm designed to recover vector flow fields from…
Kernel classifiers and regressors designed for structured data, such as sequences, trees and graphs, have significantly advanced a number of interdisciplinary areas such as computational biology and drug design. Typically, kernels are…
We present a data-driven framework for the modeling of nonlocal heat transport in plasmas using a nonlocal theory informed neural network trained on kinetic Particle-in-Cell simulations that span both local and nonlocal regimes. The model…
Approximating non-linear kernels using feature maps has gained a lot of interest in recent years due to applications in reducing training and testing times of SVM classifiers and other kernel based learning algorithms. We extend this line…
Kernel-phase is a data analysis method based on a generalization of the notion of closure-phase invented in the context of interferometry, but that applies to well corrected diffraction dominated images produced by an arbitrary aperture.…
We present diffusion-convolutional neural networks (DCNNs), a new model for graph-structured data. Through the introduction of a diffusion-convolution operation, we show how diffusion-based representations can be learned from…
We introduce a simulation method for dynamic portfolio valuation and risk management building on machine learning with kernels. We learn the dynamic value process of a portfolio from a finite sample of its cumulative cash flow. The learned…
Diffusion Transformers (DiTs) have demonstrated strong performance in generative modeling, particularly in image synthesis, making them a compelling choice for molecular conformer generation. However, applying DiTs to molecules introduces…
Computer vision is a growing field with a lot of new applications in automation and robotics, since it allows the analysis of images and shapes for the generation of numerical or analytical information. One of the most used method of…
We propose in this paper a new family of kernels to handle times series, notably speech data, within the framework of kernel methods which includes popular algorithms such as the Support Vector Machine. These kernels elaborate on the well…
Convolutional kernels are basic and vital components of deep Convolutional Neural Networks (CNN). In this paper, we equip convolutional kernels with shape attributes to generate the deep Irregular Convolutional Neural Networks (ICNN).…
Provenance is a record that describes how entities, activities, and agents have influenced a piece of data; it is commonly represented as graphs with relevant labels on both their nodes and edges. With the growing adoption of provenance in…
We propose a method to efficiently construct data-dependent kernels which can make use of large quantities of (unlabeled) data. Our construction makes an approximation in the standard construction of semi-supervised kernels in Sindhwani et…
We present a novel attention-based model for discrete event data to capture complex non-linear temporal dependence structures. We borrow the idea from the attention mechanism and incorporate it into the point processes' conditional…
Convolutional Neural Networks, as most artificial neural networks, are commonly viewed as methods different in essence from kernel-based methods. We provide a systematic translation of Convolutional Neural Networks (ConvNets) into their…
Kernelization studies polynomial-time preprocessing algorithms. Over the last 20 years, the most celebrated positive results of the field have been linear kernels for classical NP-hard graph problems on sparse graph classes. In this paper,…