Related papers: New Flexible Compact Covariance Model on a Sphere

We present an efficient convolution kernel for Convolutional Neural Networks (CNNs) on unstructured grids using parameterized differential operators while focusing on spherical signals such as panorama images or planetary signals. To this…

Many supervised learning problems involve high-dimensional data such as images, text, or graphs. In order to make efficient use of data, it is often useful to leverage certain geometric priors in the problem at hand, such as invariance to…

We consider the problem of modeling, estimating, and controlling the latent state of a spatiotemporally evolving continuous function using very few sensor measurements and actuator locations. Our solution to the problem consists of two…

This work proposes a new procedure for estimating the non-stationary spatial covariance function for Spatial-Temporal Deformation. The proposed procedure is based on a monotonic function approach. The deformation functions are expanded as a…

This paper investigates the cross-correlations across multiple climate model errors. We build a Bayesian hierarchical model that accounts for the spatial dependence of individual models as well as cross-covariances across different climate…

Many contemporary statistical learning methods assume a Euclidean feature space. This paper presents a method for defining similarity based on hyperspherical geometry and shows that it often improves the performance of support vector…

We present a novel rotation invariant architecture operating directly on point cloud data. We demonstrate how rotation invariance can be injected into a recently proposed point-based PCNN architecture, at all layers of the network,…

In this paper, a class of high order numerical schemes is proposed to solve the nonlinear parabolic equations with variable coefficients. This method is based on our previous work [10] for convection-diffusion equations, which relies on a…

In this paper, we propose a dimension reduction model for spatially dependent variables. Namely, we investigate an extension of the \emph{inverse regression} method under strong mixing condition. This method is based on estimation of the…

In this paper we investigate and compare different gradient algorithms designed for the domain expression of the shape derivative. Our main focus is to examine the usefulness of kernel reproducing Hilbert spaces for PDE constrained shape…

Estimating spot covariance is an important issue to study, especially with the increasing availability of high-frequency financial data. We study the estimation of spot covariance using a kernel method for high-frequency data. In…

We consider the problem of causal structure learning in the setting of heterogeneous populations, i.e., populations in which a single causal structure does not adequately represent all population members, as is common in biological and…

Many applications of interest involve data that can be analyzed as unit vectors on a d-dimensional sphere. Specific examples include text mining, in particular clustering of documents, biology, astronomy and medicine among others. Previous…

We propose a method for the approximation of high- or even infinite-dimensional feature vectors, which play an important role in supervised learning. The goal is to reduce the size of the training data, resulting in lower storage…

Kernel approximation via nonlinear random feature maps is widely used in speeding up kernel machines. There are two main challenges for the conventional kernel approximation methods. First, before performing kernel approximation, a good…

In this paper, we consider a partial deconvolution kernel estimator for nonparametric regression when some covariates are measured with error while others are observed without error. We focus on a general and realistic setting in which the…

We present a general method for accelerating by more than an order of magnitude the convolution of pixelated function on the sphere with a radially-symmetric kernel. Our method splits the kernel into a compact real-space, and a compact…

This paper proposes a new nonlinear approach for additive functional regression with functional response based on kernel methods along with some slight reformulation and implementation of the linear regression and the spectral additive…

Previous work generally believes that improving the spatial invariance of convolutional networks is the key to object counting. However, after verifying several mainstream counting networks, we surprisingly found too strict pixel-level…

The principle of translation equivariance (if an input image is translated an output image should be translated by the same amount), led to the development of convolutional neural networks that revolutionized machine vision. Other…