相关论文: Data-driven extrapolation via feature augmentation…

This paper aims to address the challenge of data generation beyond the training data and proposes a framework for Structural Extrapolated Data GEneration (SEDGE) based on suitable assumptions on the underlying data-generating process. We…

To model high dimensional data, Gaussian methods are widely used since they remain tractable and yield parsimonious models by imposing strong assumptions on the data. Vine copulas are more flexible by combining arbitrary marginal…

A corpus of recent work has revealed that the learned index can improve query performance while reducing the storage overhead. It potentially offers an opportunity to address the spatial query processing challenges caused by the surge in…

We present a novel framework for variable selection in Fr\'echet regression with responses in general metric spaces, a setting increasingly relevant for analyzing non-Euclidean data such as probability distributions and covariance matrices.…

We consider numerical solution of elliptic problems with heterogeneous diffusion coefficients containing thin highly conductive structures. Such problems arise e.g. in fractured porous media, reinforced materials, and electric circuits. The…

Recent work shows that inference for Gaussian processes can be performed efficiently using iterative methods that rely only on matrix-vector multiplications (MVMs). Structured Kernel Interpolation (SKI) exploits these techniques by deriving…

This paper begins by reviewing numerous theoretical advancements in the field of multivariate splines, primarily contributed by Professor Larry L. Schumaker. These foundational results have paved the way for a wide range of applications and…

Approximation/interpolation from spaces of positive definite or conditionally positive definite kernels is an increasingly popular tool for the analysis and synthesis of scattered data, and is central to many meshless methods. For a set of…

Identifying coherent spatiotemporal patterns generated by complex dynamical systems is a central problem in many science and engineering disciplines. Here, we combine ideas from the theory of operator-valued kernels with delay-embedding…

Model-based clustering is a popular approach for clustering multivariate data which has seen applications in numerous fields. Nowadays, high-dimensional data are more and more common and the model-based clustering approach has adapted to…

We develop scalable randomized kernel methods for jointly associating data from multiple sources and simultaneously predicting an outcome or classifying a unit into one of two or more classes. The proposed methods model nonlinear…

Kernel methods provide a principled way to perform non linear, nonparametric learning. They rely on solid functional analytic foundations and enjoy optimal statistical properties. However, at least in their basic form, they have limited…

Distribution regression refers to the supervised learning problem where labels are only available for groups of inputs instead of individual inputs. In this paper, we develop a rigorous mathematical framework for distribution regression…

We propose a new data-driven reduced order model (ROM) framework that centers around the hierarchical structure of the variational multiscale (VMS) methodology and utilizes data to increase the ROM accuracy at a modest computational cost.…

Random sinusoidal features are a popular approach for speeding up kernel-based inference in large datasets. Prior to the inference stage, the approach suggests performing dimensionality reduction by first multiplying each data vector by a…

Classical Gaussian processes and Kriging models are commonly based on stationary kernels, whereby correlations between observations depend exclusively on the relative distance between scattered data. While this assumption ensures analytical…

Being motivated by the multilayer RECOS (REctified-COrrelations on a Sphere) transform, we develop a data-driven Saak (Subspace approximation with augmented kernels) transform in this work. The Saak transform consists of three steps: 1)…

Reconstruction of density functions and their characteristic functions by radial basis functions with scattered data points is a popular topic in the theory of pricing of basket options. Such functions are usually entire or admit an…

Constrained radial basis function (RBF) regression has recently emerged as a powerful meshless tool for reconstructing continuous velocity fields from scattered flow measurements, particularly in image-based velocimetry. However, existing…

We investigate structured sparsity methods for variable selection in regression problems where the target depends nonlinearly on the inputs. We focus on general nonlinear functions not limiting a priori the function space to additive…