Related papers: Sliced Inverse Regression for Spatial Data

Suppose that $Y$ is a scalar and $X$ is a second-order stochastic process, where $Y$ and $X$ are conditionally independent given the random variables $\xi_1,...,\xi_p$ which belong to the closed span $L_X^2$ of $X$. This paper investigates…

Structured additive distributional regression models offer a versatile framework for estimating complete conditional distributions by relating all parameters of a parametric distribution to covariates. Although these models efficiently…

Concerning bivariate least squares linear regression, the classical results obtained for extreme structural models in earlier attempts are reviewed using a new formalism in terms of deviation (matrix) traces which, for homoscedastic data,…

To deal with non-linear relations between the predictors and the response, we can use transformations to make the data look linear or approximately linear. In practice, however, transformation methods may be ineffective, and it may be more…

The practical applications of Wasserstein distances (WDs) are constrained by their sample and computational complexities. Sliced-Wasserstein distances (SWDs) provide a workaround by projecting distributions onto one-dimensional subspaces,…

Bayesian methods and software for spatial data analysis are generally now well established in the scientific community. Despite the wide application of spatial models, the analysis of multivariate spatial data using R-INLA has not been…

Shuffled regression concerns settings in which covariates and responses are observed without their correct pairing. In dependent-data problems, a second form of missing correspondence can arise when responses are also detached from the…

The problem of inverse scattering proposed by Angles and Mallat in 2018, concerns training a deep neural network to invert the scattering transform applied to an image. After such a network is trained, it can be used as a generative model…

Local Intrinsic Dimensionality (LID) has shown strong potential for identifying anomalies and outliers in high-dimensional data across a wide range of real-world applications, including landslide failure detection in granular media. Early…

We consider a class of inverse problems where it is possible to aggregate the results of multiple experiments. This class includes problems where the forward model is the solution operator to linear ODEs or PDEs. The tremendous size of such…

Linear least squares (LLS) is perhaps the most common method of data analysis, dating back to Legendre, Gauss and Laplace. Framed as linear regression, LLS is also a backbone of mathematical statistics. Here we report on an unexpected new…

Stochastic descent methods (of the gradient and mirror varieties) have become increasingly popular in optimization. In fact, it is now widely recognized that the success of deep learning is not only due to the special deep architecture of…

We devise a one-shot approach to distributed sparse regression in the high-dimensional setting. The key idea is to average "debiased" or "desparsified" lasso estimators. We show the approach converges at the same rate as the lasso as long…

Learning the relationships between various entities from time-series data is essential in many applications. Gaussian graphical models have been studied to infer these relationships. However, existing algorithms process data in a batch at a…

We consider the nonparametric regression estimation problem of recovering an unknown response function f on the basis of spatially inhomogeneous data when the design points follow a known compactly supported density g with a finite number…

In various applications with large spatial regions, the relationship between the response variable and the covariates is expected to exhibit complex spatial patterns. We propose a spatially clustered varying coefficient model, where the…

We study adaptive data-dependent dimensionality reduction in the context of supervised learning in general metric spaces. Our main statistical contribution is a generalization bound for Lipschitz functions in metric spaces that are…

In this paper we consider the problem of bootstrapping a class of spatial regression models when the sampling sites are generated by a (possibly nonuniform) stochastic design and are irregularly spaced. It is shown that the natural…

Regression is one of the most fundamental statistical inference problems. A broad definition of regression problems is as estimation of the distribution of an outcome using a family of probability models indexed by covariates. Despite the…

Spatial clustering has been widely used for spatial data mining and knowledge discovery. An ideal multivariate spatial clustering should consider both spatial contiguity and aspatial attributes. Existing spatial clustering approaches may…