Related papers: Refining Coarse-grained Spatial Data using Auxilia…
We propose a data-driven, coarse-graining formulation in the context of equilibrium statistical mechanics. In contrast to existing techniques which are based on a fine-to-coarse map, we adopt the opposite strategy by prescribing a…
With the development of new remote sensing technology, large or even massive spatial datasets covering the globe become available. Statistical analysis of such data is challenging. This article proposes a semiparametric approach to model…
We propose a probabilistic model for inferring the multivariate function from multiple areal data sets with various granularities. Here, the areal data are observed not at location points but at regions. Existing regression-based models can…
Gaussian process is a theoretically appealing model for nonparametric analysis, but its computational cumbersomeness hinders its use in large scale and the existing reduced-rank solutions are usually heuristic. In this work, we propose a…
Spatial fields in the Earth and environmental sciences are often available at multiple scales or resolutions. While coarse-scale data (e.g., from global circulation models) are often abundant, they lack the local detail provided by…
A key challenge in spatial statistics is the analysis for massive spatially-referenced data sets. Such analyses often proceed from Gaussian process specifications that can produce rich and robust inference, but involve dense covariance…
Gaussian process regression is a powerful Bayesian nonlinear regression method. Recent research has enabled the capture of many types of observations using non-Gaussian likelihoods. To deal with various tasks in spatial modeling, we benefit…
Time series forecasting is a challenging task due to the existence of complex and dynamic temporal dependencies. This can lead to incorrect predictions by even the best forecasting models. Using more training data is one way to improve the…
ICT systems provide detailed information on computer network traffic. However, due to storage limitations, some of the information on past traffic is often only retained in an aggregated form. In this paper we show that Linear Gaussian…
Data-based discovery of effective, coarse-grained (CG) models of high-dimensional dynamical systems presents a unique challenge in computational physics and particularly in the context of multiscale problems. The present paper offers a…
We present a multivariate Gaussian process regression approach for parameter field reconstruction based on the field's measurements collected at two different scales, the coarse and fine scales. The proposed approach treats the parameter…
We consider the accuracy of an approximate posterior distribution in nonparametric regression problems by combining posterior distributions computed on subsets of the data defined by the locations of the independent variables. We show that…
We discuss a Bayesian formulation to coarse-graining (CG) of PDEs where the coefficients (e.g. material parameters) exhibit random, fine scale variability. The direct solution to such problems requires grids that are small enough to resolve…
A practical approach to evaluate performance of a Gaussian process regression models (GPR) for irregularly sampled sparse time-series is introduced. The approach entails construction of a secondary autoregressive model using the fine scale…
Fine-grained classification aims at distinguishing between items with similar global perception and patterns, but that differ by minute details. Our primary challenges come from both small inter-class variations and large intra-class…
Simulations of condensed matter systems often focus on the dynamics of a few distinguished components but require integrating the dynamics of the full system. A prime example is a molecular dynamics simulation of a (macro)molecule in…
In this paper, we study a new type of spatial sparse recovery problem, that is to infer the fine-grained spatial distribution of certain density data in a region only based on the aggregate observations recorded for each of its subregions.…
Despite the increasing visibility of fine-grained recognition in our field, "fine-grained'' has thus far lacked a precise definition. In this work, building upon clustering theory, we pursue a framework for measuring dataset granularity. We…
Deep Gaussian processes (DGPs) can model complex marginal densities as well as complex mappings. Non-Gaussian marginals are essential for modelling real-world data, and can be generated from the DGP by incorporating uncorrelated variables…
We introduce a scalable Gaussian process (GP) framework with deep product kernels for data-driven learning of parametrized spatio-temporal fields over fixed or parameter-dependent domains. The proposed framework learns a continuous…