Multi-task Learning for Aggregated Data using Gaussian Processes (2019-06-22T00:00:00.000000Z)

TL;DR

This paper presents a novel multi-task learning model based on Gaussian processes for joint learning of variables that have been aggregated at different input scales, suitable for larger datasets.

Abstract

Aggregated data is commonplace in areas such as epidemiology and demography. For example, census data for a population is usually given as averages defined over time periods or spatial resolutions (cities, regions or countries). In this paper, we present a novel multi-task learning model based on Gaussian processes for joint learning of variables that have been aggregated at different input scales. Our model represents each task as the linear combination of the realizations of latent processes that are integrated at a different scale per task. We are then able to compute the cross-covariance between the different tasks either analytically or numerically. We also allow each task to have a potentially different likelihood model and provide a variational lower bound that can be optimised in a stochastic fashion making our model suitable for larger datasets. We show examples of the model in a synthetic example, a fertility dataset, and an air pollution prediction application.

Authors

F. Yousefi

1 papers

M. Smith

1 papers

Mauricio A Álvarez

2 papers

TL;DR

Abstract

Authors

References38 items

Spatially Aggregated Gaussian Processes with Multivariate Areal Outputs

Multi-resolution Multi-task Gaussian Processes

Refining Coarse-grained Spatial Data using Auxiliary Spatial Data Sets with Various Granularities

Gaussian Process Regression for Binned Data

Survey of multifidelity methods in uncertainty propagation, inference, and optimization

Heterogeneous Multi-output Gaussian Process Prediction

Variational Learning on Aggregate Outputs with Gaussian Processes

Generalized Linear Models for Aggregated Data

Chained Gaussian Processes

From Group to Individual Labels Using Deep Features

(Almost) No Label No Cry

Scalable Variational Gaussian Process Classification

Scale in Spatial Information and Analysis

Gaussian Processes for Big Data

Stochastic variational inference

Gaussian Process Regression Networks

Kernels for Vector-Valued Functions: a Review

Combining Areal and Point Data in Geostatistical Interpolation: Applications to Soil Science and Medical Geography

Gaussian Processes Multiple Instance Learning

Efficient Multioutput Gaussian Processes through Variational Inducing Kernels

Sparse Convolved Gaussian Processes for Multi-output Regression

Estimating labels from label proportions

Multi-task Gaussian Process Prediction

Supervised Learning by Training on Aggregate Outputs

Sparse Gaussian Processes using Pseudo-inputs

Learning about Individuals from Group Statistics

Dependent Gaussian Processes

A Geostatistical Framework for Area-to-Point Spatial Interpolation

Gaussian Processes For Machine Learning

Combining Incompatible Spatial Data

Geostatistics for Natural Resources Evaluation

Supplementary Material for the Paper : ” Variational Bayesian Multiple Instance Learning with Gaussian Processes ”

Variational Weakly Supervised Gaussian Processes

Review of multi-ﬁdelity models

Carl E. Rasmussen and Christopher K. I. Williams

Semiparametric latent factor models

Variational algorithms for approximate Bayesian inference

Mining Geostatistics

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