Nonlinear Distribution Regression for Remote Sensing Applications


In many remote sensing applications one wants to estimate variables or parameters of interest from observations. When the target variable is available at a resolution that matches the remote sensing observations, standard algorithms such as neural networks, random forests or Gaussian processes are readily available to relate the two. However, we often encounter situations where the target variable is only available at the group level, i.e. collectively associated to a number of remotely sensed observations. This problem setting is known in statistics and machine learning as multiple instance learning o r distribution regression. This paper introduces a nonlinear (kernel-based) method for distribution regression that solves the previous problems without making any assumption on the statistics of the grouped data. The presented formulation considers distribution embeddings in reproducing kernel Hilbert spaces, and performs standard least squares regression with the empirical means therein. A flexible version to deal with multisource data of different dimensionality and sample sizes is also presented and evaluated. It allows working with the native spatial resolution of each sensor, avoiding the need of match-up procedures. Noting the large computational cost of the approach, we introduce an efficient version via random Fourier features to cope with millions of points and groups. We demonstrate our method in \red{synthetic controlled scenarios}, and on its application to real data. Real experiments involve SMAP Vegetation Optical Depth data for the estimation of crop production in the US Corn Belt, and MODIS and MISR reflectances for the estimation of Aerosol Optical Depth. An exhaustive empirical evaluation of the method is done against naive (linear and nonlinear) approaches based on input-space means, as well as previously presented methods for multiple-instance learning.


author={JE. Adsuara and A. Pérez-Suay and J. Muñoz-Mari and A. Mateo-Sanchis and M. Piles and G. Camps-Valls},
journal={IEEE Transactions on Geoscience and Remote Sensing},
title={Nonlinear Distribution Regression for Remote Sensing Applications},

Download source code

Source code (released v1.0 29/06/2019)

Distribution Regression: Link


If you have any question about, please, do not hesitate to write an email to Jose E Adsuara (jose.adsuara at uv dot es).

IPL logo