Probabilistic Support Vector Regression for Histogram-Valued Data: A Case Study on Peatland Data
Fathimah Al-Ma^shumah, Kurnia Novita Sari

Institut Teknologi Bandung, Institut Teknologi Bandung,

Abstract

In geostatistics, spatial distribution data of environmental variables are often represented through histograms, which depict the relative frequencies of values within specified bins. This study investigates regression methods for histogram-valued data by extending the probabilistic approach of Support Vector Machine (SVM) regression. The primary focus is on applying this methodology to carbon distribution data in peatlands, where histograms illustrate variations in carbon content across different soil depths.

The study addresses both linear and nonlinear regression problems within the context of histogram data and conducts a simulation study to assess the performance of the proposed methodology. Subsequently, the methodology is applied to two real datasets: first, carbon distribution data from tropical peatlands, demonstrating changes in carbon content at various soil depths- and second, monthly precipitation histogram data from multiple meteorological stations to evaluate the impact of rainfall on soil variability.

The results indicate that the histogram-based SVM regression model provides accurate estimates for carbon distribution in peatlands and varying precipitation patterns. These findings contribute to improved peatland management strategies and offer insights into rainfall patterns affecting carbon distribution, which are crucial for climate change studies and environmental conservation.

Keywords: Probabilistic Support Vector Machine, Regression, Histogram-valued Data, Peatland

Topic: Probability and Stochastic Analysis