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2022 | Book

Introduction Read chapter Read first chapter

On Spatio-Temporal Data Modelling and Uncertainty Quantification Using Machine Learning and Information Theory

Author: Fabian Guignard

Publisher: Springer International Publishing

Book Series : Springer Theses

Part of: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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About this book

The gathering and storage of data indexed in space and time are experiencing unprecedented growth, demanding for advanced and adapted tools to analyse them. This thesis deals with the exploration and modelling of complex high-frequency and non-stationary spatio-temporal data. It proposes an efficient framework in modelling with machine learning algorithms spatio-temporal fields measured on irregular monitoring networks, accounting for high dimensional input space and large data sets. The uncertainty quantification is enabled by specifying this framework with the extreme learning machine, a particular type of artificial neural network for which analytical results, variance estimation and confidence intervals are developed. Particular attention is also paid to a highly versatile exploratory data analysis tool based on information theory, the Fisher-Shannon analysis, which can be used to assess the complexity of distributional properties of temporal, spatial and spatio-temporal data sets. Examples of the proposed methodologies are concentrated on data from environmental sciences, with an emphasis on wind speed modelling in complex mountainous terrain and the resulting renewable energy assessment. The contributions of this thesis can find a large number of applications in several research domains where exploration, understanding, clustering, interpolation and forecasting of complex phenomena are of utmost importance.

Table of Contents

Frontmatter
Chapter 1. Introduction
Abstract
Spatio-temporal data are everywhere. Scientific observations are spatio-temporal by nature in many problems coming from various fields such as geo-environmental sciences, electricity demand management, geomarketing, neurosciences, public-health, or archaeology.
Fabian Guignard
Chapter 2. Study Area and Data Sets
Abstract
This chapter presents the study area and the data investigated as examples for the proposed methodologies along the thesis. Data wrangling, cleaning and missing values imputation processes are described. The data are explored with basic EDA tools such as summary statistics, spatial and temporal plots, box plots and kernel density estimates. The chapter also provides some basic meteorological insights.
Fabian Guignard
Chapter 3. Advanced Exploratory Data Analysis
Abstract
This chapter introduces some advanced EDA tools which can be applied to spatio-temporal data sets. They quantify and confirm some features of the wind speed data suggested by visualisation in the previous chapter and unveil hidden patterns.
Fabian Guignard
Chapter 4. Fisher-Shannon Analysis
Abstract
This chapter discusses the Fisher-Shannon analysis, an effective and computationally efficient data exploration tool based on IT quantities. This method is highly versatile and can be used in various situations such as time series discrimination, complexity quantification, detection of non-linear relationships, generation of time series features, detection of dynamical changes and non-stationarity tracking of a signal.
Fabian Guignard
Chapter 5. Spatio-Temporal Prediction with Machine Learning
Abstract
This chapter proposes a methodological framework for spatio-temporal interpolation that enables the use of any ML algorithms through data decomposition into a convenient temporal basis with spatial coefficients. For example, a basis induced by EOFs is chosen, and a multiple-output deep Feed-forward Neural Network (FNN) is used to learn the spatial coefficients jointly. Across several different experimental settings using both simulated and real-world data, it is shown that the proposed framework allows reconstructing of coherent spatio-temporal fields.
Fabian Guignard
Chapter 6. Uncertainty Quantification with Extreme Learning Machine
Abstract
On the one hand, UQ is crucial to assess the prediction quality of an ML model. It is particularly true in the previous chapter setup, where a relatively small number of points are modelled in a high-dimensional space. On the other hand, ELM is a universal approximator for non-linear regression problems that benefit from numerous advantages inherited from linear regression. It is very fast, easy to implement, has very few hyper-parameters and has a one-step optimisation process with a unique analytical solution. This chapter presents original and rigorous UQ developments of ELM.
Fabian Guignard
Chapter 7. Spatio-Temporal Modelling Using Extreme Learning Machine
Abstract
This chapter combines the developments of Chaps. 5 and 6 by using ELM to model each spatial coefficient map obtained from the EOF decomposition and extend the UQ to the spatio-temporal prediction. The modelling variance of the spatio-temporal prediction is estimated by reusing all component ELM variances obtained by the method presented in the previous chapter. The prediction variance is estimated by interpolating the expected squared residuals with a second model. However, this second modelling is performed on log-transformed data to ensure positive variance estimation, which generates the need to know the transformed variable’s variance. This issue is solved thanks again to ELM variance estimation. An application on the MeteoSwiss wind speed data is presented, providing an estimation of the power potential of aeolian energy in rural areas of Switzerland.
Fabian Guignard
Chapter 8. Conclusions, Perspectives and Recommendations
Abstract
This concluding chapter summarises and underlines the main achievements of each research topic and presents some reflections on future research.
Fabian Guignard
Metadata
Title
On Spatio-Temporal Data Modelling and Uncertainty Quantification Using Machine Learning and Information Theory
Author
Fabian Guignard
Copyright Year
2022
Electronic ISBN
978-3-030-95231-0
Print ISBN
978-3-030-95230-3
DOI
https://doi.org/10.1007/978-3-030-95231-0