Nonlinear Parsimonious Modeling with Information Filtering Networks: Theory and Practice
by Qingyang Liu
Date of Examination:2025-10-22
Date of issue:2025-11-06
Advisor:Prof. Dr. Ramin Yahyapour
Referee:Prof. Dr. Ramin Yahyapour
Referee:Prof. Dr. Thomas Kneib
Persistent Address:
http://dx.doi.org/10.53846/goediss-11616
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Abstract
English
This thesis offers a comprehensive exploration and methodological advancement of Information Filtering Networks (IFNs), emphasizing Triangulated Maximally Filtered Graphs (TMFG), Local-Global (LoGo) models, and their nonlinear extensions. IFNs represent sparse, interpretable, and computationally efficient network structures designed to retain essential information from complex datasets by systematically filtering correlations and dependencies. The principal objective of this research is to develop, validate, and demonstrate robust IFN-based frameworks across diverse domains such as financial forecasting, clustering, and image processing, showcasing their broad applicability and methodological superiority relative to traditional modeling techniques. Initially, the thesis addresses the challenges of information extraction from complex web structures through a novel hybrid web crawler that integrates dynamic and static crawling methods, enhanced by parallel computing techniques. This method significantly accelerates data extraction from online databases and websites requiring natural language processing techniques, achieving efficiency improvements of up to 100-fold compared to single conventional methods, thus providing a high-quality, large-scale financial data extraction approach essential for subsequent financial time series modeling. Subsequently, using the acquired financial data, this research advances into financial forecasting through an advanced hybrid modeling framework. This approach combines Variational Mode Decomposition (VMD) for signal preprocessing, TMFG for feature selection, and Long Short-Term Memory (LSTM) networks for predictive modeling. TMFG systematically filters and selects structurally significant features, resulting in predictive models that achieve enhanced forecasting accuracy and interpretability. This hybrid model efficiently decomposes financial signals, reduces redundancy, and captures intrinsic data patterns, notably enhancing predictive accuracy and computational efficiency over traditional statistical and machine learning models. Further contributions include integrating Grey Relational Analysis (GRA) with the LoGo framework, constructing localized sparse inverse covariance matrices for accurate short-term forecasting. Leveraging sparse precision matrices derived from IFNs, the LoGo model captures intricate global and local dependency structures. Combining GRA as a preprocessing and ranking mechanism significantly improves model robustness, especially within volatile financial environments. To address theoretical limitations of linear correlation matrices, the thesis introduces nonlinear dependency transformation techniques for effectively modeling non-Gaussian and nonlinear relationships. Applying TMFG within this transformed space generates decomposable networks suited for constructing sparse, parsimonious models. This methodological innovation overcomes the limitations of conventional Pearson-based correlation approaches, enabling more accurate modeling of complex, non-normal datasets. It turns out that Gaussian-Copula transformation outperforms other normalization methods for its effectiveness in stabilizing data distributions, significantly enhancing the performance and accuracy of nonlinear LoGo models. Building upon these developments, this thesis proposes a nonlinear parsimonious model integrating Gaussian-Copula transformations with the LoGo framework. This integration allows for a more accurate representation of nonlinear dependencies, facilitating the precise construction of sparse precision matrices from TMFG-generated decomposable networks. The proposed Copula–LoGo method significantly outperforms traditional models, such as Principal Components Analysis (PCA), Support Vector Machines (SVM), and standalone LSTM networks, in predictive accuracy and computational efficiency. However, when applying the new nonlinear Copula–LoGo model, certain drawbacks are encountered, particularly errors arising during data transformation into Copula distributions. To address this issue, a novel classification-forecast methodology utilizing the Copula–LoGo model is proposed. This approach utilizes dynamic clustering to reveal hidden structural patterns within high-dimensional time series data, subsequently employing these patterns as contextual priors in nonlinear LoGo regression models. This integration significantly enhances model adaptability, particularly beneficial for datasets characterized by dynamic regime shifts. Finally, the applicability of IFNs extends into image processing, proposing a TMFG-based framework for image segmentation and denoising. This model effectively captures spatial dependencies between pixel intensities and edge features, leveraging the sparse, planar structure of TMFG for computational efficiency and high-resolution feature preservation. This confirms the generalizability and efficacy of IFN methodologies beyond temporal data, highlighting their potential for spatial data analysis and computer vision. Collectively, this thesis contributes a robust and versatile methodological framework centered around IFNs and LoGo models. It underscores the effectiveness and adaptability of TMFG and LoGo models as powerful tools for dependency modeling, forecasting, clustering, and spatial analysis. By advancing the core principles of sparsity, decomposability, and locality inherent to IFNs, the research presented herein lays a rigorous foundation for future developments in interpretable and computationally efficient modeling across various scientific and engineering domains.
Keywords: Nonlinear Parsimonious Modeling; Information Filtering Networks; LoGo; Transformation methods; Copula
