Structural Inference via Machine Learning: Tail Dependence Modeling and Subset Selection

Abstract

Recognizing the structure of a system is of great importance in many areas, such as financial management, information retrieval, and control problems. One typically implements the statistical inferences from the observational data under untenable assumptions. However, the structure under the tenable assumption is hard to make inferences using traditional statistical methods.  In this thesis, we consider two structural inference problems: tail dependence modeling and subset selection, and conduct the structural inference with emerging machine learning methods.

Modeling extreme dependence structures among different financial assets is crucial for financial partitioners. The traditional parametric models cannot characterize the high-dimensional extreme dependence structure because it presents pair-wise heterogeneity and severe asymmetry. Our first work proposes a latent generative model capture of the high-dimensional extreme dependence structure. The proposed model demonstrates heterogeneous and asymmetric tail dependence while allowing the marginal distribution to be heavy-tailed and asymmetric. Furthermore, we propose a heavy-tailed maximum mean discrepancy (HT-MMD) method to estimate the model parameters. The HT-MMD method can adapt to distributions with asymmetric tail index and heterogeneous tail dependence. We also establish the estimator's consistency for the proposed HT-MMD method and show that the method can scale to high-dimensional data. Finally, we consider the mean-variance portfolio problem with the tail dependence constraint. Results show that the constructed portfolio strategies have superior performance to other benchmarks.

Subset selection, i.e., finding a bunch of items from a collection to achieve specific goals, has wide applications in information retrieval, statistics, and machine learning. Different relaxed differentiable operators for subset selection are proposed to implement an end-to-end learning framework. Most current work relies on either regularization method or perturbation method. Our second work provides a probabilistic interpretation for regularization relaxation and unifies two schemes. Besides, we build some concrete examples to show the generic connection between these two relaxations. Finally, we evaluate the perturbed and regularized selectors on the maximum entropy sampling problem and the feature selection problem. The experimental results show that these two methods can achieve competitive performance against other benchmarks.

Date of Award	1 Jun 2023
Original language	English
Awarding Institution	City University of Hong Kong
Supervisor	Gang HAO (Supervisor), Qi WU (Co-supervisor), Yixuan XIAO (Supervisor) & Zhan PANG (External Co-Supervisor)