Learning with Hierarchical Data

The Hong Kong University of Science and Technology
Department of Computer Science and Engineering


PhD Thesis Defence


Title: "Learning with Hierarchical Data"

By

Miss Huiru XIAO


Abstract

When coming to understand the world, human minds construct structured knowledge 
from sparse, noisy, and ambiguous data. Therefore, humanlike machine learning 
should perform inference over hierarchies of flexibly structured data. Based on 
these beliefs, people usually construct real-world data as hierarchies to 
formulate the machine learning problem, where the hierarchical data serve as 
the hypotheses or the inference queries. In this thesis, we study learning with 
hierarchical data. First, we look into the hierarchical data classification 
problem, where the hierarchical data act as hypotheses. In specific, we 
investigate hierarchical text classification and propose a path cost-sensitive 
learning algorithm to utilize the structural information of classes. Then we 
pay much attention to exploring the geometric representation learning for 
hierarchical structures in knowledge graphs, in which case the hierarchical 
data are regarded as inference queries. The choice of geometric space for 
knowledge graph embeddings can have significant effects on the multi-relational 
knowledge graph inference. Transitivity, which forms the hierarchical 
structure, is a special property that can be modeled more naturally by the 
hyperbolic geometry instead of the traditional Euclidean embedding models. To 
build a representation learning framework for various structures in knowledge 
graphs, we propose to learn the embeddings in different geometric spaces and 
apply manifold alignment to align the shared entities. We also focus on the 
representation of the single-relational hierarchical structures. To improve the 
hyperbolic embeddings, we propose to learn the embeddings of hierarchical data 
in the complex hyperbolic space, which has a more powerful representation 
capacity to capture a variety of hierarchical structures. Finally, we extend 
the representation capacity of the complex hyperbolic geometry in 
multi-relational knowledge graph embeddings. We propose to use the fast Fourier 
transform as a simple and effective solution to apply the real hyperbolic 
geometric transformations and the attention mechanism in the complex hyperbolic 
space.


Date:			Tuesday, 9 August 2022

Time:			10:00am - 12:00noon

Zoom Meeting:
https://hkust.zoom.us/j/97503630572?pwd=ajc5alFmRnY4RHcrQ3hJZjJBRjBsdz09

Chairperson:		Prof. Bradley FOREMAN (PHYS)

Committee Members:	Prof. Yangqiu SONG (Supervisor)
 			Prof. Raymond WONG
 			Prof. Dit Yan YEUNG
 			Prof. Can YANG (MATH)
 			Prof. Sinno PAN (Nanyang Technological University)


**** ALL are Welcome ****