Structured Approaches for Exploring Interpersonal Relationships in Natural Language Text

Human relationships have long been studied by scientists from domains like sociology, psychology, literature, etc. for understanding people's desires, goals, actions and expected behaviors. In this dissertation we study inter-personal relationships as expressed in natural language text. Modeling inter-personal relationships from text finds application in general natural language understanding, as well as real-world domains such as social networks, discussion forums, intelligent virtual agents, etc. We propose that the study of relationships should incorporate not only linguistic cues in text, but also the contexts in which these cues appear. Our investigations, backed by empirical evaluation, support this thesis, and demonstrate that the task benefits from using structured models that incorporate both types of information. We present such structured models to address the task of modeling the nature of relationships between any two given characters from a narrative. To begin with, we assume that relationships are of two types: cooperative and non-cooperative. We first describe an approach to jointly infer relationships between all characters in the narrative, and demonstrate how the task of characterizing the relationship between two characters can benefit from including information about their relationships with other characters in the narrative. We next formulate the relationship-modeling problem as a sequence prediction task to acknowledge the evolving nature of human relationships, and demonstrate the need to model the history of a relationship in predicting its evolution. Thereafter, we present a data-driven method to automatically discover various types of relationships such as familial, romantic, hostile, etc. Like before, we address the task of modeling evolving relationships but don't restrict ourselves to two types of relationships. We also demonstrate the need to incorporate not only local historical but also global context while solving this problem. Lastly, we demonstrate a practical application of modeling inter-personal relationships in the domain of online educational discussion forums. Such forums offer opportunities for its users to interact and form deeper relationships. With this view, we address the task of identifying initiation of such deeper relationships between a student and the instructor. Specifically, we analyze contents of the forums to automatically suggest threads to the instructors that require their intervention. By highlighting scenarios that need direct instructor-student interactions, we alleviate the need for the instructor to manually peruse all threads of the forum and also assist students who have limited avenues for communicating with instructors. We do this by incorporating the discourse structure of the thread through latent variables that abstractly represent contents of individual posts and model the flow of information in the thread. Such latent structured models that incorporate the linguistic cues without losing their context can be helpful in other related natural language understanding tasks as well. We demonstrate this by using the model for a very different task: identifying if a stated desire has been fulfilled by the end of a story.

Spectral Frame Analysis and Learning through Graph Structure

This dissertation investigates the connection between spectral analysis and frame theory. When considering the spectral properties of a frame, we present a few novel results relating to the spectral decomposition. We first show that scalable frames have the property that the inner product of the scaling coefficients and the eigenvectors must equal the inverse eigenvalues. From this, we prove a similar result when an approximate scaling is obtained. We then focus on the optimization problems inherent to the scalable frames by first showing that there is an equivalence between scaling a frame and optimization problems with a non-restrictive objective function. Various objective functions are considered, and an analysis of the solution type is presented. For linear objectives, we can encourage sparse scalings, and with barrier objective functions, we force dense solutions. We further consider frames in high dimensions, and derive various solution techniques. From here, we restrict ourselves to various frame classes, to add more specificity to the results. Using frames generated from distributions allows for the placement of probabilistic bounds on scalability. For discrete distributions (Bernoulli and Rademacher), we bound the probability of encountering an ONB, and for continuous symmetric distributions (Uniform and Gaussian), we show that symmetry is retained in the transformed domain. We also prove several hyperplane-separation results. With the theory developed, we discuss graph applications of the scalability framework. We make a connection with graph conditioning, and show the in-feasibility of the problem in the general case. After a modification, we show that any complete graph can be conditioned. We then present a modification of standard PCA (robust PCA) developed by Cand\`es, and give some background into Electron Energy-Loss Spectroscopy (EELS). We design a novel scheme for the processing of EELS through robust PCA and least-squares regression, and test this scheme on biological samples. Finally, we take the idea of robust PCA and apply the technique of kernel PCA to perform robust manifold learning. We derive the problem and present an algorithm for its solution. There is also discussion of the differences with RPCA that make theoretical guarantees difficult.