Interpretable statistics for complex modelling: quantile and topological learning

As the complexity of our data increased exponentially in the last decades, so has our need for interpretable features. This thesis revolves around two paradigms to approach this quest for insights. In the first part we focus on parametric models, where the problem of interpretability can be seen as a “parametrization selection”. We introduce a quantile-centric parametrization and we show the advantages of our proposal in the context of regression, where it allows to bridge the gap between classical generalized linear (mixed) models and increasingly popular quantile methods. The second part of the thesis, concerned with topological learning, tackles the problem from a non-parametric perspective. As topology can be thought of as a way of characterizing data in terms of their connectivity structure, it allows to represent complex and possibly high dimensional through few features, such as the number of connected components, loops and voids. We illustrate how the emerging branch of statistics devoted to recovering topological structures in the data, Topological Data Analysis, can be exploited both for exploratory and inferential purposes with a special emphasis on kernels that preserve the topological information in the data. Finally, we show with an application how these two approaches can borrow strength from one another in the identification and description of brain activity through fMRI data from the ABIDE project

Development of a client interface for a methodology independent object-oriented CASE tool : a thesis presented in partial fulfilment of the requirements for the degree of Master of Science in Computer Science at Massey University

The overall aim of the research presented in this thesis is the development of a prototype CASE Tool user interface that supports the use of arbitrary methodology notations for the construction of small-scale diagrams. This research is part of the larger CASE Tool project, MOOT (Massey's Object Oriented Tool). MOOT is a meta-system with a client-server architecture that provides a framework within which the semantics and syntax of methodologies can be described. The CASE Tool user interface is implemented in Java so it is as portable as possible and has a consistent look and feel. It has been designed as a client to the rest of the MOOT system (which acts as a server). A communications protocol has been designed to support the interaction between the CASE Tool client and a MOOT server. The user interface design of MOOT must support all possible graphical notations. No assumptions about the types of notations that a software engineer may use can be made. MOOT therefore provides a specification language called NDL for the definition of a methodology's syntax. Hence, the MOOT CASE Tool client described in this thesis is a shell that is parameterised by NDL specifications. The flexibility provided by such a high level of abstraction presents significant challenges in terms of designing effective human-computer interaction mechanisms for the MOOT user interface. Functional and non-functional requirements of the client user interface have been identified and applied during the construction of the prototype. A notation specification that defines the syntax for Coad and Yourdon OOA/OOD has been written in NDL and used as a test case. The thesis includes the iterative evaluation and extension of NDL resulting from the prototype development. The prototype has shown that the current approach to NDL is efficacious, and that the syntax and semantics of a methodology description can successfully be separated. The developed prototype has shown that it is possible to build a simple, non-intrusive, and efficient, yet flexible, useable, and helpful interface for meta-CASE tools. The development of the CASE Tool client, through its generic, methodology independent design, has provided a pilot with which future ideas may be explored

The Topology ToolKit

This system paper presents the Topology ToolKit (TTK), a software platform designed for topological data analysis in scientific visualization. TTK provides a unified, generic, efficient, and robust implementation of key algorithms for the topological analysis of scalar data, including: critical points, integral lines, persistence diagrams, persistence curves, merge trees, contour trees, Morse-Smale complexes, fiber surfaces, continuous scatterplots, Jacobi sets, Reeb spaces, and more. TTK is easily accessible to end users due to a tight integration with ParaView. It is also easily accessible to developers through a variety of bindings (Python, VTK/C++) for fast prototyping or through direct, dependence-free, C++, to ease integration into pre-existing complex systems. While developing TTK, we faced several algorithmic and software engineering challenges, which we document in this paper. In particular, we present an algorithm for the construction of a discrete gradient that complies to the critical points extracted in the piecewise-linear setting. This algorithm guarantees a combinatorial consistency across the topological abstractions supported by TTK, and importantly, a unified implementation of topological data simplification for multi-scale exploration and analysis. We also present a cached triangulation data structure, that supports time efficient and generic traversals, which self-adjusts its memory usage on demand for input simplicial meshes and which implicitly emulates a triangulation for regular grids with no memory overhead. Finally, we describe an original software architecture, which guarantees memory efficient and direct accesses to TTK features, while still allowing for researchers powerful and easy bindings and extensions. TTK is open source (BSD license) and its code, online documentation and video tutorials are available on TTK's website

Security Requirements Specification and Tracing within Topological Functioning Model

Specification and traceability of security requirements is still a challenge since modeling and analysis of security aspects of systems require additional efforts at the very beginning of software development. The topological functioning model is a formal mathematical model that can be used as a reference model for functional and non-functional requirements of the system. It can also serve as a reference model for security requirements. The purpose of this study is to determine the approach to how security requirements can be specified and traced using the topological functioning model. This article demonstrates the suggested approach and explains its potential benefits and limitations

Tuning the Performance of a Computational Persistent Homology Package

In recent years, persistent homology has become an attractive method for data analysis. It captures topological features, such as connected components, holes, and voids from point cloud data and summarizes the way in which these features appear and disappear in a filtration sequence. In this project, we focus on improving the performanceof Eirene, a computational package for persistent homology. Eirene is a 5000-line open-source software library implemented in the dynamic programming language Julia. We use the Julia profiling tools to identify performance bottlenecks and develop novel methods to manage them, including the parallelization of some time-consuming functions on multicore/manycore hardware. Empirical results show that performance can be greatly improved

Prototype system for supporting the incremental modelling of vague geometric configurations

In this paper the need for Intelligent Computer Aided Design (Int.CAD) to jointly support design and learning assistance is introduced. The paper focuses on presenting and exploring the possibility of realizing learning assistance in Int.CAD by introducing a new concept called Shared Learning. Shared Learning is proposed to empower CAD tools with more useful learning capabilities than that currently available and thereby provide a stronger interaction of learning between a designer and a computer. Controlled computational learning is proposed as a means whereby the Shared Learning concept can be realized. The viability of this new concept is explored by using a system called PERSPECT. PERSPECT is a preliminary numerical design tool aimed at supporting the effective utilization of numerical experiential knowledge in design. After a detailed discussion of PERSPECT's numerical design support, the paper presents the results of an evaluation that focuses on PERSPECT's implementation of controlled computational learning and ability to support a designer's need to learn. The paper then discusses PERSPECT's potential as a tool for supporting the Shared Learning concept by explaining how a designer and PERSPECT can jointly learn. There is still much work to be done before the full potential of Shared Learning can be realized. However, the authors do believe that the concept of Shared Learning may hold the key to truly empowering learning in Int.CAD