Feature Learning for High-dimensional Functional Time Series. This project aims to develop new methods and theories for common features on high-dimensional functional time series observed in empirical applications. The significance includes addressing a key gap in adaptive and efficient feature learning, improving forecasting accuracy and understanding forecasting-driven factors comprehensively for empirical data. Expected outcomes involve advances in big data theory and easy-to-implement algori ....Feature Learning for High-dimensional Functional Time Series. This project aims to develop new methods and theories for common features on high-dimensional functional time series observed in empirical applications. The significance includes addressing a key gap in adaptive and efficient feature learning, improving forecasting accuracy and understanding forecasting-driven factors comprehensively for empirical data. Expected outcomes involve advances in big data theory and easy-to-implement algorithms for applied researchers. This project benefits not only advanced manufacturing by finding optimal stopping time for wood panel compression, but also superior forecasting for mortality in demography, climate data in environmental science, asset returns in finance, and electricity consumption in economics. Read moreRead less
Macroeconomic and Financial Modelling in an Era of Extremes. This project aims to develop methods to allow workhorse models in economics and finance to better reflect tail events--low probability extreme events, such as the Global Financial Crisis and the COVID-19 pandemic. It intends to address fundamental technical challenges in the estimation of such models, develop a coherent framework for counterfactual analysis of these models and propose methods to apply these models in a big-data environ ....Macroeconomic and Financial Modelling in an Era of Extremes. This project aims to develop methods to allow workhorse models in economics and finance to better reflect tail events--low probability extreme events, such as the Global Financial Crisis and the COVID-19 pandemic. It intends to address fundamental technical challenges in the estimation of such models, develop a coherent framework for counterfactual analysis of these models and propose methods to apply these models in a big-data environment. Expected outcomes include new insights into the transmission of tail risks in the global economic and financial system. This should provide significant benefits, including guidance to Australian and international policymakers charged with maintaining stability in the face of extreme events.Read moreRead less
Uncertainty, Risk and Related Concepts in Machine Learning. Machine learning is the science of making sense of data. It does not and cannot remove all risk and uncertainty. This project proposes to study the foundations of how machine learning uses, represents and communicates risk and uncertainty. It aims to do so by finding new theoretical connections between diverse notions that have arisen in allied disciplines. These include risk, uncertainty, scoring rules and loss functions, divergences, ....Uncertainty, Risk and Related Concepts in Machine Learning. Machine learning is the science of making sense of data. It does not and cannot remove all risk and uncertainty. This project proposes to study the foundations of how machine learning uses, represents and communicates risk and uncertainty. It aims to do so by finding new theoretical connections between diverse notions that have arisen in allied disciplines. These include risk, uncertainty, scoring rules and loss functions, divergences, statistics and different ways of aggregating information. By building a more complete theoretical map it is expected that new machine learning methods will be developed, but more importantly that machine learning will be able to be better integrated into larger socio-technical systems.Read moreRead less
Reliable and accurate statistical solutions for modern complex data. This project aims to develop novel methods for reliable and accurate statistical modelling with modern, complex correlated and error-prone data. The project expects to make significant strides towards future-proofing statistical data analysis, equipping practitioners with a suite of robust and computationally efficient methods which provide confidence in the stability and reproducibility of results obtained, while offering guar ....Reliable and accurate statistical solutions for modern complex data. This project aims to develop novel methods for reliable and accurate statistical modelling with modern, complex correlated and error-prone data. The project expects to make significant strides towards future-proofing statistical data analysis, equipping practitioners with a suite of robust and computationally efficient methods which provide confidence in the stability and reproducibility of results obtained, while offering guarantees on their transferability over a range of populations. This will provide important benefits as they are applied in predicting endangered marine species for fisheries conservation, and in enhancing our national understanding of the relationship between education achievement and financial success. Read moreRead less
Novel statistical methods for data with non-Euclidean geometric structure. This project aims to develop new flexible regression models and classification algorithms, along with robust and efficient inference methods, applicable to a wide range of non-Euclidean data types which arise in many fields of science, business and technology. There are serious flaws with currently available methods of analysis for non-Euclidean data. This project expects to transform such analyses by providing new quanti ....Novel statistical methods for data with non-Euclidean geometric structure. This project aims to develop new flexible regression models and classification algorithms, along with robust and efficient inference methods, applicable to a wide range of non-Euclidean data types which arise in many fields of science, business and technology. There are serious flaws with currently available methods of analysis for non-Euclidean data. This project expects to transform such analyses by providing new quantitative tools within a unifying framework. The anticipated project outcomes will be of mathematical interest and valuable in applications such as finance (predicting Australian stock returns); modelling electroencephalography data; Australian geochemical data, relating to sediments; and Australian X-ray tumour image data. Read moreRead less
Topics in triangulated categories. This project in pure mathematics, more specifically in modern homological algebra, builds on work started by the chief investigator in the last five years. What has already been done has achieved striking results, solving very different problems that have been open for two decades. And there seem to be many directions in which it could be pursued further.
The international mathematical community seems intrigued by what the chief investigator has achieved recen ....Topics in triangulated categories. This project in pure mathematics, more specifically in modern homological algebra, builds on work started by the chief investigator in the last five years. What has already been done has achieved striking results, solving very different problems that have been open for two decades. And there seem to be many directions in which it could be pursued further.
The international mathematical community seems intrigued by what the chief investigator has achieved recently - judging by invitations to give prestigious talks and the feedback at these events. The expected outcome is major progress in our understanding of derived categories, as well as diverse applications. The benefit will be to enhance the international stature of Australian science.Read moreRead less
Moduli, invariants, and algebraisation. This project is in pure mathematics. It aims to address gaps in our
knowledge in the modern geometries and their associated algebraic structures that arise in classification problems that pervade mathematics and its applications.
This project expects to generate new knowledge in modern algebra and geometry.
Expected outcomes of this project include major progress in our
understanding of invariants of derived categories of algebraic stacks and the
relat ....Moduli, invariants, and algebraisation. This project is in pure mathematics. It aims to address gaps in our
knowledge in the modern geometries and their associated algebraic structures that arise in classification problems that pervade mathematics and its applications.
This project expects to generate new knowledge in modern algebra and geometry.
Expected outcomes of this project include major progress in our
understanding of invariants of derived categories of algebraic stacks and the
relationship between algebraic and other geometries.
The benefit will be to enhance the international stature of Australian science.Read moreRead less
Banking System Competition and the Macro-economy. Australia has one of the most concentrated banking sectors in the world, generating concerns regarding its efficiency. This project aims to develop unified frameworks to understand and evaluate quantitatively how the structure of the banking industry affects the macro-economy and provide policy recommendations for establishing a healthy and efficient banking industry. This project expects to improve understanding of the welfare trade-off between ....Banking System Competition and the Macro-economy. Australia has one of the most concentrated banking sectors in the world, generating concerns regarding its efficiency. This project aims to develop unified frameworks to understand and evaluate quantitatively how the structure of the banking industry affects the macro-economy and provide policy recommendations for establishing a healthy and efficient banking industry. This project expects to improve understanding of the welfare trade-off between bank competition and economic well-being to enable policymakers to better determine the optimal concentration of banking sector in Australia. This will enhance the productivity and international competitiveness of Australia’s financial system and the broader economy.Read moreRead less
Ethics and risk. This project aims to develop a theory of risk. From the extreme to the everyday, from warfare to the drive to work, the modern world is unimaginable without mutual imposition of risk. Philosophers must explain how risks can be justified, or risk irrelevance. This project will use the tools of ethics (the study of right and wrong action) and decision theory (the study of rational decision-making under uncertainty) to develop a comprehensive theory of the ethics of risk. This proj ....Ethics and risk. This project aims to develop a theory of risk. From the extreme to the everyday, from warfare to the drive to work, the modern world is unimaginable without mutual imposition of risk. Philosophers must explain how risks can be justified, or risk irrelevance. This project will use the tools of ethics (the study of right and wrong action) and decision theory (the study of rational decision-making under uncertainty) to develop a comprehensive theory of the ethics of risk. This project is expected to improve understanding of the risks people impose on others as individuals and as a society.Read moreRead less
Stability conditions: their topology and applications. This project aims to answer questions about the topology of the space of stability conditions, which has emerged as a central object in a number of different mathematical areas in the past two decades. The proposed work will have important consequences in representation theory, group theory, and algebraic geometry. The project shows that tools from previously unrelated areas, including discontinous differential equations and discrete dynam ....Stability conditions: their topology and applications. This project aims to answer questions about the topology of the space of stability conditions, which has emerged as a central object in a number of different mathematical areas in the past two decades. The proposed work will have important consequences in representation theory, group theory, and algebraic geometry. The project shows that tools from previously unrelated areas, including discontinous differential equations and discrete dynamical systems, are crucial in the theory of stability conditions. Potential benefits include the resolution of outstanding conjectures in mathematics, the initiation of new connections between different areas of mathematics, and the introduction of machine learning techniques into mathematical research.Read moreRead less