Stochastic majorization--minimization algorithms for data science. The changing nature of acquisition and storage data has made the process of drawing inference infeasible with traditional statistical and machine learning methods. Modern data are often acquired in real time, in an incremental nature, and are often available in too large a volume to process on conventional machinery. The project proposes to study the family of stochastic majorisation-minimisation algorithms for computation of inf ....Stochastic majorization--minimization algorithms for data science. The changing nature of acquisition and storage data has made the process of drawing inference infeasible with traditional statistical and machine learning methods. Modern data are often acquired in real time, in an incremental nature, and are often available in too large a volume to process on conventional machinery. The project proposes to study the family of stochastic majorisation-minimisation algorithms for computation of inferential quantities in an incremental manner. The proposed stochastic algorithms encompass and extend upon a wide variety of current algorithmic frameworks for fitting statistical and machine learning models, and can be used to produce feasible and practical algorithms for complex models, both current and future.
Read moreRead less
Large scale nonsmooth, nonconvex optimisation. This project aims to develop, analyse, test and apply (sub) gradient-based methods for solving large scale nonsmooth, nonconvex optimisation problems. Large scale problems with complex nonconvex objective and/or constraint functions are among the most difficult in optimisation. This project will generate new knowledge in numerical optimisation and machine learning. The use of structures and sparsity of large scale problems will lead to the developme ....Large scale nonsmooth, nonconvex optimisation. This project aims to develop, analyse, test and apply (sub) gradient-based methods for solving large scale nonsmooth, nonconvex optimisation problems. Large scale problems with complex nonconvex objective and/or constraint functions are among the most difficult in optimisation. This project will generate new knowledge in numerical optimisation and machine learning. The use of structures and sparsity of large scale problems will lead to the development of better models, and more accurate and robust methods. The expected outcomes of the project are ready-to-implement and apply numerical methods for solving large-scale, nonsmooth, nonconvex optimisation problems, as well as problems in machine learning and regression analysis.Read moreRead less
Exploring and exploiting structures in nonsmooth and global optimization problems. Global and non-smooth optimisation problems are among the most challenging in optimisation. Such problems arise in optimisation of many systems including financial, business and engineering systems. Achieving optimal performance of these systems will provide considerable commercial and environmental benefits. This project aims to develop new approaches to global and non-smooth optimisation using their special stru ....Exploring and exploiting structures in nonsmooth and global optimization problems. Global and non-smooth optimisation problems are among the most challenging in optimisation. Such problems arise in optimisation of many systems including financial, business and engineering systems. Achieving optimal performance of these systems will provide considerable commercial and environmental benefits. This project aims to develop new approaches to global and non-smooth optimisation using their special structures. The outcomes of this project will be new approaches to practical problems and ready-to-implement algorithms. It will major benefit to Australian society whilst also facilitating excellent international collaboration.Read moreRead less
Optimal Deployment of Wireless Sensor Networks. Wireless sensor networks consist of coordinated sensing devices that offer us new ways to understand and interact with the physical world. Australia is a leading player in developing such networks. For a given technology, the key to both optimising the quality of area monitoring and minimising the cost of a sensor network lies in deciding how best to deploy the sensors. We aim to develop powerful new methods to get the best performance from a plann ....Optimal Deployment of Wireless Sensor Networks. Wireless sensor networks consist of coordinated sensing devices that offer us new ways to understand and interact with the physical world. Australia is a leading player in developing such networks. For a given technology, the key to both optimising the quality of area monitoring and minimising the cost of a sensor network lies in deciding how best to deploy the sensors. We aim to develop powerful new methods to get the best performance from a planned sensor network. This will enhance Australia's research role in this area and directly benefit applications such as national security and environmental monitoring.
Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE200100063
Funder
Australian Research Council
Funding Amount
$394,398.00
Summary
Nonmonotone Algorithms in Operator Splitting, Optimisation and Data Science. This project aims to develop the mathematical foundations for the analysis and development of optimisation algorithms used in data science. Despite their now ubiquitous use, machine learning software packages routinely rely on a number of algorithms from mathematical optimisation which are not properly understood. By moving beyond the traditional realms of Fejér monotone algorithms, this project expects to develop the m ....Nonmonotone Algorithms in Operator Splitting, Optimisation and Data Science. This project aims to develop the mathematical foundations for the analysis and development of optimisation algorithms used in data science. Despite their now ubiquitous use, machine learning software packages routinely rely on a number of algorithms from mathematical optimisation which are not properly understood. By moving beyond the traditional realms of Fejér monotone algorithms, this project expects to develop the mathematical theory required to rigorously justify the use of such algorithms and thereby ensure the integrity of the decision tools they produce. This mathematical framework is also expected to produce new algorithms for optimisation which benefit consumers of data science such as the health-care and cybersecurity sectors.Read moreRead less
Decomposition and Duality: New Approaches to Integer and Stochastic Integer Programming. Because of their rich modelling capabilities, integer programs are widely used in industry for decision making and planning. However their solution algorithms do not have the maturity of their cousins in convex optimisation, where the theory of strong duality is ubiquitous. Efficient methods for convex optimisation under uncertainty do not apply to the integer case, which is highly non-convex. Furthermore, i ....Decomposition and Duality: New Approaches to Integer and Stochastic Integer Programming. Because of their rich modelling capabilities, integer programs are widely used in industry for decision making and planning. However their solution algorithms do not have the maturity of their cousins in convex optimisation, where the theory of strong duality is ubiquitous. Efficient methods for convex optimisation under uncertainty do not apply to the integer case, which is highly non-convex. Furthermore, integer models usually assume the data is known with certainty, which is often not the case in the real world. This project will develop new theory and algorithms to enhance the analysis of integer models, including those that incorporating uncertainty, while also enabling the use of parallel computing paradigms. Read moreRead less
Novel decomposition methods for large scale optimisation. This project will develop more effective problem decomposition methods that are critical for handling large scale problems (problems with up to several thousands of variables). The project will benefit practitioners from many different fields, and will put Australia at the very forefront of international research for large scale optimization.
Unlocking the potential for linear and discrete optimisation in knot theory and computational topology. Computational topology is a young, energetic field that uses computers to solve complex geometric problems, such as whether a loop of string is tangled. Such computations are becoming increasingly important in mathematics, and applications span biology, physics and information sciences, however many core problems in the field remain intractable for all but the simplest cases. This project unit ....Unlocking the potential for linear and discrete optimisation in knot theory and computational topology. Computational topology is a young, energetic field that uses computers to solve complex geometric problems, such as whether a loop of string is tangled. Such computations are becoming increasingly important in mathematics, and applications span biology, physics and information sciences, however many core problems in the field remain intractable for all but the simplest cases. This project unites geometric techniques with powerful methods from operations research, such as linear and discrete optimisation, to build fast, powerful tools that can for the first time systematically solve large topological problems. Theoretically, this project has significant impact on the famous open problem of detecting knottedness in fast polynomial time.Read moreRead less
Beyond black-box models: interaction in eXplainable Artificial Intelligence. This project addresses a key issue in automated decision making: explaining how a decision was reached by a computer system to its users. Its aim is to progress towards a new generation of explainable decision models, which would match the performance of current black-box systems while at the same time allow for transparency and detailed interpretation of the underlying logic. This project expects to generate new knowl ....Beyond black-box models: interaction in eXplainable Artificial Intelligence. This project addresses a key issue in automated decision making: explaining how a decision was reached by a computer system to its users. Its aim is to progress towards a new generation of explainable decision models, which would match the performance of current black-box systems while at the same time allow for transparency and detailed interpretation of the underlying logic. This project expects to generate new knowledge in modelling interdependencies of decision criteria using recent advances in the theory of capacities. The expected outcomes are sophisticated but tractable models in which mutual dependencies of decision rules and criteria are treated explicitly and can be thoroughly evaluated. Read moreRead less