Projects for Students
I am looking for highly motivated students who are interested in research in any of the following themes. If you are that student, drop me an email.
Project theme 1: Sparse-Constrained Optimization
Many real-world problems—from feature selection to compression of neural networks—can be written as
where C is any (e.g. convex) constraint set and ‖θ‖0 counts the nonzero entries of θ.
Dropping the descrete constrint ‖θ‖0 ≤ k yields a standard optimization problem, but enforcing
it makes the problem combinatorial and aften NP-hard.
Our key idea is to “decouple” the sparsity and non-sparsity constraints and introduce a Boolean relaxation, yielding a continuous problem so that modern solvers can handle efficiently to provide a better and faster sparse solution.
Key skills required: Linear Algebra, Calculus, Convex Analysis, and Coding in Python/R/Julia/C++.
Project theme 2: Importance Sampling Methods for Random Geometric Graphs
A geometric graph is a graph (a set of vertices/nodes connected by edges) where the vertices are embedded in a geometric space (e.g., Euclidean space), and edges are typically defined based on the relative positions of the vertices.
Importance sampling is a variance reduction technique in Monte Carlo methods that improves efficiency by sampling more frequently from regions of higher "importance" (e.g., where the integrand is large or the probability density is concentrated), thereby reducing estimator variance compared to naive random sampling.
Our goal to propose and analyse efficient importance sampling methods for random geometric graphs.
Key skills required: Probability Theory and Coding in Python/R/Julia/C++.
Project theme 3: Machine Learning Prediction of Bluebottle's Presence Along the Australian Coast
Many Australians have had a painful bluebottle sting when swimming at the beach, yet little is known
about the bluebottle, and when they will arrive, and if it will be in large swarms or only a few individuals.
Dr Amandine Schaeffer (UNSW)
and I are looking for a masters/honors student to work on a data driven project to investigate
machine learning techniques to address these challenges. Drop us an email if you are a student and
interested in working on this project. For more details, click here.
Key skills required: Applications of Deep Learning Models and Coding in Python.
Project theme 4: Deep Learning Models for Spatio-temporal Data
Recent advances in remote sensing has resulted in large volumes of data sets easily available.
As a result, assimilating such large dat sets into numerical hydrological models is often a computationally
demanding task.
In this study, Dr Sreekanth Janardhanan (CSIRO)
and I are aiming to study the application of deep learning models
to investigate the relationship between spatio-temporal data sets and hydrological
processes.
Key skills required: Mathematical Understanding of Deep Learning and Coding in Python.