Associate Professor Dale Roberts

Ph.D. in Mathematics (UNSW, 2012), B.Sc. 1st Class Honours in Mathematics (UTS, 2006)
Statistics (RSFAS)
College of Business& Economics
T: +61 2 612 57336

Research interests

My research interests are in high-dimensional probability theory and stochastic processes, algorithms, and their application to very large scale data science problems (i.e., Petabyte or greater sized data).

I currently teach the following two courses each year that I sprinkle with my own interests and examples:

(1) A research-led course that looks at the application of random matrix theory in high-dimensional statistics and machine learning. Particular focus is on understanding how classic approaches break down when the dimensionality of the data becomes large and how these problems may be resolved using recent mathematical results; see [STAT3017 / STAT7017].

(2) A postgraduate-level course on stochastic processes: Markov chains, Brownian motion, their properties and applications; see [STAT7004].

I also love programming, building my own research tools, and routinely release them on GitHub for others to use (see my profile). Many of my public projects are highly starred by the international community, my ranking is here.

Biography

Dale graduated from the University of Technology, Sydney (UTS) with a first class Honours in Mathematics in 2006. After his honours, Dale spent some time working in the finance industry. In 2012, he completed his Ph.D. in Mathematics at the University of New South Wales on the topic of Stochastic Partial Differential Equations (SPDE). On completion of his PhD, Dale joined ANU jointly appointed in RSFAS and the Mathematical Sciences Institute (MSI). At the start of 2014, Dale left the MSI (Mathematics) and moved full-time to CBE/RSFAS (Statistics).

Dale has published extensively since 2012 with more than 20 of his papers published in top-tiered journals (A* and A ranked). He has secured more than $2,900,000 in research funding through numerous competitive grants and external funded projects mostly as sole chief investigator.

Researcher's projects

For students seeking Honours or PhD supervision, some keywords to describe my mathematical interests are: stochastic differential equations, stochastic partial differential equations, partial differential equations, Lévy processes, Brownian motion, stochastic processes, random fields, random matrices, high-dimensional probability, random graphs, network theory, dynamics on graphs, high-dimensional statistics, multivariate statistics, statistical learning, machine learning, numerical analysis, numerical methods.

I also like taking these mathematical concepts and using them to solve real-world problems.

Past student projects

The following students have successfully completed theses under my supervision:
  1. Emma Ai. PhD in Statistics
  2. Timothy McLennan-Smith. PhD in Statistics
  3. Wayne Wang. Honours in Statistics
  4. Rui Cheng. First class Honours in Statistics
  5. Michael Winjen. First class Honours in Statistics
  6. Remy Hamilton-Smith. Statistical Learning applied to Burnscar Classification and Natural Hazard Insurance. First class Honours in Actuarial Studies.
  7. Omar Al-Ghattas. Stochastic Portfolio Theory and Information-theoretical Portfolio Tracking. First class Honours in Statistics.
  8. Chaturi Bhaskaran. Overshoots of random walks and Lévy processes. First class Honours in Mathematics.
  9. Nam Ho. Batch and sequential learning with complexity measures. First class Honours in Mathematics.
  10. Emma Ai. Multiwindowed barrier options under stochastic volatility. M.Phil. in Mathematics.
  11. Yang Liu. Existence and uniqueness of solutions to ODEs and SDEs with irregular coefficients. First class Honours in Mathematics.
  12. Anjisht Gosain. Pricing of Himalaya options under the Heston stochastic volatility model. First class Honours in Finance.
  13. Lindon Roberts. Wavelet methods for variational inequalities. First class Honours in Mathematics & University medal.

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Updated:  09 December 2021 / Responsible Officer:  Director (Research Services Division) / Page Contact:  Researchers