The ANU Mathematical Data Science Centre's main research objective is mathematical innovation relating to data science. To advance the field, we need to develop a sophisticated mathematical machinery that will allow researchers to gain insights and extract information from significant volumes of data. As it happens, the same machinery is important in pure mathematics.

We will explore the links between the theory of Machine Learning and high dimensional geometry. The introduction of the high-dimensional geometric viewpoint to machine learning, pioneered by Professor Shahar Mendelson, has already led to ground-breaking progress on the way theoretical data science is understood today.

Statistical recovery problems are, fundamentally, questions on preservation of structure. Recovery from given data is possible because randomness – even at minimal levels – preserves and exposes structure. Structure preservation is the real reason why recovery algorithms perform well, and key problems in data science may be recast as geometric questions on preservation of structure in high dimension.

Despite the considerable progress made thanks to this geometric viewpoint, what has been discovered so far is just the tip of the iceberg – there is a long way to go before we reach our goal and have a true understanding of statistical recovery.