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Upcoming Colloquiums

Title: Topological Data Analysis
15:10 Fri 31 August, 2018 :: Napier 208 :: Dr Vanessa Robins :: Australian National University
Abstract:
Topological Data Analysis has grown out of work focussed on deriving qualitative and yet quantifiable information about the shape of data. The underlying assumption is that knowledge of shape – the way the data are distributed – permits high-level reasoning and modelling of the processes that created this data. The 0-th order aspect of shape is the number pieces: “connected components” to a topologist; “clustering” to a statistician. Higher-order topological aspects of shape are holes, quantified as “non-bounding cycles” in homology theory.  These signal the existence of some type of constraint on the data-generating process.
Homology lends itself naturally to computer implementation, but its naive application is not robust to noise. This inspired the development of persistent homology: an algebraic topological tool that measures changes in the topology of a growing sequence of spaces (a filtration). Persistent homology provides invariants called the barcodes or persistence diagrams that are sets of intervals recording the birth and death parameter values of each homology class in the filtration.  It captures information about the shape of data over a range of length scales, and enables the identification of “noisy” topological structure.
Statistical analysis of persistent homology has been challenging because the raw information (the persistence diagrams) are provided as sets of intervals rather than functions. Various approaches to converting persistence diagrams to functional forms have been developed recently, and have found application to data ranging from the distribution of galaxies, to porous materials, and cancer detection.

Title: Mathematical modelling of the emergence and spread of antimalarial drug resistance
15:10 Fri 14 Sep, 2018 :: Napier 208 :: Dr Jennifer Flegg :: University of Melbourne
Abstract:
Malaria parasites have repeatedly evolved resistance to antimalarial drugs, thwarting efforts to eliminate the disease and contributing to an increase in mortality. In this talk, I will introduce several statistical and mathematical models for monitoring the emergence and spread of antimalarial drug resistance. For example, results will be presented from Bayesian geostatistical models that have quantified the space-time trends in drug resistance in Africa and Southeast Asia. I will discuss how the results of these models have been used to update public health policy.

Title: TBA
15:10 Fri 5 October, 2018 :: Napier 208 :: A/Prof Scott Morrison :: Australian National University

Title: TBA
15:10 Fri 12 October, 2018 :: Napier 208 :: A/Prof Kais Hamza :: Monash University

Title: TBA
15:10 Fri 26 October, 2018 :: Napier 208 :: A/Prof Chris Drovandi :: Queensland University of Technology

Recent Colloquiums

Title: Tales of Multiple Regression: Informative missingness, Recommender Systems, and R2-D2
15:10 Fri 17 August, 2018: Napier 208: Prof Howard Bondell: University of Melbourne
Abstract:
In this talk, we briefly discuss two projects tangentially related under the umbrella of high-dimensional regression. The first part of the talk investigates informative missingness in the framework of recommender systems. In this setting, we envision a potential rating for every object-user pair. The goal of a recommender system is to predict the unobserved ratings in order to recommend an object that the user is likely to rate highly. A typically overlooked piece is that the combinations are not missing at random. For example, in movie ratings, a relationship between the user ratings and their viewing history is expected, as human nature dictates the user would seek out movies that they anticipate enjoying. We model this informative missingness, and place the recommender system in a shared-variable regression framework which can aid in prediction quality. The second part of the talk deals with a new class of prior distributions for shrinkage regularization in sparse linear regression, particularly the high dimensional case. Instead of placing a prior on the coefficients themselves, we place a prior on the regression R-squared. This is then distributed to the coefficients by decomposing it via a Dirichlet Distribution. We call the new prior R2-D2 in light of its R-Squared Dirichlet Decomposition. Compared to existing shrinkage priors, we show that the R2-D2 prior can simultaneously achieve both high prior concentration at zero, as well as heavier tails. These two properties combine to provide a higher degree of shrinkage on the irrelevant coefficients, along with less bias in estimation of the larger signals.