We are happy to announce a seminar by Dr Gery Geenens and Qian Jin. We hope to see you all there.
Any questions, please feel free to contact: secretary.nswbranch@statsoc.org.au.
Date: Wednesday, 17th May 2023
Time:
5:30pm - 6:15pm: Qian Jin
6:15pm - 6:30pm: Break
6:30pm - 7:30pm: Gery Geenens
7:30pm onwards: Dinner (at a nearby restaurant). Please RSVP for dinner to attend.
Venue: Room 4082, Anita B Lawrence Centre (formerly Red Centre), UNSW Australia or via zoom (link to be sent).
RSVP: Please use the register via this page if you are attending in person. Please register here if you would like to attend online and receive zoom link and details.
Title : Towards a universal representation of statistical dependence
Speaker: Dr Gery Geenens
Dependence is undoubtedly a central concept in statistics. Though, it proves difficult to locate in the literature a formal definition of statistical dependence which goes beyond the self-evident 'two variables are dependent if they are not independent' (The Dictionary of Statistical Terms, Kendall and Buckland, 1971, 2006). This ‘non-independence’ interpretation quickly proves inadequate, though. In particular, quantifying dependence appears essential in many situations; yet, if dependence is to be quantifiable, then the above non-independence definition falls short -- and this without any obvious substitute. This absence has allowed the term 'dependence' and its declination to be used vaguely and indiscriminately for qualifying a variety of disparate notions, leading to numerous incongruities. For example, the classical Pearson's, Spearman's or Kendall's correlations are widely regarded as 'dependence measures' of major interest, in spite of returning 0 in some cases of deterministic relationship between the variables at play -- evidently not measuring dependence at all.
Arguing that research on such a fundamental topic would benefit from a slightly more rigid framework, in this work I suggest a general definition of the dependence between two random variables defined on the same probability space. Natural enough for aligning with intuition, that definition is still sufficiently precise for allowing unequivocal identification of a 'universal' representation of the dependence structure of any bivariate distribution, regardless of its nature (discrete, continuous, mixed or hybrid). Links between this representation and familiar concepts will be highlighted. I will also discuss the role of copulas from that perspective, showing that copulas provide a sensible approach for analysing and modelling dependence in a continuous vector but cannot be justified in other situations.
Biography
Dr Geenens attained his PhD from the Louvain Catholic University (UCL, Belgium) in July 2008. He later moved to Australia to take up a post-doctoral research position at the University of Melbourne under the supervision of Professor Peter Hall. In October 2009, I was offered an academic position at UNSW Sydney.
Most of Dr Geenens's research lies in developing nonparametric and semiparametric methods in various contexts. In particular, his is interested in nonparametric regression models (mainly kernel smoothing methods), semiparametric regression models (mainly Single-Index Models), nonparametric copula models for dependence modelling and nonparametric methods for functional data analysis.
Title : Generalized Partial Least Square with Deep Neural Networks
Speaker: Qian Jin
While deep learning has shown exceptional performance in many applications, the model's mathematical understanding, model designing, and model interpretation are still new areas. Combining the two cultures of deep and statistical learning can provide insight into model interpretation and high-dimensional data applications. This work focuses on combing deep learning with generalized partial least square estimation. In particular, Bilodeau et al. (2015) proposed a generalized regression with orthogonal components (GROC) model, which is more flexible than standard partial least square (PLS), because it may involve more complex structure of dependence and the use generalized additive model (GAM) instead of linear regression. We propose a deep-GROC (DGROC) model, which allows for different measures of dependence (through their copula representation) to be used and shows a high prediction accuracy. Hyperparameter selection and transfer learning in training loop in included to boost model performance. The superiority of the proposed method is demonstrated on simulations and real datasets, which show that our method achieves competitive performance compared to GROC, PLS and traditional Neural Networks.
Biography
Qian Jin started her Ph.D. in the School of Mathematics and Statistics at University of New South Wales. She completed my Bachelor's degree in Applied Mathematics from Shanghai University and a Master's Degree in Statistics in Statistics from Australian National University.
Her current research interest is mainly in developing Machine Learning and Deep Learning models. Her talk is going to be about the introduction of Deep Groc model, which is combining the idea of the lightweight deep neural network from the perspective of the generalized Regression on Orthogonal Components (Groc) model. The transformation invariance dependence measurement based on copula is investigated and tried to be involved as a measure of dependence in this work.
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