Statistics Across Campuses

   Far and Close: Selective Sample Enrichment to Deal with Multicollinearity in Geographically Weighted Regression Date :  Friday, 30 July 2021 Time:   12-1pm Speaker:  Dr P atricia Menendez  ( Department of Econometrics and Business Statistics at Monash University ) Abstract: Geographically weighted regression (GWR) is a popular technique to deal with spatially varying relationships between a response variable and a set of predictors. However, GWR estimates might be affected by multicollinearity issues related to locally poor designs. In this study, we propose two regularization methods to deal with those issues. The first one is based on a generalized ridge regression, which can also be seen as an empirical Bayes method. We show that it can be implemented using ordinary GWR software with an appropriate choice of the weights. The second one augments the local sample using an enrichment strategy. The methods will be illustrated with simulations and with an ...

   Robust post-selection inference of high-dimensional mean regression with heavy-tailed asymmetric errors Date :  Wednesday, 28 July 2021 Time:   3-4 pm Speaker:  Associate Professor Yuanyuan LIN  (Chinese University of Hong Kong) Abstract: We propose a robust post-selection inference method based on the Huber loss for the regression coefficients, when the error distribution is heavy-tailed and asymmetric in a high-dimensional linear model with an intercept term. The asymptotic properties of the resulting estimators are established under mild conditions. We also extend the proposed method to accommodate heteroscedasticity assuming the error terms are symmetric and other suitable conditions. Statistical tests for low-dimensional parameters or individual coefficient in the high-dimensional linear model are also studied. Simulation studies demonstrate desirable properties of the proposed method. An application to a genomic dataset about riboflavin production ...

Semi-Supervised Learning of a Classifier from a Statistical Perspective Date: 23 July 2021, Friday Time: 4pm AEDT Speaker: Prof Geoffrey McLachlan (University fo Queensland) Abstract: With the considerable interest on machine learning these days, there is increasing attention being given to a semi-supervised learning (SSL) approach to constructing a classifier. From a statistical perspective, it goes back over 50 years (McLachlan, 1975, JASA). As is well known, the (Fisher) information in an unclassified feature with unknown class label is less (considerably less for weakly separated classes) than that of a classified feature which has known class label. Hence in the case where the absence of class labels does not depend on the data, the expected error rate of a classifier formed from the classified and unclassified features in a partially classified sample can be relatively much greater than that if the sample were completely classified (Ganesalingam and McLa...

Quantum Natural Gradient for Variational Bayes Date: 25 June 2021, Friday Time: 11:00am - 12:00pm AEDT Speaker: Anna Lopatnikova (University of Sydney) Abstract: In this talk, we start by providing a general introduction to quantum computing.   We then focus on Variational Bayes (VB) -- a critical method in machine learning and statistics, underpinning the recent success of Bayesian deep learning.  Even though VB is efficient and scalable relative to alternative methods, it remains too computationally intensive for many practical applications, particularly in high-dimensional settings.   We propose a quantum-classical algorithm to speed up VB through efficient computation of natural gradient – one of the most promising speedup methods, but too computationally intensive in high-dimensions.   To achieve quantum speedup, we proceed in two steps:  First, we reformulate the problem of natural gradient estimation for VB into a linear problem. ...

Spatial Confounding and Restricted Spatial Regression Methods Date: 18 June 2021, Friday Time: 10am AEDT Speaker: Prof Catherine Calder (University of Texas at Austin) Abstract: Over the last fifteen years, spatial confounding has emerged as a significant source of concern when interpretable inferences on regression coefficients is a primary goal in a spatial regression analysis. Numerous approaches to alleviate spatial confounding have been proposed in the literature, many of which have close connections to dimension reduction techniques used for facilitating faster model fitting. In this presentation, I discuss the issue of spatial confounding in the context of the spatial generalized mixed model for areal data. In particular, I show how many of the techniques for dealing with spatial confounding in this setting can be viewed as a special case of what we refer to as restricted spatial regression (RSR) models. Theoretical characterizations of the posterior distribution of regress...

Variational Bayes on Manifolds Date: 17 June 2021, Thursday Time: 12pm AEDT Contact the organizer: Andriy Olenko a.olenko@latrobe.edu.au Speaker: A/Prof Minh-Ngoc Tran (University of Sydney) Abstract: Variational Bayes (VB) has become a widely-used tool for Bayesian inference in statistics and machine learning. Nonetheless, the development of the existing VB algorithms is so far generally restricted to the case where the variational parameter space is Euclidean, which hinders the potential broad application of VB methods. This paper extends the scope of VB to the case where the variational parameter space is a Riemannian manifold. We develop an efficient manifold-based VB algorithm that exploits both the geometric structure of the constraint parameter space and the information geometry of the manifold of VB approximating probability distributions. Our algorithm is provably convergent and achieves a decent convergence rate. We develop in particular several manifold VB algorithms includi...

  On hyperparameter tuning in general clustering problems Date :  Thursday, 10 June 2021 Time:   10 -11 am Speaker:  Dr Rachel (Ying) Wang  (The University of Sydney) Abstract: Selecting hyperparameters for unsupervised learning problems is challenging in general due to the lack of ground truth for validation. Despite the prevalence of this issue in statistics and machine learning, especially in clustering problems, there are not many methods for tuning these hyperparameters with theoretical guarantees. In this paper, we provide a framework with provable guarantees for selecting hyperparameters in a number of distinct models. We consider both the subgaussian mixture model and network models to serve as examples of iid and non-iid data. We demonstrate that the same framework can be used to choose the Lagrange multipliers of penalty terms in semi-definite programming (SDP) relaxations for community detection, and the bandwidth parameter for constructing kernel sim...

Weak differentiability applied to the profile likelihood estimation in a joint model of longitudinal and survival data. Date :  Thursday, 3 June 2021 Time:   10 -11 am Speaker:  Dr Yuichi Hirose  ( Victoria University of Wellington) . Abstract: There is a difficulty in finding an estimate of variance of the profile likelihood estimator in the joint model of longitudinal and survival data.  We solve the difficulty by applying the weak differentiation to the implicit function in the profile likelihood estimation.  The derivative is used to show the asymptotic normality of the profile likelihood estimator without assuming the second derivative of the profile likelihood exists. Zoom Link:  Please contact Yanrong Yang ( yanrong.yang@anu.edu.au ) to obtain the zoom link for this seminar.

On bivariate extreme value copulas with polynomial dependence functions. Date:  Friday, 4 June 2021 Time:   3-4pm Speaker :  Associate Professor Berwin Turlach (University of Western Australia) Abstract:  We discuss how the mixed model and the asymmetric mixed model family of bivariate extreme value can be extended to bivariate extreme value copulas with polynomial dependence function of arbitrary degree. An algorithm for fitting extreme value copulas with polynomial dependence functions to data will be presented and various practical issues that arise when fitting bivariate extreme value copula models will be discussed. Zoom Link:   https://macquarie.zoom.us/j/86987542903?pwd=SUVsVXpsbVVPckFaL0wwUTlJeFJ6dz09 Bio:  Berwin Turlach is an Associate Professor at the University of Western Australia, having previously worked at the Australian National University, the University of Adelaide, and the National University of Singapore.  He received a degree...

Max-Infinitely Divisible Models and Inference for Spatial Extremes, with Application to Non-Stationary Heatwave Hazard Assessment Date: 07 June 2021, Monday Time: 4pm AEDT Speaker: Dr Raphaël Huser (King Abdullah University of Science and Technology) Abstract: The modeling of spatio-temporal trends in temperature extremes can help better understand the structure and frequency of heatwaves in a changing climate. Here, we study annual temperature maxima over Southern Europe using a century-spanning dataset observed at 44 monitoring stations. Extending the spectral representation of max-stable processes, our modeling framework relies on a novel construction of max-infinitely divisible processes, which include covariates to capture spatio-temporal non-stationarities. Our new model keeps a popular max-stable process on the boundary of the parameter space, while flexibly capturing weakening extremal dependence at increasing quantile levels and asymptotic independence. This is achieved by li...