Statistics Across Campuses

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...

    Most Powerful Test against High Dimensional Local Alternatives Date :  Thursday, 27 May 2021 Time:   3 - 4 pm AEDT Canberra Speaker:  Dr Yi He (University of Amsterdam) Abstract: We develop a powerful quadratic test for the overall significance of many covariates in a dense regression model in the presence of nuisance parameters. By equally weighting the sample moments, the test is asymptotically correct in high dimensions even when the number of coefficients is larger than the sample size. Our theory allows a non-parametric error distribution and weakly exogenous nuisance variables, in particular autoregressors in many applications. Using random matrix theory, we show that the test has the optimal asymptotic testing power among a large class of competitors against local alternatives whose coordinates are dense in the eigenbasis of the high dimensional sample covariance matrix among regressors.  The asymptotic results are adaptive to the covariates’ cro...

Monte Carlo variance reduction using Stein operators  Date :  Friday, 21 May 2021 Time:  2 -3 pm Speaker:   Dr. Leah South ( Queensland University of Technology ) Abstract: This talk will focus on two new methods for estimating posterior expectations when the derivatives of the log posterior are available. The proposed methods are in a class of estimators that use Stein operators to generate control variates or control functionals. The first method applies regularisation to improve the performance of popular Stein-based control variates for high-dimensional Monte Carlo integration. The second method, referred to as semi-exact control functionals (SECF), is based on control functionals and Sard’s approach to numerical integration. The use of Sard’s approach ensures that our control functionals are exact on all polynomials up to a fixed degree in the Bernstein-von-Mises limit. Several Bayesian inference examples will be used to illustrate the potential for reduction in...

     Functional limit theorems for financial markets with long-range dependence Date :  Friday, 21 May 2021 Time:   4-5 pm Speaker:   Professor  Yuliya Mishura (Kyiv National University, Ukraine) Abstract: We start with an additive stochastic sequence that is based on the sequence of independent identically distributed (iid) random variables and has the coefficients that allow for dependency on the past. Then we formulate the conditions of the weak convergence to some limit process in terms of coefficients and characteristic function of  any  basic  random variable. We adapt the general conditions to the case where the limit process is Gaussian. Then we move onto the multiplicative scheme in order to get a positive limit process (with the probability 1) that can be used for modelling of some asset prices from financial markets. Hence, we assume that all multipliers in the prelimit multiplicative scheme are p...