Day: June 24, 2020

UNSW Seminar: Tiangang Cui (Monash)

Title: Tensorised Rosenblatt Transport for High-Dimensional Stochastic Computation

Speaker: Tiangang Cui (Monash University)

Date: Tue, 07/07/2020 – 11:05am

Venue: Zoom meeting (connection details here)

Abstract: 

Characterising intractable high-dimensional random variables is one of the fundamental challenges in stochastic computation. It has broad applications in statistical physics, machine learning, uncertainty quantification, econometrics, and beyond. The recent surge of transport maps offers a mathematical foundation and new insights for tackling this challenge.

In this talk, we present a functional tensor-train (FTT) based monotonicity-preserving construction of inverse Rosenblatt transport in high dimensions. It characterises intractable random variables via couplings with tractable reference random variables. By integrating our FTT-based approach into a nested approximation framework inspired by deep neural networks, we are able to significantly expand its capability to random variables with complicated nonlinear interactions and concentrated density functions. We demonstrate the efficacy of the FTT-based inverse Rosenblatt transport on a range of applications in statistical learning and uncertainty quantification, including parameter estimation for dynamical systems, PDE-constrained inverse problems, and Bayesian filtering.

This is joint work with Dr. Sergey Dolgov (Bath) and Mr. Yiran Zhao (Monash)

Seminars, Uncategorized

VA & Opt Webinar: Hoa Bui (Curtin University)

Title: Zero Duality Gap Conditions via Abstract Convexity.

Speaker: Hoa Bui (Curtin University)

Date and Time: July 8th, 2020, 17:00 AEST (Register here for remote connection via Zoom)

Abstract: Using tools provided by the theory of abstract convexity, we extend conditions for zero duality gap to the context of nonconvex and nonsmooth optimization. Substituting the classical setting, an abstract convex function is the upper envelope of a subset of a family of abstract affine functions (being conventional vertical translations of the abstract linear functions). We establish new characterizations of the zero duality gap under no assumptions on the topology on the space of abstract linear functions. Endowing the latter space with the topology of pointwise convergence, we extend several fundamental facts of the conventional convex analysis. In particular, we prove that the zero duality gap property can be stated in terms of an inclusion involving 𝜀-subdifferentials, which are shown to possess a sum rule. These conditions are new even in conventional convex cases. The Banach-Alaoglu-Bourbaki theorem is extended to the space of abstract linear functions. The latter result extends a fact recently established by Borwein, Burachik and Yao in the conventional convex case.

This talk is based on a joint work with Regina Burachik, Alex Kruger and David Yost.

Seminars