Generative Modeling Explained

Score-Based Generative Modeling through Stochastic Differential Equations

ICLR'21, 2021. [All Versions]

Latent Space Factorisation and Manipulation via Matrix Subspace Projection

ICML'20, 2020. [All Versions]

Parameter Expansion for Data Augmentation

Journal of the American Statistical Association, 1999. [All Versions]. [Preprint]. Viewing the observed data of a statistical model as incomplete and augmenting its missing parts are useful for clarifying concepts and central to the invention of two well-known statistical algorithms: expectation-maximization (EM) and data augmentation. Recently, the authors demonstrated that expanding the parameter space along with augmenting the missing data is useful for accelerating iterative computation in an EM algorithm. The main purpose of this article is to rigorously define a parameter expanded data augmentation (PX-DA) algorithm and to study its theoretical properties. The PX-DA is a special way of using auxiliary variables to accelerate Gibbs sampling algorithms and is closely related to reparameterization techniques

Filters, random fields and maximum entropy (FRAME): Towards a unified theory for texture modeling

International Journal of Computer Vision, 1998. [All Versions]. [Preprint]. This article presents a statistical theory for texture modeling. This theory combines filtering theory and Markov random field modeling through the maximum entropy principle, and interprets and clarifies many previous concepts and methods for texture analysis and synthesis from a unified point of view. The theory characterizes the ensemble of images I with the same texture appearance by a probability distribution f(I) on a random field, and the objective of texture modeling is to make inference about f(I), given a set of observed texture examples