Research

Current Research

Generalized Gaussian Process Models for Computer Vision [Under Supervision of Prof. A. B. Chan]

Brief Introduction

A generalized Gaussian process model (GGPM) is a unifying framework that encompasses many existing Gaussian process (GP) models, such as GP regression, classification, and counting. In the GGPM framework, the observation likelihood of the GP model is itself parameterized using the exponential family distribution (EFD). In this paper, we consider efficient algorithms for approximate inference on GGPMs using the general form of the EFD. A particular GP model and its associated inference algorithms can then be formed by changing the parameters of the EFD, thus greatly simplifying its creation for task-specific output domains. We demonstrate the efficacy of this framework by creating several new GP models for regressing to non-negative reals and to real intervals. We also propose a closed-form Taylor approximation for efficient inference on GGPMs, and elaborate on its connections with other model-specific closed-form approximations. Finally, we present a comprehensive set of experiments to compare approximate inference algorithms on a wide variety of GGPM.

Encompasses many existing models

*The hash symbol represents some new models developed by us

Regression Example

Tokyo Rainfall dataset

The dataset records the number of occurrences of rainfall in Tokyo for every calendar day in 1983 and 1984.

The following figure shows two interpretations of binomial-GGPM

Sample code

% Matlab Code

models{1}.inffunc = @infTaylor; % inference methods

models{1}.likfunc = @likExGamma; % likelihood functions

hypinit.cov = zeros(nhyp,1); % initialize kernel function hyper-parameters

hypinit.lik = zeros(nlik,1); % initialize likelihood function hyper-parameters

likFun = (models{mm}.likfunc); % bundle to generic likelihood function

models{mm}.likfunc = @(varargin) likExpo_generic(likFun, varargin{:});

% use scaled conjugate gradient method to optimize hyper-parameters

hyp = minimize(hypinit, @gp, numIter, models{mm}.inffunc, meanfunc, covfunc, models{mm}.likfunc, X', YY(:));

GGPM_Toolbox download