Nonparametric Bayesian Mixed-effects Models for Multi-task Learning.
Abstract: In many
real world problems we are interested in learning multiple tasks while the training set
for each task is quite small. When the different tasks are related, one can learn all
tasks simultaneously and aim to get improved predictive performance by taking advantage
of the common aspects of all tasks. This general idea is known as multi-task learning
and it has been successfully ... read moreinvestigated in several technical settings, with
applications in many areas. In this thesis we explore a Bayesian realization of this
idea especially using Gaussian Processes (GP) where sharing the prior and its parameters
among the tasks can be seen to implement multi-task learning. Our focus is on the
functional mixed-effects model. More specifically, we propose a family of novel
Nonparametric Bayesian models, Grouped mixed-effects GP models, where each individual
task is given by a fixed-effect, taken from one of a set of unknown groups, plus a
random individual effect function that captures variations among individuals. The
proposed models provide a unified algorithmic framework to solve time series prediction,
clustering and classification. We propose the shift-invariant version of Grouped
mixed-effects GP to cope with periodic time series that arise in astrophysics when using
data for periodic variable stars. We develop an efficient EM algorithm to learn the
parameters of the model, and as a special case we obtain the Gaussian mixture model and
EM algorithm for phased-shifted periodic time series. Furthermore, we extend the
proposed model by using a Dirichlet Process prior, thereby leading to an infinite
mixture model. A Variational Bayesian approach is developed for inference in this model,
leading to an efficient algorithm for model selection that automatically chooses an
appropriate model order for the data. We present the first sparse solution to learn the
Grouped mixed-effects GP. We show that, given a desired model order, how the sparse
approximation can be obtained by maximizing a variational lower bound on the marginal
likelihood, generalizing ideas from single-task Gaussian processes to handle the
mixed-effects model as well as grouping. Finally, the thesis investigates the period
estimation problem through the lens of machine learning. Using GP, we propose a novel
method for period finding that does not make assumptions on the shape of the periodic
function. The algorithm combines gradient optimization with grid search and incorporates
several mechanisms to overcome the high computational complexity of GP. We also propose
a novel approach for using domain knowledge, in the form of a probabilistic generative
model, and incorporate such knowledge into the period estimation algorithm, yielding
significant improvements in the accuracy of period
Thesis (Ph.D.)--Tufts University, 2013.
Submitted to the Dept. of Computer Science.
Advisor: Roni Khardon.
Committee: Roni Khardon, Carla Brodley, Anselm Blumer, Shuchin Aeron, and Stan Sclaroff.
Keyword: Computer science.read less