Sparse multivariate models for pattern detection in high-dimensional biological data
File(s)
Author(s)
Wang, Zi
Type
Thesis
Abstract
Recent advances in technology have made it possible and affordable to collect biological
data of unprecedented size and complexity. While analysing such data, traditional statistical
methods and machine learning algorithms suffer from the curse of dimensionality.
Parsimonious models, which may refer to parsimony in model structure and/or model parameters, have been shown to improve both biological interpretability of the model and the
generalisability to new data.
In this thesis we are concerned with model selection in both supervised and unsupervised
learning tasks. For supervised learnings, we propose a new penalty called graphguided
group lasso (GGGL) and employ this penalty in penalised linear regressions. GGGL
is able to integrate prior structured information with data mining, where variables sharing
similar biological functions are collected into groups and the pairwise relatedness between
groups are organised into a network. Such prior information will guide the selection of
variables that are predictive to a univariate response, so that the model selects variable
groups that are close in the network and important variables within the selected groups.
We then generalise the idea of incorporating network-structured prior knowledge to association
studies consisting of multivariate predictors and multivariate responses and propose
the network-driven sparse reduced-rank regression (NsRRR). In NsRRR, pairwise relatedness between predictors and between responses are represented by two networks, and
the model identifies associations between a subnetwork of predictors and a subnetwork of
responses such that both subnetworks tend to be connected. For unsupervised learning,
we are concerned with a multi-view learning task in which we compare the variance of
high-dimensional biological features collected from multiple sources which are referred
as “views”. We propose the sparse multi-view matrix factorisation (sMVMF) which is parsimonious in both model structure and model parameters. sMVMF can identify latent
factors that regulate variability shared across all views and the variability which is characteristic
to a specific view, respectively. For each novel method, we also present simulation
studies and an application on real biological data to illustrate variable selection and model
interpretability perspectives.
data of unprecedented size and complexity. While analysing such data, traditional statistical
methods and machine learning algorithms suffer from the curse of dimensionality.
Parsimonious models, which may refer to parsimony in model structure and/or model parameters, have been shown to improve both biological interpretability of the model and the
generalisability to new data.
In this thesis we are concerned with model selection in both supervised and unsupervised
learning tasks. For supervised learnings, we propose a new penalty called graphguided
group lasso (GGGL) and employ this penalty in penalised linear regressions. GGGL
is able to integrate prior structured information with data mining, where variables sharing
similar biological functions are collected into groups and the pairwise relatedness between
groups are organised into a network. Such prior information will guide the selection of
variables that are predictive to a univariate response, so that the model selects variable
groups that are close in the network and important variables within the selected groups.
We then generalise the idea of incorporating network-structured prior knowledge to association
studies consisting of multivariate predictors and multivariate responses and propose
the network-driven sparse reduced-rank regression (NsRRR). In NsRRR, pairwise relatedness between predictors and between responses are represented by two networks, and
the model identifies associations between a subnetwork of predictors and a subnetwork of
responses such that both subnetworks tend to be connected. For unsupervised learning,
we are concerned with a multi-view learning task in which we compare the variance of
high-dimensional biological features collected from multiple sources which are referred
as “views”. We propose the sparse multi-view matrix factorisation (sMVMF) which is parsimonious in both model structure and model parameters. sMVMF can identify latent
factors that regulate variability shared across all views and the variability which is characteristic
to a specific view, respectively. For each novel method, we also present simulation
studies and an application on real biological data to illustrate variable selection and model
interpretability perspectives.
Version
Open Access
Date Issued
2015-05
Date Awarded
2015-08
Copyright Statement
Attribution NoDerivatives 4.0 International Licence (CC BY-ND)
Advisor
Montana, Giovanni
Sponsor
Biotechnology and Biological Sciences Research Council (Great Britain)
Grant Number
DCIM-P31665
Publisher Department
Mathematics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)