arXiv subjects

Zi Wang

Publications and source records attributed to Zi Wang.

167 records · Page 10Linked to original sources

arXiv2016

A Parallelizable Dual Smoothing Method for Large Scale Convex Regression Problems

Convex regression (CR) is an approach for fitting a convex function to a finite number of observations. It arises in various applications from diverse fields such as statistics, operations research, economics, and electrical engineering. The least squares (LS) estimator, which can be computed via solving a quadratic program (QP), is an intuitive method for convex regression with already established strong theoretical guarantees. On the other hand, since the number of constraints in the QP formulation increases quadratically in the number of observed data points, the QP quickly becomes impractical to solve using traditional interior point methods. To address this issue, we propose a first-order method based on dual smoothing that carefully manages the memory usage through parallelization in order to efficiently compute the LS estimator in practice for large-scale CR instances.

math.OC↗

arXiv2016

Studying the brain from adolescence to adulthood through sparse multi-view matrix factorisations

Men and women differ in specific cognitive abilities and in the expression of several neuropsychiatric conditions. Such findings could be attributed to sex hormones, brain differences, as well as a number of environmental variables. Existing research on identifying sex-related differences in brain structure have predominantly used cross-sectional studies to investigate, for instance, differences in average gray matter volumes (GMVs). In this article we explore the potential of a recently proposed multi-view matrix factorisation (MVMF) methodology to study structural brain changes in men and women that occur from adolescence to adulthood. MVMF is a multivariate variance decomposition technique that extends principal component analysis to "multi-view" datasets, i.e. where multiple and related groups of observations are available. In this application, each view represents a different age group. MVMF identifies latent factors explaining shared and age-specific contributions to the observed overall variability in GMVs over time. These latent factors can be used to produce low-dimensional visualisations of the data that emphasise age-specific effects once the shared effects have been accounted for. The analysis of two datasets consisting of individuals born prematurely as well as healthy controls provides evidence to suggest that the separation between males and females becomes increasingly larger as the brain transitions from adolescence to adulthood. We report on specific brain regions associated to these variance effects.

stat.AP↗

arXiv2015

Sparse multi-view matrix factorisation: a multivariate approach to multiple tissue comparisons

Gene expression levels in a population vary extensively across tissues. Such heterogeneity is caused by genetic variability and environmental factors, and is expected to be linked to disease development. The abundance of experimental data now enables the identification of features of gene expression profiles that are shared across tissues, and those that are tissue-specific. While most current research is concerned with characterising differential expression by comparing mean expression profiles across tissues, it is also believed that a significant difference in a gene expression's variance across tissues may also be associated to molecular mechanisms that are important for tissue development and function. We propose a sparse multi-view matrix factorisation (sMVMF) algorithm to jointly analyse gene expression measurements in multiple tissues, where each tissue provides a different "view" of the underlying organism. The proposed methodology can be interpreted as an extension of principal component analysis in that it provides the means to decompose the total sample variance in each tissue into the sum of two components: one capturing the variance that is shared across tissues, and one isolating the tissue-specific variances. sMVMF has been used to jointly model mRNA expression profiles in three tissues - adipose, skin and LCL - which are available for a large and well-phenotyped twins cohort, TwinsUK. Using sMVMF, we are able to prioritise genes based on whether their variation patterns are specific to each tissue. Furthermore, using DNA methylation profiles available, we provide supporting evidence that adipose-specific gene expression patterns may be driven by epigenetic effects.

stat.ML↗

arXiv2015

An Asynchronous Distributed Proximal Gradient Method for Composite Convex Optimization

We propose a distributed first-order augmented Lagrangian (DFAL) algorithm to minimize the sum of composite convex functions, where each term in the sum is a private cost function belonging to a node, and only nodes connected by an edge can directly communicate with each other. This optimization model abstracts a number of applications in distributed sensing and machine learning. We show that any limit point of DFAL iterates is optimal; and for any $ε>0$, an $ε$-optimal and $ε$-feasible solution can be computed within $\mathcal{O}(\log(ε^{-1}))$ DFAL iterations, which require $\mathcal{O}(\frac{ψ_{\max}^{1.5}}{d_{\min}} ε^{-1})$ proximal gradient computations and communications per node in total, where $ψ_{\max}$ denotes the largest eigenvalue of the graph Laplacian, and $d_{\min}$ is the minimum degree of the graph. We also propose an asynchronous version of DFAL by incorporating randomized block coordinate descent methods; and demonstrate the efficiency of DFAL on large scale sparse-group LASSO problems.

math.OC↗

arXiv2014

A Parallel Method for Large Scale Convex Regression Problems

Convex regression (CR) problem deals with fitting a convex function to a finite number of observations. It has many applications in various disciplines, such as statistics, economics, operations research, and electrical engineering. Computing the least squares (LS) estimator via solving a quadratic program (QP) is the most common technique to fit a piecewise-linear convex function to the observed data. Since the number of constraints in the QP formulation increases quadratically in N, the number of observed data points, computing the LS estimator is not practical using interior point methods when N is very large. The first-order method proposed in this paper carefully manages the memory usage through parallelization, and efficiently solves large-scale instances of CR.

math.OC↗