arXiv subjects

Gen Li

Publications and source records attributed to Gen Li.

257 records · Page 15Linked to original sources

arXiv2017

Structural Learning and Integrative Decomposition of Multi-View Data

The increased availability of the multi-view data (data on the same samples from multiple sources) has led to strong interest in models based on low-rank matrix factorizations. These models represent each data view via shared and individual components, and have been successfully applied for exploratory dimension reduction, association analysis between the views, and further learning tasks such as consensus clustering. Despite these advances, there remain significant challenges in modeling partially-shared components, and identifying the number of components of each type (shared/partially-shared/individual). In this work, we formulate a novel linked component model that directly incorporates partially-shared structures. We call this model SLIDE for Structural Learning and Integrative DEcomposition of multi-view data. We prove the existence of SLIDE decomposition and explicitly characterize the identifiability conditions. The proposed model fitting and selection techniques allow for joint identification of the number of components of each type, in contrast to existing sequential approaches. In our empirical studies, SLIDE demonstrates excellent performance in both signal estimation and component selection. We further illustrate the methodology on the breast cancer data from The Cancer Genome Atlas repository.

stat.ML↗

arXiv2017

Varying-coefficient models for dynamic networks

Dynamic networks are commonly used in applications where relational data is observed over time. Statistical models for such data should capture not only the temporal dependencies between networks observed in time, but also the structural dependencies among the nodes and edges in each network. As a consequence, effectively making inference on dynamic networks is a computationally challenging task, and many models established for dynamic networks are intractable even for moderately sized networks. In this paper, we propose and investigate a family of dynamic network models, known as varying-coefficient exponential random graph models (VCERGMs), that characterize the evolution of network topology through smoothly varying parameters in an exponential family of distributions. The VCERGM provides an interpretable dynamic network model that enables the inference of temporal heterogeneity in a dynamic network. We establish how to fit the VCERGM through maximum pseudo-likelihood techniques, and thus provide a computationally tractable method for statistical inference of complex dynamic networks. We furthermore devise a bootstrap hypothesis testing framework for testing the temporal heterogeneity of an observed dynamic network sequence. We apply the VCERGM to the US Congress co-voting network and a resting-state brain connectivity case study and show that our method provides relevant and interpretable patterns describing each data set. Comprehensive simulation studies demonstrate the advantages of our proposed method over existing methods.

stat.ME↗

arXiv2017

Incorporating Covariates into Integrated Factor Analysis of Multi-View Data

In modern biomedical research, it is ubiquitous to have multiple data sets measured on the same set of samples from different views (i.e., multi-view data). For example, in genetic studies, multiple genomic data sets at different molecular levels or from different cell types are measured for a common set of individuals to investigate genetic regulation. Integration and reduction of multi-view data have the potential to leverage information in different data sets, and to reduce the magnitude and complexity of data for further statistical analysis and interpretation. In this paper, we develop a novel statistical model, called supervised integrated factor analysis (SIFA), for integrative dimension reduction of multi-view data while incorporating auxiliary covariates. The model decomposes data into joint and individual factors, capturing the joint variation across multiple data sets and the individual variation specific to each set respectively. Moreover, both joint and individual factors are partially informed by auxiliary covariates via nonparametric models. We devise a computationally efficient Expectation-Maximization (EM) algorithm to fit the model under some identifiability conditions. We apply the method to the Genotype-Tissue Expression (GTEx) data, and provide new insights into the variation decomposition of gene expression in multiple tissues. Extensive simulation studies and an additional application to a pediatric growth study demonstrate the advantage of the proposed method over competing methods.

stat.ME↗

arXiv2016

Approximation of Gram-Schmidt Orthogonalization by Data Matrix

For a matrix ${\bf A}$ with linearly independent columns, this work studies to use its normalization $\bar{\bf A}$ and ${\bf A}$ itself to approximate its orthonormalization $\bf V$. We theoretically analyze the order of the approximation errors as $\bf A$ and $\bar{\bf A}$ approach ${\bf V}$, respectively. Our conclusion is able to explain the fact that a high dimensional Gaussian matrix can well approximate the corresponding truncated Haar matrix. For applications, this work can serve as a foundation of a wide variety of problems in signal processing such as compressed subspace clustering.

math.RA↗

arXiv2013

Direction-Projection-Permutation for High Dimensional Hypothesis Tests

Motivated by the prevalence of high dimensional low sample size datasets in modern statistical applications, we propose a general nonparametric framework, Direction-Projection-Permutation (DiProPerm), for testing high dimensional hypotheses. The method is aimed at rigorous testing of whether lower dimensional visual differences are statistically significant. Theoretical analysis under the non-classical asymptotic regime of dimension going to infinity for fixed sample size reveals that certain natural variations of DiProPerm can have very different behaviors. An empirical power study both confirms the theoretical results and suggests DiProPerm is a powerful test in many settings. Finally DiProPerm is applied to a high dimensional gene expression dataset.

stat.ME↗