Gen Li

Gen Li
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Gen Li
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Statistics - Methodology (5)
 
Statistics - Machine Learning (2)
 
Computer Science - Information Theory (2)
 
Mathematics - Information Theory (2)
 
Mathematics - Rings and Algebras (1)
 
Statistics - Applications (1)
 
Computer Science - Learning (1)

Publications Authored By Gen Li

Dimension reduction plays an essential role when decreasing the complexity of solving large-scale problems. The well-known Johnson-Lindenstrauss (JL) Lemma and Restricted Isometry Property (RIP) admit the use of random projection to reduce the dimension while keeping the Euclidean distance, which leads to the boom of Compressed Sensing and the field of sparsity related signal processing. Recently, successful applications of sparse models in computer vision and machine learning have increasingly hinted that the underlying structure of high dimensional data looks more like a union of subspaces (UoS). Read More

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). Read More

We study a spectral initialization method that serves a key role in recent work on estimating signals in nonconvex settings. Previous analysis of this method focuses on the phase retrieval problem and provides only performance bounds. In this paper, we consider arbitrary generalized linear sensing models and present a precise asymptotic characterization of the performance of the method in the high-dimensional limit. Read More

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. Read More

Expression quantitative trait loci (eQTL) analysis identifies genetic markers associated with the expression of a gene. Most existing eQTL analyses and methods investigate association in a single, readily available tissue, such as blood. Joint analysis of eQTL in multiple tissues has the potential to improve, and expand the scope of, single-tissue analyses. Read More

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. Read More

We describe a probabilistic PARAFAC/CANDECOMP (CP) factorization for multiway (i.e., tensor) data that incorporates auxiliary covariates, SupCP. Read More

Expression quantitative trait loci (eQTL) analyses, which identify genetic markers associated with the expression of a gene, are an important tool in the understanding of diseases in human and other populations. While most eQTL studies to date consider the connection between genetic variation and expression in a single tissue, complex, multi-tissue data sets are now being generated by the GTEx initiative. These data sets have the potential to improve the findings of single tissue analyses by borrowing strength across tissues, and the potential to elucidate the genotypic basis of differences between tissues. Read More

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. Read More