arXiv subjects

Su-Yun Huang

Publications and source records attributed to Su-Yun Huang.

23 records · Page 2Linked to original sources

arXiv2015

On the Weak Convergence and Central Limit Theorem of Blurring and Nonblurring Processes with Application to Robust Location Estimation

This article studies the weak convergence and associated Central Limit Theorem for blurring and nonblurring processes. Then, they are applied to the estimation of location parameter. Simulation studies show that the location estimation based on the convergence point of blurring process is more robust and often more efficient than that of nonblurring process.

math.ST↗

arXiv2014

$γ$-SUP: A clustering algorithm for cryo-electron microscopy images of asymmetric particles

Cryo-electron microscopy (cryo-EM) has recently emerged as a powerful tool for obtaining three-dimensional (3D) structures of biological macromolecules in native states. A minimum cryo-EM image data set for deriving a meaningful reconstruction is comprised of thousands of randomly orientated projections of identical particles photographed with a small number of electrons. The computation of 3D structure from 2D projections requires clustering, which aims to enhance the signal to noise ratio in each view by grouping similarly oriented images. Nevertheless, the prevailing clustering techniques are often compromised by three characteristics of cryo-EM data: high noise content, high dimensionality and large number of clusters. Moreover, since clustering requires registering images of similar orientation into the same pixel coordinates by 2D alignment, it is desired that the clustering algorithm can label misaligned images as outliers. Herein, we introduce a clustering algorithm $γ$-SUP to model the data with a $q$-Gaussian mixture and adopt the minimum $γ$-divergence for estimation, and then use a self-updating procedure to obtain the numerical solution. We apply $γ$-SUP to the cryo-EM images of two benchmark macromolecules, RNA polymerase II and ribosome. In the former case, simulated images were chosen to decouple clustering from alignment to demonstrate $γ$-SUP is more robust to misalignment outliers than the existing clustering methods used in the cryo-EM community. In the latter case, the clustering of real cryo-EM data by our $γ$-SUP method eliminates noise in many views to reveal true structure features of ribosome at the projection level.

stat.AP↗

arXiv2013

Detection of Gene-Gene Interactions by Multistage Sparse and Low-Rank Regression

A daunting challenge faced by modern biological sciences is finding an efficient and computationally feasible approach to deal with the curse of high dimensionality. The problem becomes even more severe when the research focus is on interactions. To improve the performance, we propose a low-rank interaction model, where the interaction effects are modeled using a low-rank matrix. With parsimonious parameterization of interactions, the proposed model increases the stability and efficiency of statistical analysis. Built upon the low-rank model, we further propose an Extended Screen-and-Clean approach, based on the Screen and Clean (SC) method (Wasserman and Roeder, 2009; Wu et al., 2010), to detect gene-gene interactions. In particular, the screening stage utilizes a combination of a low-rank structure and a sparsity constraint in order to achieve higher power and higher selection-consistency probability. We demonstrate the effectiveness of the method using simulations and apply the proposed procedure on the warfarin dosage study. The data analysis identified main and interaction effects that would have been neglected using conventional methods.

stat.ME↗

arXiv2012

Robust Independent Component Analysis via Minimum Divergence Estimation

Independent component analysis (ICA) has been shown to be useful in many applications. However, most ICA methods are sensitive to data contamination and outliers. In this article we introduce a general minimum U-divergence framework for ICA, which covers some standard ICA methods as special cases. Within the U-family we further focus on the gamma-divergence due to its desirable property of super robustness, which gives the proposed method gamma-ICA. Statistical properties and technical conditions for the consistency of gamma-ICA are rigorously studied. In the limiting case, it leads to a necessary and sufficient condition for the consistency of MLE-ICA. This necessary and sufficient condition is weaker than the condition known in the literature. Since the parameter of interest in ICA is an orthogonal matrix, a geometrical algorithm based on gradient flows on special orthogonal group is introduced to implement gamma-ICA. Furthermore, a data-driven selection for the gamma value, which is critical to the achievement of gamma-ICA, is developed. The performance, especially the robustness, of gamma-ICA in comparison with standard ICA methods is demonstrated through experimental studies using simulated data and image data.

stat.ME↗

arXiv2011

On Multilinear Principal Component Analysis of Order-Two Tensors

Principal Component Analysis (PCA) is a commonly used tool for dimension reduction in analyzing high dimensional data; Multilinear Principal Component Analysis (MPCA) has the potential to serve the similar function for analyzing tensor structure data. MPCA and other tensor decomposition methods have been proved effective to reduce the dimensions for both real data analyses and simulation studies (Ye, 2005; Lu, Plataniotis and Venetsanopoulos, 2008; Kolda and Bader, 2009; Li, Kim and Altman, 2010). In this paper, we investigate MPCA's statistical properties and provide explanations for its advantages. Conventional PCA, vectorizing the tensor data, may lead to inefficient and unstable prediction due to its extremely large dimensionality. On the other hand, MPCA, trying to preserve the data structure, searches for low-dimensional multilinear projections and decreases the dimensionality efficiently. The asymptotic theories for order-two MPCA, including asymptotic distributions for principal components, associated projections and the explained variance, are developed. Finally, MPCA is shown to improve conventional PCA on analyzing the {\sf Olivetti Faces} data set, by constructing more module oriented basis in reconstructing the test faces.

math.ST↗