arXiv subjects

Qinghua Liu

Publications and source records attributed to Qinghua Liu.

41 records · Page 3Linked to original sources

arXiv2019

BayesMallows: An R Package for the Bayesian Mallows Model

BayesMallows is an R package for analyzing data in the form of rankings or preferences with the Mallows rank model, and its finite mixture extension, in a Bayesian probabilistic framework. The Mallows model is a well-known model, grounded on the idea that the probability density of an observed ranking decreases exponentially fast as its distance to the location parameter increases. Despite the model being quite popular, this is the first Bayesian implementation that allows a wide choice of distances, and that works well with a large amount of items to be ranked. BayesMallows supports footrule, Spearman, Kendall, Cayley, Hamming and Ulam distances, allowing full use of the rich expressiveness of the Mallows model. This is possible thanks to the implementation of fast algorithms for approximating the partition function of the model under various distances. Although developed for being used in computing the posterior distribution of the model, these algorithms may be of interest in their own right. BayesMallows handles non-standard data: partial rankings and pairwise comparisons, even in cases including non-transitive preference patterns. The advantage of the Bayesian paradigm in this context comes from its ability to coherently quantify posterior uncertainties of estimates of any quantity of interest. These posteriors are fully available to the user, and the package comes with convienient tools for summarizing and visualizing the posterior distributions.

stat.CO↗

arXiv2019

Distributed Change Detection via Average Consensus over Networks

Distributed change-point detection has been a fundamental problem when performing real-time monitoring using sensor-networks. We propose a distributed detection algorithm, where each sensor only exchanges CUSUM statistic with their neighbors based on the average consensus scheme, and an alarm is raised when local consensus statistic exceeds a pre-specified global threshold. We provide theoretical performance bounds showing that the performance of the fully distributed scheme can match the centralized algorithms under some mild conditions. Numerical experiments demonstrate the good performance of the algorithm especially in detecting asynchronous changes.

eess.SP↗

arXiv2018

Rigorous Restricted Isometry Property of Low-Dimensional Subspaces

Dimensionality reduction is in demand to reduce the complexity of solving large-scale problems with data lying in latent low-dimensional structures in machine learning and computer version. Motivated by such need, in this work we study the Restricted Isometry Property (RIP) of Gaussian random projections for low-dimensional subspaces in $\mathbb{R}^N$, and rigorously prove that the projection Frobenius norm distance between any two subspaces spanned by the projected data in $\mathbb{R}^n$ ($n<N$) remain almost the same as the distance between the original subspaces with probability no less than $1 - {\rm e}^{-\mathcal{O}(n)}$. Previously the well-known Johnson-Lindenstrauss (JL) Lemma and RIP for sparse vectors have been the foundation of sparse signal processing including Compressed Sensing. As an analogy to JL Lemma and RIP for sparse vectors, this work allows the use of random projections to reduce the ambient dimension with the theoretical guarantee that the distance between subspaces after compression is well preserved.

cs.IT↗

arXiv2017

Linearized ADMM for Non-convex Non-smooth Optimization with Convergence Analysis

Linearized alternating direction method of multipliers (ADMM) as an extension of ADMM has been widely used to solve linearly constrained problems in signal processing, machine leaning, communications, and many other fields. Despite its broad applications in nonconvex optimization, for a great number of nonconvex and nonsmooth objective functions, its theoretical convergence guarantee is still an open problem. In this paper, we propose a two-block linearized ADMM and a multi-block parallel linearized ADMM for problems with nonconvex and nonsmooth objectives. Mathematically, we present that the algorithms can converge for a broader class of objective functions under less strict assumptions compared with previous works. Furthermore, our proposed algorithm can update coupled variables in parallel and work for less restrictive nonconvex problems, where the traditional ADMM may have difficulties in solving subproblems.

math.OC↗

arXiv2014

The local structure and optical absorption characteristic investigation on Fe doped TiO2 nanoparticles

The local structures and optical absorption characteristic of Fe doped TiO2 nanoparticles synthesized by the sol-gel method were characterized by X-ray Diffraction (XRD), X-ray absorption fine structure spectroscopy (XAFS) and UV-Vis absorption spectroscopy (UV-Vis). XRD patterns show that all Fe-doped TiO2 samples have the characteristic anatase structure. Accurate Fe and Ti K-edge EXAFS analysis further reveal that all Fe atoms replace Ti atoms in the anatase lattice. The analysis of UV-Vis data shows a red shift to the visible range. According to the above results, we claim that substitutional Fe atoms lead to the formation of structural defects and new intermediate energy levels appear, narrowing the band gap and extending the optical absorption edge towards the visible region.

physics.chem-ph↗