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Qing Zhou

Publications and source records attributed to Qing Zhou.

At least 91 records · Page 5Linked to original sources
arXiv2015

Energy-Efficient Data Transmission with Non-FIFO Packets

This paper investigates the problem of energy-efficient packet transmission with arbitrary arrival instants and deadline constraints over a point-to-point Additive White Gaussian Noise (AWGN) channel. This is different from previous work where it is assumed that the packets follow a First-In-First-Out (FIFO) order in that the packets that arrive earlier will have a deadline that is also earlier. We first investigate the necessary and sufficient conditions of the optimal transmission scheduler. We then propose an algorithm which finds the transmission schedule of each packet in the order of the packets with the largest transmission rate to the packets with the smallest transmission rate. Finally, we show that our algorithm satisfies the sufficient conditions of the optimal transmission scheduler and thus, is optimal.

cs.NI↗
arXiv2015

Iterative Subsampling in Solution Path Clustering of Noisy Big Data

We develop an iterative subsampling approach to improve the computational efficiency of our previous work on solution path clustering (SPC). The SPC method achieves clustering by concave regularization on the pairwise distances between cluster centers. This clustering method has the important capability to recognize noise and to provide a short path of clustering solutions; however, it is not sufficiently fast for big datasets. Thus, we propose a method that iterates between clustering a small subsample of the full data and sequentially assigning the other data points to attain orders of magnitude of computational savings. The new method preserves the ability to isolate noise, includes a solution selection mechanism that ultimately provides one clustering solution with an estimated number of clusters, and is shown to be able to extract small tight clusters from noisy data. The method's relatively minor losses in accuracy are demonstrated through simulation studies, and its ability to handle large datasets is illustrated through applications to gene expression datasets. An R package, SPClustering, for the SPC method with iterative subsampling is available at http://www.stat.ucla.edu/~zhou/Software.html.

stat.ME↗
arXiv2015

From Silicene to Half-Silicane by Hydrogenation

Graphane is graphene fully hydrogenated from both sides, forming a 1x1 structure, where all C atoms are in sp3 configuration. In silicene, the Si atoms are in a mix-sp2/sp3 configuration, it is therefore natural to imagine silicane in analogue to graphane. However, monoatomic silicene sheet grown on substrates generally reconstructs into different phases, and only partially hydrogenated silicene with reconstructions had been reported before. In this report we produce half-silicane, where one Si sublattice is fully H-saturated and the other sublattice is intact, forming a perfect 1x1 structure. By hydrogenating various silicene phases on Ag(111) substrate, we found that only the (2r3x2r3)R30° phase can produce half-silicane. Interestingly, this phase was previous considered to be a highly defective or incomplete silicene structure. Our results indicate that the structure of (2r3x2r3)R30° phase involves a complete silicene-1x1 lattice instead of defective fragments, and the formation mechanism of half-silicane was discussed with the help of first principles calculations.

cond-mat.mtrl-sci↗
arXiv2015

Concave Penalized Estimation of Sparse Gaussian Bayesian Networks

We develop a penalized likelihood estimation framework to estimate the structure of Gaussian Bayesian networks from observational data. In contrast to recent methods which accelerate the learning problem by restricting the search space, our main contribution is a fast algorithm for score-based structure learning which does not restrict the search space in any way and works on high-dimensional datasets with thousands of variables. Our use of concave regularization, as opposed to the more popular $\ell_0$ (e.g. BIC) penalty, is new. Moreover, we provide theoretical guarantees which generalize existing asymptotic results when the underlying distribution is Gaussian. Most notably, our framework does not require the existence of a so-called faithful DAG representation, and as a result the theory must handle the inherent nonidentifiability of the estimation problem in a novel way. Finally, as a matter of independent interest, we provide a comprehensive comparison of our approach to several standard structure learning methods using open-source packages developed for the R language. Based on these experiments, we show that our algorithm is significantly faster than other competing methods while obtaining higher sensitivity with comparable false discovery rates for high-dimensional data. In particular, the total runtime for our method to generate a solution path of 20 estimates for DAGs with 8000 nodes is around one hour.

stat.ME↗
arXiv2014

Monte Carlo Simulation for Lasso-Type Problems by Estimator Augmentation

Regularized linear regression under the $\ell_1$ penalty, such as the Lasso, has been shown to be effective in variable selection and sparse modeling. The sampling distribution of an $\ell_1$-penalized estimator $\hatβ$ is hard to determine as the estimator is defined by an optimization problem that in general can only be solved numerically and many of its components may be exactly zero. Let $S$ be the subgradient of the $\ell_1$ norm of the coefficient vector $β$ evaluated at $\hatβ$. We find that the joint sampling distribution of $\hatβ$ and $S$, together called an augmented estimator, is much more tractable and has a closed-form density under a normal error distribution in both low-dimensional ($p\leq n$) and high-dimensional ($p>n$) settings. Given $β$ and the error variance $σ^2$, one may employ standard Monte Carlo methods, such as Markov chain Monte Carlo and importance sampling, to draw samples from the distribution of the augmented estimator and calculate expectations with respect to the sampling distribution of $\hatβ$. We develop a few concrete Monte Carlo algorithms and demonstrate with numerical examples that our approach may offer huge advantages and great flexibility in studying sampling distributions in $\ell_1$-penalized linear regression. We also establish nonasymptotic bounds on the difference between the true sampling distribution of $\hatβ$ and its estimator obtained by plugging in estimated parameters, which justifies the validity of Monte Carlo simulation from an estimated sampling distribution even when $p\gg n\to \infty$.

stat.ME↗
arXiv2014

Solution Path Clustering with Adaptive Concave Penalty

Fast accumulation of large amounts of complex data has created a need for more sophisticated statistical methodologies to discover interesting patterns and better extract information from these data. The large scale of the data often results in challenging high-dimensional estimation problems where only a minority of the data shows specific grouping patterns. To address these emerging challenges, we develop a new clustering methodology that introduces the idea of a regularization path into unsupervised learning. A regularization path for a clustering problem is created by varying the degree of sparsity constraint that is imposed on the differences between objects via the minimax concave penalty with adaptive tuning parameters. Instead of providing a single solution represented by a cluster assignment for each object, the method produces a short sequence of solutions that determines not only the cluster assignment but also a corresponding number of clusters for each solution. The optimization of the penalized loss function is carried out through an MM algorithm with block coordinate descent. The advantages of this clustering algorithm compared to other existing methods are as follows: it does not require the input of the number of clusters; it is capable of simultaneously separating irrelevant or noisy observations that show no grouping pattern, which can greatly improve data interpretation; it is a general methodology that can be applied to many clustering problems. We test this method on various simulated datasets and on gene expression data, where it shows better or competitive performance compared against several clustering methods.

stat.ME↗
arXiv2014

On optimal mean-field type control problems of stochastic systems with jump processes under partial information

This paper considers the problem of partially observed optimal control for forward stochastic systems which are driven by Brownian motions and an independent Poisson random measure with a feature that the cost functional is of mean-field type. When all the system coefficients and the objective performance functionals are allowed to be random, possibly non-Markovian, Malliavin calculus is employed to derive a maximum principle for the optimal control of such a system where the adjointprocess is explicitly expressed. We also investigate the mean-field type optimal control problems for systems driven by mean-field type stochastic differential equations (SDEs in short) with jump processes, in which the coefficients contain not only the state process but also its marginal distribution under partially observed information. The maximum principle is established using convex variational technique with an illustrating example about linear-quadratic optimal control.

math.PR↗
arXiv2012

Path covering number and L(2,1)-labeling number of graphs

A {\it path covering} of a graph $G$ is a set of vertex disjoint paths of $G$ containing all the vertices of $G$. The {\it path covering number} of $G$, denoted by $P(G)$, is the minimum number of paths in a path covering of $G$. An {\sl $k$-L(2,1)-labeling} of a graph $G$ is a mapping $f$ from $V(G)$ to the set ${0,1,...,k}$ such that $|f(u)-f(v)|\ge 2$ if $d_G(u,v)=1$ and $|f(u)-f(v)|\ge 1$ if $d_G(u,v)=2$. The {\sl L(2,1)-labeling number $λ(G)$} of $G$ is the smallest number $k$ such that $G$ has a $k$-L(2,1)-labeling. The purpose of this paper is to study path covering number and L(2,1)-labeling number of graphs. Our main work extends most of results in [On island sequences of labelings with a condition at distance two, Discrete Applied Maths 158 (2010), 1-7] and can answer an open problem in [On the structure of graphs with non-surjective L(2,1)-labelings, SIAM J. Discrete Math. 19 (2005), 208-223].

math.CO↗
arXiv2011

Multi-Domain Sampling With Applications to Structural Inference of Bayesian Networks

When a posterior distribution has multiple modes, unconditional expectations, such as the posterior mean, may not offer informative summaries of the distribution. Motivated by this problem, we propose to decompose the sample space of a multimodal distribution into domains of attraction of local modes. Domain-based representations are defined to summarize the probability masses of and conditional expectations on domains of attraction, which are much more informative than the mean and other unconditional expectations. A computational method, the multi-domain sampler, is developed to construct domain-based representations for an arbitrary multimodal distribution. The multi-domain sampler is applied to structural learning of protein-signaling networks from high-throughput single-cell data, where a signaling network is modeled as a causal Bayesian network. Not only does our method provide a detailed landscape of the posterior distribution but also improves the accuracy and the predictive power of estimated networks.

stat.ME↗
arXiv2011

Multivalued stochastic Dirichlet-Neumann problems and generalized backward doubly stochastic differential equations

In this paper, a class of generalized backward doubly stochastic differential equations whose coefficient contains the subdifferential operators of two convex functions (also called generalized backward doubly stochastic variational inequalities) are considered. By means of a penalization argument based on Yosida approximation, we establish the existence and uniqueness of the solution. As an application, this result is used to derive existence result of stochastic viscosity solution for a class of multivalued stochastic Dirichlet-Neumann problems.

math.PR↗
arXiv2011

Random Walk over Basins of Attraction to Construct Ising Energy Landscapes

An efficient algorithm is developed to construct disconnectivity graphs by a random walk over basins of attraction. This algorithm can detect a large number of local minima, find energy barriers between them, and estimate local thermal averages over each basin of attraction. It is applied to the SK spin glass Hamiltonian where existing methods have difficulties even for a moderate number of spins. Finite-size results are used to make predictions in the thermodynamic limit that match theoretical approximations and recent findings on the free energy landscapes of SK spin glasses.

cond-mat.stat-mech↗
arXiv2010

On Weight Matrix and Free Energy Models for Sequence Motif Detection

The problem of motif detection can be formulated as the construction of a discriminant function to separate sequences of a specific pattern from background. In computational biology, motif detection is used to predict DNA binding sites of a transcription factor (TF), mostly based on the weight matrix (WM) model or the Gibbs free energy (FE) model. However, despite the wide applications, theoretical analysis of these two models and their predictions is still lacking. We derive asymptotic error rates of prediction procedures based on these models under different data generation assumptions. This allows a theoretical comparison between the WM-based and the FE-based predictions in terms of asymptotic efficiency. Applications of the theoretical results are demonstrated with empirical studies on ChIP-seq data and protein binding microarray data. We find that, irrespective of underlying data generation mechanisms, the FE approach shows higher or comparable predictive power relative to the WM approach when the number of observed binding sites used for constructing a discriminant decision is not too small.

q-bio.GN↗
arXiv2009

Reconstructing the energy landscape of a distribution from Monte Carlo samples

Defining the energy function as the negative logarithm of the density, we explore the energy landscape of a distribution via the tree of sublevel sets of its energy. This tree represents the hierarchy among the connected components of the sublevel sets. We propose ways to annotate the tree so that it provides information on both topological and statistical aspects of the distribution, such as the local energy minima (local modes), their local domains and volumes, and the barriers between them. We develop a computational method to estimate the tree and reconstruct the energy landscape from Monte Carlo samples simulated at a wide energy range of a distribution. This method can be applied to any arbitrary distribution on a space with defined connectedness. We test the method on multimodal distributions and posterior distributions to show that our estimated trees are accurate compared to theoretical values. When used to perform Bayesian inference of DNA sequence segmentation, this approach reveals much more information than the standard approach based on marginal posterior distributions.

stat.AP↗
arXiv2007

Coupling hidden Markov models for the discovery of Cis-regulatory modules in multiple species

Cis-regulatory modules (CRMs) composed of multiple transcription factor binding sites (TFBSs) control gene expression in eukaryotic genomes. Comparative genomic studies have shown that these regulatory elements are more conserved across species due to evolutionary constraints. We propose a statistical method to combine module structure and cross-species orthology in de novo motif discovery. We use a hidden Markov model (HMM) to capture the module structure in each species and couple these HMMs through multiple-species alignment. Evolutionary models are incorporated to consider correlated structures among aligned sequence positions across different species. Based on our model, we develop a Markov chain Monte Carlo approach, MultiModule, to discover CRMs and their component motifs simultaneously in groups of orthologous sequences from multiple species. Our method is tested on both simulated and biological data sets in mammals and Drosophila, where significant improvement over other motif and module discovery methods is observed.

stat.AP↗
arXiv2006

On tame embeddings of solenoids into 3-space

Solenoids are ``inverse limits'' of the circle, and the classical knot theory is the theory of tame embeddings of the circle into the 3-space. We give some general study, including certain classification results, of tame embeddings of solenoids into the 3-space as the ``inverse limits'' of the tame embeddings of the circle. Some applications are discussed. In particular, there are ``tamely'' embedded solenoids $Σ\subset \R^3$ which are strictly achiral. Since solenoids are non-planar, this contrasts sharply with the known fact that if there is a strictly achiral embedding $Y\subset \R^3$ of a compact polyhedron $Y$, then $Y$ must be planar.

math.GT↗
arXiv2006

Equi-energy sampler with applications in statistical inference and statistical mechanics

We introduce a new sampling algorithm, the equi-energy sampler, for efficient statistical sampling and estimation. Complementary to the widely used temperature-domain methods, the equi-energy sampler, utilizing the temperature--energy duality, targets the energy directly. The focus on the energy function not only facilitates efficient sampling, but also provides a powerful means for statistical estimation, for example, the calculation of the density of states and microcanonical averages in statistical mechanics. The equi-energy sampler is applied to a variety of problems, including exponential regression in statistics, motif sampling in computational biology and protein folding in biophysics.

math.ST↗
arXiv2005

Embedding infinite cyclic covers of knot spaces into 3-space

We say a knot $k$ in the 3-sphere $\mathbb S^3$ has {\it Property $IE$} if the infinite cyclic cover of the knot exterior embeds into $\mathbb S^3$. Clearly all fibred knots have Property $IE$. There are infinitely many non-fibred knots with Property $IE$ and infinitely many non-fibred knots without property $IE$. Both kinds of examples are established here for the first time. Indeed we show that if a genus 1 non-fibred knot has Property $IE$, then its Alexander polynomial $Δ_k(t)$ must be either 1 or $2t^2-5t+2$, and we give two infinite families of non-fibred genus 1 knots with Property $IE$ and having $Δ_k(t)=1$ and $2t^2-5t+2$ respectively. Hence among genus one non-fibred knots, no alternating knot has Property $IE$, and there is only one knot with Property $IE$ up to ten crossings. We also give an obstruction to embedding infinite cyclic covers of a compact 3-manifold into any compact 3-manifold.

math.GT↗