arXiv subjects

Qing Zhou

Publications and source records attributed to Qing Zhou.

At least 73 records · Page 4Linked to original sources

arXiv2020

Causal network learning with non-invertible functional relationships

Discovery of causal relationships from observational data is an important problem in many areas. Several recent results have established the identifiability of causal DAGs with non-Gaussian and/or nonlinear structural equation models (SEMs). In this paper, we focus on nonlinear SEMs defined by non-invertible functions, which exist in many data domains, and propose a novel test for non-invertible bivariate causal models. We further develop a method to incorporate this test in structure learning of DAGs that contain both linear and nonlinear causal relations. By extensive numerical comparisons, we show that our algorithms outperform existing DAG learning methods in identifying causal graphical structures. We illustrate the practical application of our method in learning causal networks for combinatorial binding of transcription factors from ChIP-Seq data.

stat.ML↗

arXiv2020

Quantum Search on Encrypted Data Based on Quantum Homomorphic Encryption

We propose a homomorphic search protocol based on quantum homomorphic encryption, in which a client Alice with limited quantum ability can give her encrypted data to a powerful but untrusted quantum server and let the server search for her without decryption. By outsourcing the interactive key-update process to a trusted key center, Alice only needs to prepare and encrypt her original data and to decrypt the ciphered search result in linear time. Besides, we also present a compact and perfectly secure quantum homomorphic evaluation protocol for Cliford circuits, where the decryption key can be calculated by Alice with polynomial overhead with respect to the key length.

quant-ph↗

arXiv2019

On perfectness in Gaussian graphical models

Knowing when a graphical model is perfect to a distribution is essential in order to relate separation in the graph to conditional independence in the distribution, and this is particularly important when performing inference from data. When the model is perfect, there is a one-to-one correspondence between conditional independence statements in the distribution and separation statements in the graph. Previous work has shown that almost all models based on linear directed acyclic graphs as well as Gaussian chain graphs are perfect, the latter of which subsumes Gaussian graphical models (i.e., the undirected Gaussian models) as a special case. However, the complexity of chain graph models leads to a proof of this result which is indirect and mired by the complications of parameterizing this general class. In this paper, we directly approach the problem of perfectness for the Gaussian graphical models, and provide a new proof, via a more transparent parametrization, that almost all such models are perfect. Our approach is based on, and substantially extends, a construction of Lněnička and Matúš showing the existence of a perfect Gaussian distribution for any graph.

math.ST↗

arXiv2019

Honest confidence sets for high-dimensional regression by projection and shrinkage

The issue of honesty in constructing confidence sets arises in nonparametric regression. While optimal rate in nonparametric estimation can be achieved and utilized to construct sharp confidence sets, severe degradation of confidence level often happens after estimating the degree of smoothness. Similarly, for high-dimensional regression, oracle inequalities for sparse estimators could be utilized to construct sharp confidence sets. Yet the degree of sparsity itself is unknown and needs to be estimated, causing the honesty problem. To resolve this issue, we develop a novel method to construct honest confidence sets for sparse high-dimensional linear regression. The key idea in our construction is to separate signals into a strong and a weak group, and then construct confidence sets for each group separately. This is achieved by a projection and shrinkage approach, the latter implemented via Stein estimation and the associated Stein unbiased risk estimate. Our confidence set is honest over the full parameter space without any sparsity constraints, while its diameter adapts to the optimal rate of $n^{-1/4}$ when the true parameter is indeed sparse. Through extensive numerical comparisons, we demonstrate that our method outperforms other competitors with big margins for finite samples, including oracle methods built upon the true sparsity of the underlying model.

stat.ME↗

arXiv2019

Optimizing regularized Cholesky score for order-based learning of Bayesian networks

Bayesian networks are a class of popular graphical models that encode causal and conditional independence relations among variables by directed acyclic graphs (DAGs). We propose a novel structure learning method, annealing on regularized Cholesky score (ARCS), to search over topological sorts, or permutations of nodes, for a high-scoring Bayesian network. Our scoring function is derived from regularizing Gaussian DAG likelihood, and its optimization gives an alternative formulation of the sparse Cholesky factorization problem from a statistical viewpoint, which is of independent interest. We combine global simulated annealing over permutations with a fast proximal gradient algorithm, operating on triangular matrices of edge coefficients, to compute the score of any permutation. Combined, the two approaches allow us to quickly and effectively search over the space of DAGs without the need to verify the acyclicity constraint or to enumerate possible parent sets given a candidate topological sort. The annealing aspect of the optimization is able to consistently improve the accuracy of DAGs learned by local search algorithms. In addition, we develop several techniques to facilitate the structure learning, including pre-annealing data-driven tuning parameter selection and post-annealing constraint-based structure refinement. Through extensive numerical comparisons, we show that ARCS achieves substantial improvements over existing methods, demonstrating its great potential to learn Bayesian networks from both observational and experimental data.

stat.ML↗

arXiv2019

Learning big Gaussian Bayesian networks: partition, estimation, and fusion

Structure learning of Bayesian networks has always been a challenging problem. Nowadays, massive-size networks with thousands or more of nodes but fewer samples frequently appear in many areas. We develop a divide-and-conquer framework, called partition-estimation-fusion (PEF), for structure learning of such big networks. The proposed method first partitions nodes into clusters, then learns a subgraph on each cluster of nodes, and finally fuses all learned subgraphs into one Bayesian network. The PEF method is designed in a flexible way so that any structure learning method may be used in the second step to learn a subgraph structure as either a DAG or a CPDAG. In the clustering step, we adapt the hierarchical clustering method to automatically choose a proper number of clusters. In the fusion step, we propose a novel hybrid method that sequentially add edges between subgraphs. Extensive numerical experiments demonstrate the competitive performance of our PEF method, in terms of both speed and accuracy compared to existing methods. Our method can improve the accuracy of structure learning by 20% or more, while reducing running time up to two orders-of-magnitude.

stat.ML↗

arXiv2019

The neighborhood lattice for encoding partial correlations in a Hilbert space

Neighborhood regression has been a successful approach in graphical and structural equation modeling, with applications to learning undirected and directed graphical models. We extend these ideas by defining and studying an algebraic structure called the neighborhood lattice based on a generalized notion of neighborhood regression. We show that this algebraic structure has the potential to provide an economic encoding of all conditional independence statements in a Gaussian distribution (or conditional uncorrelatedness in general), even in the cases where no graphical model exists that could "perfectly" encode all such statements. We study the computational complexity of computing these structures and show that under a sparsity assumption, they can be computed in polynomial time, even in the absence of the assumption of perfectness to a graph. On the other hand, assuming perfectness, we show how these neighborhood lattices may be "graphically" computed using the separation properties of the so-called partial correlation graph. We also draw connections with directed acyclic graphical models and Bayesian networks. We derive these results using an abstract generalization of partial uncorrelatedness, called partial orthogonality, which allows us to use algebraic properties of projection operators on Hilbert spaces to significantly simplify and extend existing ideas and arguments. Consequently, our results apply to a wide range of random objects and data structures, such as random vectors, data matrices, and functions.

math.ST↗

arXiv2019

Quantum Differential Cryptanalysis

In this paper, we propose a quantum version of the differential cryptanalysis which offers a quadratic speedup over the existing classical one and show the quantum circuit implementing it. The quantum differential cryptanalysis is based on the quantum minimum/maximum-finding algorithm, where the values to be compared and filtered are obtained by calling the quantum counting algorithm. Any cipher which is vulnerable to the classical differential cryptanalysis based on counting procedures can be cracked more quickly under this quantum differential attack.

quant-ph↗

arXiv2018

The Economics of Video Websites with Membership-Advertising Mode in Wireless Networks

In this paper, we consider a novel business model of video websites via Membership-Advertising Mode in wireless network, where the video websites provide three video services for mobile users: \textit{VIP-Member} service, Regular-Member service and Non-Member service. The VIP-Member (Regular-Member) service provides the highest level (middle level) quality and non-advertising video service with high (low) price, while the Non-Member service provides the lowest level quality and advertising-containing video service for free. Meanwhile, the video websites sell their advertising spaces to the advertiser to create extra revenues. We formulate the interactions among the advertiser, video websites and mobile users as a three-stage Stackelberg game. Specifically, in Stage I, the advertiser decides the advertising budget; in Stage II, the video websites determine their advertising spaces selling strategies for advertiser and the membership pricing strategies for mobile users; in Stage III, the mobile users make their own decisions on video watching strategies for each video website. We analyze the equilibrium of each sub-game. Particularly, we derive the closed-form solutions of each mobile user's optimal video watching strategies, each video website's optimal membership price and the optimal advertising spaces selling number. In addition, we also investigate the piece-wise structure of the advertiser's utility function, and further propose an efficient algorithm to obtain the optimal advertising budget. Finally, numerical results show the impacts of different parameters' values on each entity's utility as well as the key indicators.

cs.NI↗

arXiv2018

Learning Large-Scale Bayesian Networks with the sparsebn Package

Learning graphical models from data is an important problem with wide applications, ranging from genomics to the social sciences. Nowadays datasets often have upwards of thousands---sometimes tens or hundreds of thousands---of variables and far fewer samples. To meet this challenge, we have developed a new R package called sparsebn for learning the structure of large, sparse graphical models with a focus on Bayesian networks. While there are many existing software packages for this task, this package focuses on the unique setting of learning large networks from high-dimensional data, possibly with interventions. As such, the methods provided place a premium on scalability and consistency in a high-dimensional setting. Furthermore, in the presence of interventions, the methods implemented here achieve the goal of learning a causal network from data. Additionally, the sparsebn package is fully compatible with existing software packages for network analysis.

stat.ML↗

arXiv2018

Penalized Estimation of Directed Acyclic Graphs From Discrete Data

Bayesian networks, with structure given by a directed acyclic graph (DAG), are a popular class of graphical models. However, learning Bayesian networks from discrete or categorical data is particularly challenging, due to the large parameter space and the difficulty in searching for a sparse structure. In this article, we develop a maximum penalized likelihood method to tackle this problem. Instead of the commonly used multinomial distribution, we model the conditional distribution of a node given its parents by multi-logit regression, in which an edge is parameterized by a set of coefficient vectors with dummy variables encoding the levels of a node. To obtain a sparse DAG, a group norm penalty is employed, and a blockwise coordinate descent algorithm is developed to maximize the penalized likelihood subject to the acyclicity constraint of a DAG. When interventional data are available, our method constructs a causal network, in which a directed edge represents a causal relation. We apply our method to various simulated and real data sets. The results show that our method is very competitive, compared to many existing methods, in DAG estimation from both interventional and high-dimensional observational data.

stat.ME↗

arXiv2017

Smaller desert dust cooling effect estimated from analysis of dust size and abundance

Desert dust aerosols affect Earth's global energy balance through direct interactions with radiation, and through indirect interactions with clouds and ecosystems. But the magnitudes of these effects are so uncertain that it remains unclear whether atmospheric dust has a net warming or cooling effect on global climate. Consequently, it is still uncertain whether large changes in atmospheric dust loading over the past century have slowed or accelerated anthropogenic climate change, or what the effects of potential future changes in dust loading will be. Here we present an analysis of the size and abundance of dust aerosols to constrain the direct radiative effect of dust. Using observational data on dust abundance, in situ measurements of dust optical properties and size distribution, and climate and atmospheric chemical transport model simulations of dust lifetime, we find that the dust found in the atmosphere is substantially coarser than represented in current global climate models. Since coarse dust warms climate, the global dust direct radiative effect is likely to be less cooling than the ~-0.4 W/m2 estimated by models in a current global aerosol model ensemble. Instead, we constrain the dust direct radiative effect to a range between -0.48 and +0.20 W/m2, which includes the possibility that dust causes a net warming of the planet.

physics.ao-ph↗

arXiv2017

Learning Directed Acyclic Graphs with Penalized Neighbourhood Regression

We study a family of regularized score-based estimators for learning the structure of a directed acyclic graph (DAG) for a multivariate normal distribution from high-dimensional data with $p\gg n$. Our main results establish support recovery guarantees and deviation bounds for a family of penalized least-squares estimators under concave regularization without assuming prior knowledge of a variable ordering. These results apply to a variety of practical situations that allow for arbitrary nondegenerate covariance structures as well as many popular regularizers including the MCP, SCAD, $\ell_{0}$ and $\ell_{1}$. The proof relies on interpreting a DAG as a recursive linear structural equation model, which reduces the estimation problem to a series of neighbourhood regressions. We provide a novel statistical analysis of these neighbourhood problems, establishing uniform control over the superexponential family of neighbourhoods associated with a Gaussian distribution. We then apply these results to study the statistical properties of score-based DAG estimators, learning causal DAGs, and inferring conditional independence relations via graphical models. Our results yield---for the first time---finite-sample guarantees for structure learning of Gaussian DAGs in high-dimensions via score-based estimation.

math.ST↗

arXiv2017

Uncertainty Quantification Under Group Sparsity

Quantifying the uncertainty in penalized regression under group sparsity is an important open question. We establish, under a high-dimensional scaling, the asymptotic validity of a modified parametric bootstrap method for the group lasso, assuming a Gaussian error model and mild conditions on the design matrix and the true coefficients. Simulation of bootstrap samples provides simultaneous inferences on large groups of coefficients. Through extensive numerical comparisons, we demonstrate that our bootstrap method performs much better than popular competitors, highlighting its practical utility. The theoretical result is generalized to other block norm penalization and sub-Gaussian errors, which further broadens the potential applications.

math.ST↗

arXiv2017

VMDV: A 3D Visualization Tool for Modeling, Demonstration, and Verification

The output of an automated theorem prover is usually presented by using a text format, they are often too heavy to be understood. In model checking setting, it would be helpful if one can observe the structure of models and the verification procedures. A 3D visualization tool (\textsf{VMDV}) is proposed in this paper to address these problems. The facility of \vmdv is illustrated by applying it to a proof systems.

cs.LO↗

arXiv2016

Estimator Augmentation with Applications in High-Dimensional Group Inference

To make inference about a group of parameters on high-dimensional data, we develop the method of estimator augmentation for the block Lasso, which is defined via the block norm. By augmenting a block Lasso estimator $\hatβ$ with the subgradient $S$ of the block norm evaluated at $\hatβ$, we derive a closed-form density for the joint distribution of $(\hatβ,S)$ under a high-dimensional setting. This allows us to draw from an estimated sampling distribution of $\hatβ$, or more generally any function of $(\hatβ,S)$, by Monte Carlo algorithms. We demonstrate the application of estimator augmentation in group inference with the group Lasso and a de-biased group Lasso constructed as a function of $(\hatβ,S)$. Our numerical results show that importance sampling via estimator augmentation can be orders of magnitude more efficient than parametric bootstrap in estimating tail probabilities for significance tests. This work also brings new insights into the geometry of the sample space and the solution uniqueness of the block Lasso.

stat.ME↗

arXiv2015

Energy-Efficient Data Transmission with A Non-FIFO Packet

This paper investigates the problem of energy-efficient packet transmission with a non-FIFO Packet over a point-to-point additive white Gaussian noise (AWGN) time-invariant channel under the feasibility constraints. More specifically, we consider the scenario where there is a packet that has a deadline that is earlier than that of the previously arrived packet. For this problem, the First-In-First-Out (FIFO) transmission mode adopted in the existing literatures is no longer optimal. We first propose a novel packet split and reorder process which convert the inconsistency in the order of deadlines and arrival instants of the packet sequence into a consistent one. After the split and reorder process, the original problem considered in this paper is transformed into the problem of finding the optimal split factor. We propose an algorithm that finds the split factor which consists of checking four possibilities by applying the existing optimal transmission strategy \emph{"String Tautening"} for FIFO packets. In addition, we prove the optimality of the proposed algorithm in the presence of a non-FIFO packet by exploiting the optimality properties of the most energy efficient transmission strategy. Based on the proposed optimal offline scheme, an efficient online policy which assumes causal arrival information is also studied and shown to achieve a comparable performance to the proposed optimal offline scheme.

cs.NI↗

arXiv2015

Learning-Based Distributed Detection-Estimation in Sensor Networks with Unknown Sensor Defects

We consider the problem of distributed estimation of an unknown deterministic scalar parameter (the target signal) in a wireless sensor network (WSN), where each sensor receives a single snapshot of the field. We assume that the observation at each node randomly falls into one of two modes: a valid or an invalid observation mode. Specifically, mode one corresponds to the desired signal plus noise observation mode (\emph{valid}), and mode two corresponds to the pure noise mode (\emph{invalid}) due to node defect or damage. With no prior information on such local sensing modes, we introduce a learning-based distributed procedure, called the mixed detection-estimation (MDE) algorithm, based on iterative closed-loop interactions between mode learning (detection) and target estimation. The online learning step re-assesses the validity of the local observations at each iteration, thus refining the ongoing estimation update process. The convergence of the MDE algorithm is established analytically. Asymptotic analysis shows that, in the high signal-to-noise ratio (SNR) regime, the MDE estimation error converges to that of an ideal (centralized) estimator with perfect information about the node sensing modes. This is in contrast to the estimation performance of a naive average consensus based distributed estimator (without mode learning), whose estimation error blows up with an increasing SNR.

cs.IT↗