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Qing Han

Publications and source records attributed to Qing Han.

At least 55 records · Page 3Linked to original sources

Latent Dirichlet Allocation Model Training with Differential Privacy

Latent Dirichlet Allocation (LDA) is a popular topic modeling technique for hidden semantic discovery of text data and serves as a fundamental tool for text analysis in various applications. However, the LDA model as well as the training process of LDA may expose the text information in the training data, thus bringing significant privacy concerns. To address the privacy issue in LDA, we systematically investigate the privacy protection of the main-stream LDA training algorithm based on Collapsed Gibbs Sampling (CGS) and propose several differentially private LDA algorithms for typical training scenarios. In particular, we present the first theoretical analysis on the inherent differential privacy guarantee of CGS based LDA training and further propose a centralized privacy-preserving algorithm (HDP-LDA) that can prevent data inference from the intermediate statistics in the CGS training. Also, we propose a locally private LDA training algorithm (LP-LDA) on crowdsourced data to provide local differential privacy for individual data contributors. Furthermore, we extend LP-LDA to an online version as OLP-LDA to achieve LDA training on locally private mini-batches in a streaming setting. Extensive analysis and experiment results validate both the effectiveness and efficiency of our proposed privacy-preserving LDA training algorithms.

cs.LG↗

PDE-based Dynamic Density Estimation for Large-scale Agent Systems

Large-scale agent systems have foreseeable applications in the near future. Estimating their macroscopic density is critical for many density-based optimization and control tasks, such as sensor deployment and city traffic scheduling. In this paper, we study the problem of estimating their dynamically varying probability density, given the agents' individual dynamics (which can be nonlinear and time-varying) and their states observed in real-time. The density evolution is shown to satisfy a linear partial differential equation uniquely determined by the agents' dynamics. We present a density filter which takes advantage of the system dynamics to gradually improve its estimation and is scalable to the agents' population. Specifically, we use kernel density estimators (KDE) to construct a noisy measurement and show that, when the agents' population is large, the measurement noise is approximately ``Gaussian''. With this important property, infinite-dimensional Kalman filters are used to design density filters. It turns out that the covariance of measurement noise depends on the true density. This state-dependence makes it necessary to approximate the covariance in the associated operator Riccati equation, rendering the density filter suboptimal. The notion of input-to-state stability is used to prove that the performance of the suboptimal density filter remains close to the optimal one. Simulation results suggest that the proposed density filter is able to quickly recognize the underlying modes of the unknown density and automatically ignore outliers, and is robust to different choices of kernel bandwidth of KDE.

eess.SY↗

OL4EL: Online Learning for Edge-cloud Collaborative Learning on Heterogeneous Edges with Resource Constraints

Distributed machine learning (ML) at network edge is a promising paradigm that can preserve both network bandwidth and privacy of data providers. However, heterogeneous and limited computation and communication resources on edge servers (or edges) pose great challenges on distributed ML and formulate a new paradigm of Edge Learning (i.e. edge-cloud collaborative machine learning). In this article, we propose a novel framework of 'learning to learn' for effective Edge Learning (EL) on heterogeneous edges with resource constraints. We first model the dynamic determination of collaboration strategy (i.e. the allocation of local iterations at edge servers and global aggregations on the Cloud during collaborative learning process) as an online optimization problem to achieve the tradeoff between the performance of EL and the resource consumption of edge servers. Then, we propose an Online Learning for EL (OL4EL) framework based on the budget-limited multi-armed bandit model. OL4EL supports both synchronous and asynchronous learning patterns, and can be used for both supervised and unsupervised learning tasks. To evaluate the performance of OL4EL, we conducted both real-world testbed experiments and extensive simulations based on docker containers, where both Support Vector Machine and K-means were considered as use cases. Experimental results demonstrate that OL4EL significantly outperforms state-of-the-art EL and other collaborative ML approaches in terms of the trade-off between learning performance and resource consumption.

cs.DC↗

Exploring EOSIO via Graph Characterization

Designed for commercial decentralized applications (DApps), EOSIO is a Delegated Proof-of-Stake (DPoS) based blockchain system. It has overcome some shortages of the traditional blockchain systems like Bitcoin and Ethereum with its outstanding features (e.g., free for usage, high throughput and eco-friendly), and thus becomes one of the mainstream blockchain systems. Though there exist billions of transactions in EOSIO, the ecosystem of EOSIO is still relatively unexplored. To fill this gap, we conduct a systematic graph analysis on the early EOSIO by investigating its four major activities, namely account creation, account vote, money transfer and contract authorization. We obtain some novel observations via graph metric analysis, and our results reveal some abnormal phenomenons like voting gangs and sham transactions.

cs.SI↗

Asymptotic expansions of solutions of the Yamabe equation and the $σ_k$-Yamabe equation near isolated singular points

We study asymptotic behaviors of positive solutions to the Yamabe equation and the $σ$k-Yamabe equation near isolated singular points and establish expansions up to arbitrary orders. Such results generalize an earlier pioneering work by Caffarelli, Gidas, and Spruck, and a work by Korevaar, Mazzeo, Pacard, and Schoen, on the Yamabe equation, and a work by Han, Li, and Teixeira on the $σ_k$-Yamabe equation. The study is based on a combination of classification of global singular solutions and an analysis of linearized operators at these global singular solutions. Such linearized equations are uniformly elliptic near singular points for $1 \leq k \leq n/2$ and become degenerate for $n/2 < k \leq n$. In a significant portion of the paper, we establish a degree 1 expansion for the $σ_k$-Yamabe equation for $n/2 < k < n$, generalizing a similar result for $k = 1$ by Korevaar, Mazzeo, Pacard, and Schoen and for $2 \leq k \leq n/2$ by Han, Li, and Teixeira.

math.DG↗

An elementary proof of a result Ma and Chen

In 1956, Je$\acute{s}$manowicz conjectured that, for positive integers $m$ and $n$ with $m>n, \, \gcd(m,\, n)=1$ and $m\not\equiv n\pmod{2}$, the exponential Diophantine equation $(m^2-n^2)^x+(2mn)^y=(m^2+n^2)^z$ has only the positive integer solution $(x,\,y,\, z)=(2,\,2,\,2)$. Recently, Ma and Chen \cite{MC17} proved the conjecture if $4\not|mn$ and $y\ge2$. In this paper, we present an elementary proof of the result of Ma and Chen \cite{MC17}.

math.NT↗

The Conformal Flow of Metrics and the General Penrose Inequality

The conformal flow of metrics [2] has been used to successfully establish a special case of the Penrose inequality, which yields a lower bound for the total mass of a spacetime in terms of horizon area. Here we show how to adapt the conformal flow of metrics, so that it may be applied to the Penrose inequality for general initial data sets of the Einstein equations. The Penrose conjecture without the assumption of time symmetry is then reduced to solving a system of PDE with desirable properties.

gr-qc↗

The convergence of boundary expansions and the analyticity of minimal surfaces in the hyperbolic space

We study expansions near the boundary of solutions to the Dirichlet problem for minimal graphs in the hyperbolic space and prove the local convergence of such expansions if the boundary is locally analytic. As a consequence, we prove a conjecture by F.-H. Lin that the minimal graph is analytic up to the boundary if the boundary is analytic and the minimal graph is smooth up to the boundary.

math.AP↗

An invariant related to the existence of conformally compact Einstein fillings

We define an invariant for compact spin manifolds $X$ of dimension $4k$ equipped with a metric $h$ of positive Yamabe invariant on its boundary. The vanishing of this invariant is a necessary condition for the conformal class of $h$ to be the conformal infinity of a conformally compact Einstein metric on $X$.

math.DG↗

Asymptotics for Null-timelike Boundary Problems for General Linear Wave Equations

We study the linear wave equation $\Box_{g}u=0$ in Bondi-Sachs coordinates, for an asymptotically flat Lorentz metric $g$. We consider the null-timelike boundary problem, where an initial value is given on the null surface $τ=0$ and a boundary value on the timelike surface $r=r_{0}$. We obtain spacetime $H^{p}$-estimates of $ru$ for $r>r_0$ and derive an asymptotic exapnsion of $ru$ in terms of ${1}/{r}$ as $r\to\infty$.

math.AP↗

Boundary Behaviors for Liouville's Equation in Planar Singular Domains

We study asymptotic behaviors near the boundary of complete metrics of constant curvature in planar singular domains and establish an optimal estimate of these metrics by the corresponding metrics in tangent cones near isolated singular points on boundary. The conformal structure plays an essential role.

math.AP↗

Leak Event Identification in Water Systems Using High Order CRF

Today, detection of anomalous events in civil infrastructures (e.g. water pipe breaks and leaks) is time consuming and often takes hours or days. Pipe breakage as one of the most frequent types of failure of water networks often causes community disruptions ranging from temporary interruptions in services to extended loss of business and relocation of residents. In this project, we design and implement a two-phase approach for leak event identification, which leverages dynamic data from multiple information sources including IoT sensing data (pressure values and/or flow rates), geophysical data (water systems), and human inputs (tweets posted on Twitter). In the approach, a high order Conditional Random Field (CRF) is constructed that enforces predictions based on IoT observations consistent with human inputs to improve the performance of event identifications. Considering the physical water network as a graph, a CRF model is built and learned by the Structured Support Vector Machine (SSVM) using node features such as water pressure and flow rate. After that, we built the high order CRF system by enforcing twitter leakage detection information. An optimal inference algorithm is proposed for the adapted high order CRF model. Experimental results show the effectiveness of our system.

cs.LG↗

Poincaré-Einstein metrics and Yamabe invariants

In this note we prove the existence of infinitely many positive conformal classes on $S^7$ which cannot be the conformal infinity of a Poincaré-Einstein metric on the ball $B^8$. We also prove a sharp inequality between the Yamabe invariant of the conformal infinity and the Yamabe invariant of the interior (after a suitable compactification).

math.DG↗

Boundary Expansions for Constant Mean Curvature Surfaces in the Hyperbolic Space

We study expansions near the boundary of solutions to the Dirichlet problem for the constant mean curvature equation in the hyperbolic space. With a characterization of remainders of the expansion by multiple integrals, we establish optimal asymptotic expansions of solutions with boundary values of finite regularity and demonstrate a slight loss of regularity for coefficients.

math.AP↗

Minimal Graphs in the Hyperbolic Space with Singular Asymptotic Boundaries

We study asymptotic behaviors of solutions $f$ to the Dirichlet problem for minimal graphs in the hyperbolic space with singular asymptotic boundaries under the assumption that the boundaries are piecewise regular with positive curvatures. We derive an estimate of such solutions by the corresponding solutions in the intersections of interior tangent balls. The positivity of curvatures plays an important role.

math.AP↗

Prescribed Scaler Curvatures for Homogeneous Toric Bundles

In this paper, we study the generalized Abreu equation on a Delzant ploytope $Δ\subset \mathbb{R}^2$ and prove the existence of the constant scalar metrics of homogeneous toric bundles under the assumption of an appropriate stability.

math.DG↗

Optimal regularity of minimal graphs in the hyperbolic space

We discuss the global regularity of solutions $f$ to the Dirichlet problem for minimal graphs in the hyperbolic space when the boundary of the domain $Ω\subset\mathbb R^n$ has a nonnegative mean curvature and prove an optimal regularity $f\in C^{\frac{1}{n+1}}(\barΩ)$. We can improve the Hölder exponent for $f$ if certain combinations of principal curvatures of the boundary do not vanish, a phenomenon observed by F.-H. Lin.

math.AP↗