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PRIMAL-GMM: PaRametrIc MAnifold Learning of Gaussian Mixture Models

IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE 2022年第6期44卷 3197-3211页

作者： Liu, Ziquan Yu, Lei Hsiao, Janet H. Chan, Antoni B. City Univ Hong Kong Dept Comp Sci Kowloon Hong Kong Peoples R China Univ Hong Kong Dept Stat & Actuarial Sci Pok Fu Lam Hong Kong Peoples R China Univ Hong Kong Dept Psychol Pok Fu Lam Hong Kong Peoples R China

We propose a ParametRIc MAnifold Learning (PRIMAL) algorithm for Gaussian mixtures models (GMM), assuming that GMMs lie on or near to a manifold of probability distributions that is generated from a low-dimensional hierarchical latent space through parametric mappings. Inspired by principal component analysis (PCA), the generative processes for priors, means and covariance matrices are modeled by their respective latent space and parametric mapping. Then, the dependencies between latent spaces are captured by a hierarchical latent space by a linear or kernelized mapping. The function parameters and hierarchical latent space are learned by minimizing the reconstruction error between ground-truth GMMs and manifold-generated GMMs, measured by Kullback-Leibler Divergence (KLD). Variational approximation is employed to handle the intractable KLD between GMMs and a variational EM algorithm is derived to optimize the objective function. Experiments on synthetic data, flow cytometry analysis, eye-fixation analysis and topic models show that PRIMAL learns a continuous and interpretable manifold of GMM distributions and achieves a minimum reconstruction error.

关键词： Manifolds Hidden Markov models Kernel Data models Probabilistic logic approximation algorithms Analytical models Dimensionality reduction and manifold learning Gaussian mixture models interpretability unsupervised learning probabilistic models

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Secure Deterministic Wallet and Stealth Address: Key-Insulated and Privacy-Preserving Signature Scheme With Publicly Derived Public Key

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IEEE TRANSACTIONS ON DEPENDABLE AND SECURE COMPUTING 2022年第5期19卷 2934-2951页

作者： Liu, Zhen Yang, Guomin Wong, Duncan S. Khoa Nguyen Wang, Huaxiong Ke, Xiaorong Liu, Yining Shanghai Jiao Tong Univ Shanghai 200240 Peoples R China Univ Wollongong Wollongong NSW 2522 Australia CryptoBLK Hong Kong Peoples R China Nanyang Technol Univ Sch Phys & Math Sci Singapore 639798 Singapore Huawei Technol Co Ltd Shenzhen 518129 Peoples R China Univ Southern Calif Los Angeles CA 90007 USA

Deterministic Wallet (DW) and Stealth Address (SA) mechanisms have been widely adopted in the cryptocurrency community, due to their virtues on functionality and privacy protection, which come from a key derivation mechanism that allows an arbitrary number of derived keys to be generated from a master key. However, these algorithms suffer a vulnerability that, when one derived key is compromised somehow, the damage is not limited to the leaked derived key only, but to the master key and in consequence all derived keys are compromised. In this article, we introduce and formalize a new signature variant, called Key-Insulated and Privacy-Preserving Signature Scheme with Publicly Derived Public Key (PDPKS), which fully captures and improves the functionality, security, and privacy requirements of DW and SA. We propose a PDPKS construction and prove its security and privacy in the random oracle model. Furthermore, we implement the construction with parameters for 128-bit security, and the results show that it is practically efficient for the setting of cryptocurrencies. With its solid guarantee on functionality, security and privacy, as well as its practical efficiency, our PDPKS construction provides a practical cryptographic tool that refines DW and SA, without security vulnerability.

关键词： Public key Privacy Companies Bitcoin Digital signatures approximation algorithms Solids Signature scheme publicly derived public key key-insulated security privacy cryptocurrency stealth addresses deterministic wallets

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Macroscopic Analysis of Vector Approximate Message Passing in a Model-Mismatched Setting

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IEEE TRANSACTIONS ON INFORMATION THEORY 2022年第8期68卷 5579-5600页

作者： Takahashi, Takashi Kabashima, Yoshiyuki Univ Tokyo Grad Sch Sci Inst Phys Intelligence Dept Phys Bunkyo City Tokyo 1130033 Japan

In this study, macroscopic properties of the vector approximate message passing (VAMP) algorithm for inference of generalized linear models are investigated using a non-rigorous heuristic method of statistical mechanics when the true posterior cannot be used and the measurement matrix is a sample from rotation-invariant random matrix ensembles. The focus is on the correspondence between the non-rigorous replica analysis of statistical mechanics and the performance assessment of VAMP in the model-mismatched setting. The correspondence of this kind is well-known when the measurement matrix has independent and identically distributed entries. However, when the measurement matrix follows a general rotation-invariant matrix ensemble, the correspondence has been validated only under limited cases, such as the Bayes optimal inference or the convex empirical risk minimization. The result presented in this paper is to extend the scope of such correspondence. Herein, we heuristically derive the explicit formula of state-evolution equations, which macroscopically describe VAMP dynamics for the current model-mismatched case, and show that their fixed point is generally consistent with the replica symmetric solution obtained by the replica method of statistical mechanics. We also show that the fixed point of VAMP can exhibit a microscopic instability, which indicates that message variables continue to move by VAMP while their macroscopically summarized quantities converge to fixed values. The critical condition the for microscopic instability agrees with that for breaking the replica symmetry that is derived within the non-rigorous replica analysis. The results of the numerical experiments cross-check our findings.

关键词： Mathematical models Analytical models approximation algorithms Message passing Heuristic algorithms Inference algorithms Rotation measurement Message passing algorithms inference algorithms random matrices statistical mechanics phase transitions compressive sensing

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Event-Triggered Consensus Control for Nonlinear Multiagent Systems With Unmeasured State Variables

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IEEE ACCESS 2022年 10卷 77030-77038页

作者： Li, Fei Yang, Fangyan Li, Qingdu Univ Shanghai Sci & Technol Sch Mech Engn Shanghai 200093 Peoples R China Univ Shanghai Sci & Technol Inst Machine Intelligence Shanghai 200093 Peoples R China

This article is concerned with event-triggered consensus control for nonlinear multi-agent systems with unknown nonlinear functions, unmatched disturbances, and unmeasured state variables. A novel distributed control algorithm is designed for high-order nonlinear multi-agent systems by using input-driven filters and defining dynamic feedback systems. In addition, the salient features of the proposed control algorithm are highlighted as follows: 1) our proposed control algorithm employs only local information from itself and its neighboring agents, 2) only a binary signal is transmitted to the actuator during the control process, and 3) the proposed control scheme avoids the use of approximate structures and lacks complex calculations. Finally, the simulation of the inverted pendulum verifies the validity of our theoretical findings.

关键词： Multi-agent systems Heuristic algorithms Output feedback approximation algorithms Consensus control Costs Backstepping Multi-agent systems output feedback event-triggered binary signals

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Robust Policy Iteration for Continuous-Time Linear Quadratic Regulation

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2022年第1期67卷 504-511页

作者： Pang, Bo Bian, Tao Jiang, Zhong-Ping NYU Tandon Sch Engn Dept Elect & Comp Engn Control & Networks Lab Brooklyn NY 11201 USA Bank Amer Merrill Lynch New York NY 10036 USA

This article studies the robustness of policy iteration in the context of continuous-time infinite-horizon linear quadratic regulator (LQR) problem. It is shown that Kleinman's policy iteration algorithm is small-disturbance input-to-state stable, a property that is stronger than Sontag's local input-to-state stability but weaker than global input-to-state stability. More precisely, whenever the error in each iteration is bounded and small, the solutions of the policy iteration algorithm are also bounded and enter a small neighborhood of the optimal solution of the LQR problem. Based on this result, an off-policy data-driven policy iteration algorithm for the LQR problem is shown to be robust when the system dynamics are subject to small additive unknown bounded disturbances. The theoretical results are validated by a numerical example.

关键词： Robustness Biological system modeling Optimal control Numerical stability Heuristic algorithms approximation algorithms Symmetric matrices Adaptive dynamic programming adaptive optimal control data-driven control policy iteration reinforcement learning robustness

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Online Service Function Chain Placement for Cost-Effectiveness and Network Congestion Control

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IEEE TRANSACTIONS ON COMPUTERS 2022年第1期71卷 27-39页

作者： Shang, Xiaojun Liu, Zhenhua Yang, Yuanyuan Stony Brook Univ 12301 Stony Brook NY 11794 USA

The emerging network function virtualization is migrating traditional middleboxes, e.g., firewalls, load balancers, proxies, from dedicated hardware to virtual network functions (VNFs) running on commercial servers defined as network points of presence (N-PoPs). VNFs further chain up for more complex network services called service function chains (SFCs). SFCs introduce new flexibility and scalability which greatly reduce expenses and rolling out time of network services. However, chasing the lowest cost may lead to congestion on popular N-PoPs and links, thus resulting in performance degradation or violation of service-level agreements. To address this problem, we propose a novel scheme that reduces the operating cost and controls network congestion at the same time. It does so by placing VNFs and routing flows among them jointly. Given the problem is NP-hard, we design an approximation algorithm named candidate path selection (CPS) with a theoretical performance guarantee. We then consider cases when SFC demands fluctuate frequently. We propose an online candidate path selection (OCPS) algorithm to handle such cases considering the VNF migration cost. OCPS is designed to preserve good performance under various migration costs and prediction errors. Extensive simulation results highlight that CPS and OCPS algorithms perform better than baselines and comparably to the optimal solution.

关键词： Routing Prediction algorithms Bandwidth approximation algorithms Servers Optimization Hardware Cloud computing virtual network function service function chain network congestion load balancing

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algorithms for Persuasion with Limited Communication

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MATHEMATICS OF OPERATIONS RESEARCH 2022年第3期47卷 1707-2545, C2页

作者： Gradwohl, Ronen Hahn, Niklas Hoefer, Martin Smorodinsky, Rann Ariel Univ Dept Econ & Business Adm IL-40700 Ariel Israel Goethe Univ Frankfurt Inst Comp Sci D-60325 Frankfurt Germany Technion Fac Ind Engn & Management IL-3200003 Haifa Israel

The Bayesian persuasion paradigm of strategic communication models interaction between a privately informed sender and an ignorant but rational receiver. The goal is typically to design a (near-)optimal communication (or signaling) scheme for the sender. It enables the sender to disclose information to the receiver in a way as to incentivize her to take an action that is preferred by the sender. Finding the optimal signaling scheme is known to be computationally difficult in general. This hardness is further exacerbated when the message space is constrained, leading to NP-hardness of approximating the optimal sender utility within any constant factor. In this paper, we show that in several natural and prominent cases the optimization problem is tractable even when the message space is limited. In particular, we study signaling under a symmetry or an independence assumption on the distribution of utility values for the actions. For symmetric distributions, we provide a novel characterization of the optimal signaling scheme. It results in a polynomial-time algorithm to compute an optimal scheme for many compactly represented symmetric distributions. In the independent cage, we design a constant-factor approximation algorithm, which stands in marked contrast to the hardness of approximation in the general case.

关键词： persuasion approximation algorithms

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A Novel Approximate Spectral Clustering Algorithm With Dense Cores and Density Peaks

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IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS 2022年第4期52卷 2348-2360页

作者： Cheng, Dongdong Huang, Jinlong Zhang, Sulan Zhang, Xiaohua Luo, Xin Yangtze Normal Univ Coll Big Data & Intelligent Engn Chongqing 408100 Peoples R China Hiroshima Inst Technol Dept Informat & Commun Hiroshima 7315193 Japan Chinese Acad Sci Chongqing Key Lab Big Data & Intelligent Comp Chongqing 400714 Peoples R China Chinese Acad Sci Chongqing Inst Green & Intelligent Technol Chongqing Engn Res Ctr Big Data Applicat Smart Ci Chongqing 400714 Peoples R China Univ Chinese Acad Sci Chongqing Sch Chongqing 400714 Peoples R China

Spectral clustering is becoming more and more popular because it has good performance in discovering clusters with varying characteristics. However, it suffers from high computational cost, unstable clustering results and noises. This work presents a novel approximate spectral clustering based on dense cores and density peaks, called DCDP-ASC. It first finds a reduced data set by introducing the concept of dense cores;then defines a new distance based on the common neighborhood of dense cores and calculates geodesic distances between dense cores according to the new defined distance;after that constructs a decision graph with a parameter-free local density and geodesic distance for obtaining initial centers;finally calculates the similarity between dense cores with their new defined geodesic distance, employs normalized spectral clustering method to divide dense cores, and expands the result on dense cores to the whole data set by assigning each point to its representative. The results on some challenging data sets and the comparison of our algorithm with some other excellent methods demonstrate that the proposed method DCDP-ASC is more advantageous in identifying complex structured clusters containing a lot of noises.

关键词： Clustering algorithms Manifolds Matrix decomposition Sparse matrices Partitioning algorithms approximation algorithms Level measurement Approximate spectral clustering common neighborhood-based distance dense cores density peaks geodesic distance

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Maximizing User Service Satisfaction for Delay-Sensitive IoT Applications in Edge Computing

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IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS 2022年第5期33卷 1199-1212页

作者： Li, Jing Liang, Weifa Xu, Wenzheng Xu, Zichuan Jia, Xiaohua Zhou, Wanlei Zhao, Jin Australian Natl Univ Sch Comp Canberra ACT 2601 Australia City Univ Hong Kong Dept Comp Sci Kowloon Hong Kong Peoples R China Sichuan Univ Coll Comp Sci Chengdu 610065 Sichuan Peoples R China Dalian Univ Technol Sch Software Dalian 116024 Liaoning Peoples R China City Univ Macau Inst Data Sci Macau 999078 Peoples R China Fudan Univ Sch Comp Sci Shanghai 200433 Peoples R China Fudan Univ Shanghai Key Lab Intelligent Informat Proc Shanghai 200433 Peoples R China

The Internet of Things (IoT) technology provisions unprecedented opportunities to evolve the interconnection among human beings. However, the latency brought by unstable wireless networks and computation failures caused by limited resources on IoT devices prevents users from experiencing high efficiency and seamless user experience. To address these shortcomings, the integrated Mobile Edge Computing (MEC) with remote clouds is a promising platform to enable delay-sensitive service provisioning for IoT applications, where edge-clouds (cloudlets) are co-located with wireless access points in the proximity of IoT devices. Thus, computation-intensive and sensing data from IoT devices can be offloaded to the MEC network immediately for processing, and the service response latency can be significantly reduced. In this paper, we first formulate two novel optimization problems for delay-sensitive IoT applications, i.e., the total utility maximization problems under both static and dynamic offloading task request settings, with the aim to maximize the accumulative user satisfaction on the use of the services provided by the MEC, and show the NP-hardness of the defined problems. We then devise efficient approximation and online algorithms with provable performance guarantees for the problems in a special case where the bandwidth capacity constraint is negligible. We also develop efficient heuristic algorithms for the problems with the bandwidth capacity constraint. We finally evaluate the performance of the proposed algorithms through experimental simulations. Experimental results demonstrate that the proposed algorithms are promising in reducing service delays and enhancing user satisfaction, and the proposed algorithms outperform their counterparts by at least 10.8 percent.

关键词： Internet of Things Task analysis Cloud computing Delays Heuristic algorithms approximation algorithms Bandwidth Cost modeling resource optimization and allocation service provisioning delay-sensitive IoT applications maximum profit generalized assignment problems approximation algorithms online algorithms task offloading and scheduling service delay user satisfaction of using services mobile edge computing (MEC)

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Enclosing Points with Geometric Objects 40

Enclosing Points with Geometric Objects

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40th International Symposium on Computational Geometry, SoCG 2024

作者： Chan, Timothy M. He, Qizheng Xue, Jie Department of Computer Science University of Illinois Urbana-Champaign IL United States Department of Computer Science New York University Shanghai China

ISBN: (纸本)9783959773164

Let X be a set of points in R2 and O be a set of geometric objects in R2, where |X| + |O| = n. We study the problem of computing a minimum subset O∗ ⊆ O that encloses all points in X. Here a point x ∈ X is enclosed by O∗ if it lies in a bounded connected component of R2\(SO∈O∗ O). We propose two algorithmic frameworks to design polynomial-time approximation algorithms for the problem. The first framework is based on sparsification and min-cut, which results in O(1)approximation algorithms for unit disks, unit squares, etc. The second framework is based on LP rounding, which results in an O(α(n) log n)-approximation algorithm for segments, where α(n) is the inverse Ackermann function, and an O(log n)-approximation algorithm for disks. © Timothy M. Chan, Qizheng He, and Jie Xue.

关键词： approximation algorithms

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