arXiv subjects

Yu Xing

Publications and source records attributed to Yu Xing.

36 records · Page 2Linked to original sources

arXiv2024

On final opinions of the Friedkin-Johnsen model over random graphs with partially stubborn community

This paper studies the formation of final opinions for the Friedkin-Johnsen (FJ) model with a community of partially stubborn agents. The underlying network of the FJ model is symmetric and generated from a random graph model, in which each link is added independently from a Bernoulli distribution. It is shown that the final opinions of the FJ model will concentrate around those of an FJ model over the expected graph as the network size grows, on the condition that the stubborn agents are well connected to other agents. Probability bounds are proposed for the distance between these two final opinion vectors, respectively for the cases where there exist non-stubborn agents or not. Numerical experiments are provided to illustrate the theoretical findings. The simulation shows that, in presence of non-stubborn agents, the link probability between the stubborn and the non-stubborn communities affect the distance between the two final opinion vectors significantly. Additionally, if all agents are stubborn, the opinion distance decreases with the agent stubbornness.

eess.SY↗

arXiv2024

Concentration in Gossip Opinion Dynamics over Random Graphs

We study concentration inequalities in gossip opinion dynamics over random graphs. In the model, a network is generated from a random graph model with independent edges, and agents interact pairwise randomly over the network. During the process, regular agents average neighbors' opinions and then update, whereas stubborn agents do not change opinions. To approximate the original process, we introduce a gossip model over an expected graph, obtained by averaging all possible networks generated from the random graph model. Using concentration inequalities, we derive high-probability bounds for the distance between the expected final opinion vectors over the random graph and over the expected graph. Leveraging matrix perturbation results, we show how such concentration can help study the effect of network structure on the expected final opinions in two cases: (i) When the influence of stubborn agents is large, the expected final opinions polarize and are close to stubborn agents' opinions. (ii) When the influence of stubborn agents is small, the expected final opinions are close to each other. With the help of concentration inequalities for Markov chains, we obtain high-probability bounds for the distance between time-averaged opinions and the expected final opinions over the expected graph. In simulation, we validate the theoretical findings, and study a gossip model over a stochastic block model that has community structure.

eess.SY↗

arXiv2023

Transient Behavior of Gossip Opinion Dynamics with Community Structure

We study transient behavior of gossip opinion dynamics, in which agents randomly interact pairwise over a weighted graph with two communities. Edges within a community have identical weights different from edge weights between communities. We first derive an upper bound for the second moment of agent opinions. Using this bound, we obtain upper bounds for probability that a large proportion of agents have opinions close to average ones. The results imply a phase transition of transient behavior of the process: When edge weights within communities are larger than those between communities and those between regular and stubborn agents, most agents in the same community hold opinions close to the average opinion of that community with large probability, at an early stage of the process. However, if the difference between intra- and inter-community weights is small, most of the agents instead hold opinions close to everyone's average opinion at the early stage. In contrast, when the influence of stubborn agents is large, agent opinions settle quickly to steady state. We then conduct numerical experiments to validate the theoretical results. Different from traditional asymptotic analysis in most opinion dynamics literature, the paper characterizes the influences of stubborn agents and community structure on the initial phase of the opinion evolution.

physics.soc-ph↗

arXiv2023

Almost Exact Recovery in Gossip Opinion Dynamics over Stochastic Block Models

We study community detection based on state observations from gossip opinion dynamics over stochastic block models (SBM). It is assumed that a network is generated from a two-community SBM where each agent has a community label and each edge exists with probability depending on its endpoints' labels. A gossip process then evolves over the sampled network. We propose two algorithms to detect the communities out of a single trajectory of the process. It is shown that, when the influence of stubborn agents is small and the link probability within communities is large, an algorithm based on clustering transient agent states can achieve almost exact recovery of the communities. That is, the algorithm can recover all but a vanishing part of community labels with high probability. In contrast, when the influence of stubborn agents is large, another algorithm based on clustering time average of agent states can achieve almost exact recovery. Numerical experiments are given for illustration of the two algorithms and the theoretical results of the paper.

eess.SY↗

arXiv2023

Community Structure Recovery and Interaction Probability Estimation for Gossip Opinion Dynamics

We study how to jointly recover the community structure and estimate the interaction probabilities of gossip opinion dynamics. In this process, agents randomly interact pairwise, and there are stubborn agents never changing their states. Such a model illustrates how disagreement and opinion fluctuation arise in a social network. It is assumed that each agent is assigned with one of two community labels, and the agents interact with probabilities depending on their labels. The considered problem is to jointly recover the community labels of the agents and estimate interaction probabilities between the agents, based on a single trajectory of the model. We first study stability and limit theorems of the model, and then propose a joint recovery and estimation algorithm based on a trajectory. It is verified that the community recovery can be achieved in finite time, and the interaction estimator converges almost surely. We derive a sample-complexity result for the recovery, and analyze the estimator's convergence rate. Simulations are presented for illustration of the performance of the proposed algorithm.

eess.SY↗

arXiv2023

Joint Learning of Network Topology and Opinion Dynamics Based on Bandit Algorithms

We study joint learning of network topology and a mixed opinion dynamics, in which agents may have different update rules. Such a model captures the diversity of real individual interactions. We propose a learning algorithm based on multi-armed bandit algorithms to address the problem. The goal of the algorithm is to find each agent's update rule from several candidate rules and to learn the underlying network. At each iteration, the algorithm assumes that each agent has one of the updated rules and then modifies network estimates to reduce validation error. Numerical experiments show that the proposed algorithm improves initial estimates of the network and update rules, decreases prediction error, and performs better than other methods such as sparse linear regression and Gaussian process regression.

cs.SI↗

arXiv2023

What is the Expected Transient Behavior of Opinion Evolution for Two Communities?

We study the transient behavior of a gossip model, in which agents randomly interact pairwise over a weighted graph with two communities. Edges within each community have identical weights, different from the weights between communities. It is shown that, at the early stage of the opinion evolution, the expected agent states in the same community have identical sign, despite influence of stubborn agents. Moreover, it is shown that the expected states of the agents in the same community concentrate around the initial average opinion of that community, if the weights within communities are larger than between. In contrast, if the edge weights between communities are larger, then the expected states of all agents concentrate around everyone's initial average opinion. Different from the traditional asymptotic analysis in the opinion dynamics literature, these results focus on the initial phase of opinion evolution and establish a correspondence between community structure and transient behavior of the gossip model. The results are illustrated by numerical examples.

eess.SY↗

arXiv2022

Identification of Linear Systems with Multiplicative Noise from Multiple Trajectory Data

The paper studies identification of linear systems with multiplicative noise from multiple-trajectory data. An algorithm based on the least-squares method and multiple-trajectory data is proposed for joint estimation of the nominal system matrices and the covariance matrix of the multiplicative noise. The algorithm does not need prior knowledge of the noise or stability of the system, but requires only independent inputs with pre-designed first and second moments and relatively small trajectory length. The study of identifiability of the noise covariance matrix shows that there exists an equivalent class of matrices that generate the same second-moment dynamic of system states. It is demonstrated how to obtain the equivalent class based on estimates of the noise covariance. Asymptotic consistency of the algorithm is verified under sufficiently exciting inputs and system controllability conditions. Non-asymptotic performance of the algorithm is also analyzed under the assumption that the system is bounded. The analysis provides high-probability bounds vanishing as the number of trajectories grows to infinity. The results are illustrated by numerical simulations.

eess.SY↗

arXiv2022

On the Convergence of mSGD and AdaGrad for Stochastic Optimization

As one of the most fundamental stochastic optimization algorithms, stochastic gradient descent (SGD) has been intensively developed and extensively applied in machine learning in the past decade. There have been some modified SGD-type algorithms, which outperform the SGD in many competitions and applications in terms of convergence rate and accuracy, such as momentum-based SGD (mSGD) and adaptive gradient algorithm (AdaGrad). Despite these empirical successes, the theoretical properties of these algorithms have not been well established due to technical difficulties. With this motivation, we focus on convergence analysis of mSGD and AdaGrad for any smooth (possibly non-convex) loss functions in stochastic optimization. First, we prove that the iterates of mSGD are asymptotically convergent to a connected set of stationary points with probability one, which is more general than existing works on subsequence convergence or convergence of time averages. Moreover, we prove that the loss function of mSGD decays at a certain rate faster than that of SGD. In addition, we prove the iterates of AdaGrad are asymptotically convergent to a connected set of stationary points with probability one. Also, this result extends the results from the literature on subsequence convergence and the convergence of time averages. Despite the generality of the above convergence results, we have relaxed some assumptions of gradient noises, convexity of loss functions, as well as boundedness of iterates.

cs.LG↗

arXiv2021

Event-Triggered Distributed Estimation With Decaying Communication Rate

We study distributed estimation of a high-dimensional static parameter vector through a group of sensors whose communication network is modeled by a fixed directed graph. Different from existing time-triggered communication schemes, an event-triggered asynchronous scheme is investigated in order to reduce communication while preserving estimation convergence. A distributed estimation algorithm with a single step size is first proposed based on an event-triggered communication scheme with a time-dependent decaying threshold. With the event-triggered scheme, each sensor sends its estimate to neighbor sensors only when the difference between the current estimate and the last sent-out estimate is larger than the triggering threshold. We prove that the proposed algorithm has mean-square and almost-sure convergence respectively, under an integrated condition of sensor network topology and sensor measurement matrices. The condition is satisfied if the topology is a balanced digraph containing a spanning tree and the system is collectively observable. Moreover, we provide estimates for the convergence rates, which are related to the step size as well as the triggering threshold. Furthermore, as an essential metric of sensor communication intensity in the event-triggered distributed algorithms, the communication rate is proved to decay to zero with a certain speed almost surely as time goes to infinity. We show that given the step size, adjusting the decay speed of the triggering threshold can lead to a tradeoff between the convergence rate of the estimation error and the decay speed of the communication rate. Specifically, increasing the decay speed of the threshold would make the communication rate decay faster, but reduce the convergence rate of the estimation error. Numerical simulations are provided to illustrate the developed results.

eess.SY↗

arXiv2020

Community Detection for Gossip Dynamics with Stubborn Agents

We consider a community detection problem for gossip dynamics with stubborn agents in this paper. It is assumed that the communication probability matrix for agent pairs has a block structure. More specifically, we assume that the network can be divided into two communities, and the communication probability of two agents depends on whether they are in the same community. Stability of the model is investigated, and expectation of stationary distribution is characterized, indicating under the block assumption, the stationary behaviors of agents in the same community are similar. It is also shown that agents in different communities display distinct behaviors if and only if state averages of stubborn agents in different communities are not identical. A community detection algorithm is then proposed to recover community structure and to estimate communication probability parameters. It is verified that the community detection part converges in finite time, and the parameter estimation part converges almost surely. Simulations are given to illustrate algorithm performance.

eess.SY↗

arXiv2020

Linear System Identification Under Multiplicative Noise from Multiple Trajectory Data

The study of multiplicative noise models has a long history in control theory but is re-emerging in the context of complex networked systems and systems with learning-based control. We consider linear system identification with multiplicative noise from multiple state-input trajectory data. We propose exploratory input signals along with a least-squares algorithm to simultaneously estimate nominal system parameters and multiplicative noise covariance matrices. Identifiability of the covariance structure and asymptotic consistency of the least-squares estimator are demonstrated by analyzing first and second moment dynamics of the system. The results are illustrated by numerical simulations.

eess.SY↗

arXiv2019

Recursive Network Estimation From Binary-Valued Observation Data

This paper studies the problem of recursively estimating the weighted adjacency matrix of a network out of a temporal sequence of binary-valued observations. The observation sequence is generated from nonlinear networked dynamics in which agents exchange and display binary outputs. Sufficient conditions are given to ensure stability of the observation sequence and identifiability of the system parameters. It is shown that stability and identifiability can be guaranteed under the assumption of independent standard Gaussian disturbances. Via a maximum likelihood approach, the estimation problem is transformed into an optimization problem, and it is verified that its solution is the true parameter vector under the independent standard Gaussian assumption. A recursive algorithm for the estimation problem is then proposed based on stochastic approximation techniques. Its strong consistency is established and convergence rate analyzed. Finally, numerical simulations are conducted to illustrate the results and to show that the proposed algorithm is insensitive to small unmodeled factors.

eess.SY↗

arXiv2019

A Novel User Representation Paradigm for Making Personalized Candidate Retrieval

Candidate retrieval is a fundamental issue in recommendation system. Given user's recommendation request, relevant candidates need to be retrieved in realtime for subsequent ranking operations. Considering that the retrieval operation is conducted over considerable items, it has to be both precise and scalable so that high-quality candidates can be acquired within tolerable latency. Unfortunately, conventional methods would trade off precision for high running efficiency, which leads to inferior retrieval quality. In contrast, those deep learning-based approaches can be highly accurate in identifying relevant items; yet, they are unsuitable for candidate retrieval due to their inherent limitation on scalability. In this work, a novel framework is proposed to address the above challenges. The underlying intuition is to rely on a well-trained ranking model for the supervision of an efficient retrieval model, such that it will unify the scalability and precision as a whole. We have implemented our conceptual framework and made comprehensive evaluation for it, where promising results are achieved against representative baselines. Our work is undergoing a anonymous review, and it will soon be released after the notification. If you're also interested in this problem, please feel free to contact us.

cs.IR↗

arXiv2019

DNNVM : End-to-End Compiler Leveraging Heterogeneous Optimizations on FPGA-based CNN Accelerators

The convolutional neural network (CNN) has become a state-of-the-art method for several artificial intelligence domains in recent years. The increasingly complex CNN models are both computation-bound and I/O-bound. FPGA-based accelerators driven by custom instruction set architecture (ISA) achieve a balance between generality and efficiency, but there is much on them left to be optimized. We propose the full-stack compiler DNNVM, which is an integration of optimizers for graphs, loops and data layouts, and an assembler, a runtime supporter and a validation environment. The DNNVM works in the context of deep learning frameworks and transforms CNN models into the directed acyclic graph: XGraph. Based on XGraph, we transform the optimization challenges for both the data layout and pipeline into graph-level problems. DNNVM enumerates all potentially profitable fusion opportunities by a heuristic subgraph isomorphism algorithm to leverage pipeline and data layout optimizations, and searches for the best choice of execution strategies of the whole computing graph. On the Xilinx ZU2 @330 MHz and ZU9 @330 MHz, we achieve equivalently state-of-the-art performance on our benchmarks by naïve implementations without optimizations, and the throughput is further improved up to 1.26x by leveraging heterogeneous optimizations in DNNVM. Finally, with ZU9 @330 MHz, we achieve state-of-the-art performance for VGG and ResNet50. We achieve a throughput of 2.82 TOPs/s and an energy efficiency of 123.7 GOPs/s/W for VGG. Additionally, we achieve 1.38 TOPs/s for ResNet50 and 1.41 TOPs/s for GoogleNet.

cs.DC↗

arXiv2019

Network Weight Estimation for Binary-Valued Observation Models

This paper studies the estimation of network weights for a class of systems with binary-valued observations. In these systems only quantized observations are available for the network estimation. Furthermore, system states are coupled with observations, and the quantization parts are unknown inherent components, which hinder the design of inputs and quantizers. To fulfill the estimation, we propose a recursive algorithm based on stochastic approximation techniques. More precisely, to deal with the temporal dependency of observations and achieve the recursive estimation of network weights, a deterministic objective function is constructed based on the likelihood function by extending the dimension of observations and applying ergodic properties of Markov chains. It is shown that this function is strictly concave and has unique maximum identical to the true parameter vector. Finally, the strong consistency of the algorithm is established. Our recursive algorithm can be applied to online tasks like real-time decision-making and surveillance for networked systems. This work also provides a new scheme for the identification of systems with quantized observations.

eess.SY↗

arXiv2018

A Strategic Learning Algorithm for State-based Games

Learning algorithm design for state-based games is investigated. A heuristic uncoupled learning algorithm, which is a two memory better reply with inertia dynamics, is proposed. Under certain reasonable conditions it is proved that for any initial state, if all agents in the state-based game follow the proposed learning algorithm, the action state pair converges almost surely to an action invariant set of recurrent state equilibria. The design relies on global and local searches with finite memory, inertia, and randomness. Finally, existence of time-efficient universal learning algorithm is studied. A class of state-based games is presented to show that there is no universal learning algorithm converging to a recurrent state equilibrium.

math.OC↗

arXiv2011

Broadband polarization transformation via enhanced asymmetric transmission through arrays of twisted complementary split-ring resonators

This study proposes an ultrathin chiral metamaterial slab stacked with twisted complementary split-ring resonators (CSRRs) for highly efficient broadband polarization transformation. The polarization of linearly polarized electromagnetic waves can be rotated in a specific direction by passing it through such a slab having a thickness of about one-tenth the operational wavelength. Microwave experiments verified the theoretically predicted conversion efficiency of up to 96% covering a bandwidth of 24% of the central wavelength. CSRRs with circular symmetry provide increased interlayer coupling strength, which produces a high-efficiency broadband response and strong isolation of the original polarization.

physics.optics↗