Graph signal processing (GSP) is a framework to analyze and process graph-structured data. Many r... more Graph signal processing (GSP) is a framework to analyze and process graph-structured data. Many research works focus on developing tools such as Graph Fourier transforms (GFT), filters, and neural network models to handle graph signals. Such approaches have successfully taken care of "signal processing" in many circumstances. In this paper, we want to put emphasis on "graph signals" themselves. Although there are characterizations of graph signals using the notion of bandwidth derived from GFT, we want to argue here that graph signals may contain hidden geometric information of the network, independent of (graph) Fourier theories. We shall provide a framework to understand such information, and demonstrate how new knowledge on "graph signals" can help with "signal processing".
Estimating Kullback-Leibler (KL) divergence from data samples is a strenuous task, with existing ... more Estimating Kullback-Leibler (KL) divergence from data samples is a strenuous task, with existing approaches either imposing restrictive assumptions on the domain knowledge of the underlying model or requiring density approximation like space partitioning. The use of kernel maximum mean discrepancy (MMD) yields an alternative non-parametric approach to compare two populations by finding the maximum mean difference generated by measurable functions in the unit ball in a reproducing kernel Hilbert space (RKHS). Predicated on the universal approximation of universal kernels, we propose two corresponding classes of functions in a RKHS that can bound the KL divergence from below and above, and derive the RKHS representations of these bounds. This allows us to develop asymptotically consistent estimates for the derived bounds. We evaluate the proposed bounds as mutual information proxies on an image dataset, and demonstrate that these bounds can stably track variations in mutual information.
2021 IEEE Statistical Signal Processing Workshop (SSP)
In this paper, we develop a signal processing framework of a network without explicit knowledge o... more In this paper, we develop a signal processing framework of a network without explicit knowledge of the network topology. Instead, we make use of knowledge on the distribution of operators on the network. This makes the framework flexible and useful when accurate knowledge of graph topology is unavailable. Moreover, the usual graph signal processing is a special case of our framework by using the delta distribution. The main elements of the theory include Fourier transform, theory of filtering and sampling.
2017 International Conference on Indoor Positioning and Indoor Navigation (IPIN), 2017
This paper considers the problem of decentralized, cooperative, and dynamic self-localization in ... more This paper considers the problem of decentralized, cooperative, and dynamic self-localization in wireless sensor networks. In particular, we are interested in a restrictive but very realistic scenario where few anchors are deployed and each anchor whose location is priori known may only communicate with very few agents (e.g. just one agent) whose location is unknown and to-be-estimated. The lack of agent-to-anchor communication links renders slow estimation convergence thereby demanding more message exchanges among the nodes i.e. agent-to-agent and agent-to-anchor. This urges us to propose an efficient localization method that needs less iterations (i.e. less message exchanges) to achieve a certain accuracy.
Graph signal processing allows us to analyze a graph signal by transforming it into the frequency... more Graph signal processing allows us to analyze a graph signal by transforming it into the frequency domain. In general, the procedure requires one to know the signal value at every node. In real situations, it is possible that only partial observations are made, called subgraph signals. In this paper, we introduce a subgraph signal processing framework. It allows us to define Fourier transform and the notion of frequency domain with signals available on a subset of nodes. As a consequence, we are able to give meaningful frequency interpretation of subgraph signals and perform standard signal processing tasks.
ICASSP 2021 - 2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2021
A heterogeneous graph consists of different vertices and edges types. Learning on heterogeneous g... more A heterogeneous graph consists of different vertices and edges types. Learning on heterogeneous graphs typically employs meta-paths to deal with the heterogeneity by reducing the graph to a homogeneous network, guide random walks or capture semantics. These methods are however sensitive to the choice of meta-paths, with suboptimal paths leading to poor performance. In this paper, we propose an approach for learning on heterogeneous graphs without using metapaths. Specifically, we decompose a heterogeneous graph into different homogeneous relation-type graphs, which are then combined to create higher-order relation-type representations. These representations preserve the heterogeneity of edges and retain their edge directions while capturing the interaction of different vertex types multiple hops apart. This is then complemented with attention mechanisms to distinguish the importance of the relation-type based neighbors and the relation-types themselves. Experiments demonstrate that our model generally outperforms other state-of-the-art baselines in the vertex classification task on three commonly studied heterogeneous graph datasets.
The goal of an infection source node (e.g., a rumor or computer virus source) in a network is to ... more The goal of an infection source node (e.g., a rumor or computer virus source) in a network is to spread its infection to as many nodes as possible, while remaining hidden from the network administrator. On the other hand, the network administrator aims to identify the source node based on knowledge of which nodes have been infected. We model the infection spreading and source identification problem as a strategic game, where the infection source and the network administrator are the two players. As the Jordan center estimator is a minimax source estimator that has been shown to be robust in recent works, we assume that the network administrator utilizes a source estimation strategy that can probe any nodes within a given radius of the Jordan center. Given any estimation strategy, we design a best-response infection strategy for the source. Given any infection strategy, we design a best-response estimation strategy for the network administrator. We derive conditions under which a Nash equilibrium of the strategic game exists. Simulations in both synthetic and real-world networks demonstrate that our proposed infection strategy infects more nodes while maintaining the same safety margin between the true source node and the Jordan center source estimator.
Proceedings of the AAAI Conference on Artificial Intelligence
Though deep learning has been applied successfully in many scenarios, malicious inputs with human... more Though deep learning has been applied successfully in many scenarios, malicious inputs with human-imperceptible perturbations can make it vulnerable in real applications. This paper proposes an error-correcting neural network (ECNN) that combines a set of binary classifiers to combat adversarial examples in the multi-class classification problem. To build an ECNN, we propose to design a code matrix so that the minimum Hamming distance between any two rows (i.e., two codewords) and the minimum shared information distance between any two columns (i.e., two partitions of class labels) are simultaneously maximized. Maximizing row distances can increase the system fault tolerance while maximizing column distances helps increase the diversity between binary classifiers. We propose an end-to-end training method for our ECNN, which allows further improvement of the diversity between binary classifiers. The end-to-end training renders our proposed ECNN different from the traditional error-co...
IEEE Transactions on Knowledge and Data Engineering
The problem of estimating event truths from conflicting agent opinions in a social network is inv... more The problem of estimating event truths from conflicting agent opinions in a social network is investigated. An autoencoder learns the complex relationships between event truths, agent reliabilities and agent observations. A Bayesian network model is proposed to guide the learning process by modeling the relationship of the autoencoder's outputs with different variables. At the same time, it also models the social relationships between agents in the network. The proposed approach is unsupervised and is applicable when ground truth labels of events are unavailable. A variational inference method is used to jointly estimate the hidden variables in the Bayesian network and the parameters in the autoencoder. Experiments on three real datasets demonstrate that our proposed approach is competitive with, and in most cases better than, several state-of-the-art benchmark methods.
2019 IEEE Global Conference on Signal and Information Processing (GlobalSIP)
In a linear stochastic bandit model, each arm is a vector in an Euclidean space and the observed ... more In a linear stochastic bandit model, each arm is a vector in an Euclidean space and the observed return at each time step is an unknown linear function of the chosen arm at that time step. In this paper, we investigate the problem of learning the best arm in a linear stochastic bandit model, where each arm's expected reward is an unknown linear function of the projection of the arm onto a subspace. We call this the projection reward. Unlike the classical linear bandit problem in which the observed return corresponds to the reward, the projection reward at each time step is unobservable. Such a model is useful in recommendation applications where the observed return includes corruption by each individual's biases, which we wish to exclude in the learned model. In the case where there are finitely many arms, we develop a strategy to achieve O(|D| log n) regret, where n is the number of time steps and |D| is the number of arms. In the case where each arm is chosen from an infinite compact set, our strategy achieves O(n 2/3 (log n) 1/2) regret. Experiments verify the efficiency of our strategy.
This paper considers Lorden's minimax quickest change detection (QCD) problem with a privacy ... more This paper considers Lorden's minimax quickest change detection (QCD) problem with a privacy constraint. The goal is to sanitize a signal to satisfy inference privacy requirements while being able to detect a change quickly. We show that the Generalized Likelihood Ratio (GLR) CuSum achieves asymptotic optimality with a properly designed sanitization channel. We formulate the design of this sanitization channel as an optimization problem, which is however challenging to solve. We propose relaxations to the optimization problem and develop algorithms to obtain a solution. We also consider the privacy-aware QCD problem under a decentralized framework and propose algorithms to solve the relaxed channel design problem under this framework.
We investigate the problem of truth discovery based on opinions from multiple agents who may be u... more We investigate the problem of truth discovery based on opinions from multiple agents who may be unreliable or biased. We consider the case where agents' reliabilities or biases are correlated if they belong to the same community, which defines a group of agents with similar opinions regarding a particular event. An agent can belong to different communities for different events, and these communities are unknown a priori. We incorporate knowledge of the agents' social network in our truth discovery framework and develop Laplace variational inference methods to estimate agents' reliabilities, communities, and the event states. We also develop a stochastic variational inference method to scale our model to large social networks. Simulations and experiments on real data suggest that when observations are sparse, our proposed methods perform better than several other inference methods, including majority voting, TruthFinder, AccuSim, the Confidence-Aware Truth Discovery metho...
In a linear stochastic bandit model, each arm is a vector in an Euclidean space and the observed ... more In a linear stochastic bandit model, each arm is a vector in an Euclidean space and the observed return at each time step is an unknown linear function of the chosen arm at that time step. In this paper, we investigate the problem of learning the best arm in a linear stochastic bandit model, where each arm's expected reward is an unknown linear function of the projection of the arm onto a subspace. We call this the projection reward. Unlike the classical linear bandit problem in which the observed return corresponds to the reward, the projection reward at each time step is unobservable. Such a model is useful in recommendation applications where the observed return includes corruption by each individual's biases, which we wish to exclude in the learned model. In the case where there are finitely many arms, we develop a strategy to achieve $O(|\bbD|\log n)$ regret, where $n$ is the number of time steps and $|\bbD|$ is the number of arms. In the case where each arm is chosen f...
Graph sampling approach allows a multidimensional signal generated on a graph to be represented b... more Graph sampling approach allows a multidimensional signal generated on a graph to be represented by the signal at a smaller set of sampled nodes. Currently, self-reset analog-to-digital converters (ADCs) are used to sample high dynamic range signals resulting in modulo-operation based folded signal at the sampled nodes. In this paper, we study the problem of signal recovery from the folded samples of a graph signal. We present a theoretical graph sampling rate that is sufficient and necessary for successful reconstruction of the graph signals from the folded samples. It is shown that the entire signal can be recovered by using an additional sampling node, with a different folding rate, while using the Shannon's rate for the signal at each node. An integer programming based formulation has been proposed to recover the lost information on the folding number at the sampled nodes. Furthermore, we propose a scalable sparse optimization based recovery method for graph signals satisfyin...
Deep neural networks (DNNs) are well-known to be vulnerable to adversarial attacks, where malicio... more Deep neural networks (DNNs) are well-known to be vulnerable to adversarial attacks, where malicious human-imperceptible perturbations are included in the input to the deep network to fool it into making a wrong classification. Recent studies have demonstrated that neural Ordinary Differential Equations (ODEs) are intrinsically more robust against adversarial attacks compared to vanilla DNNs. In this work, we propose a stable neural ODE with Lyapunov-stable equilibrium points for defending against adversarial attacks (SODEF). By ensuring that the equilibrium points of the ODE solution used as part of SODEF is Lyapunov-stable, the ODE solution for an input with a small perturbation converges to the same solution as the unperturbed input. We provide theoretical results that give insights into the stability of SODEF as well as the choice of regularizers to ensure its stability. Our analysis suggests that our proposed regularizers force the extracted feature points to be within a neighbo...
Graph Neural Networks (GNN) has demonstrated the superior performance in many challenging applica... more Graph Neural Networks (GNN) has demonstrated the superior performance in many challenging applications, including the few-shot learning tasks. Despite its powerful capacity to learn and generalize from few samples, GNN usually suffers from severe over-fitting and over-smoothing as the model becomes deep, which limit the model scalability. In this work, we propose a novel Attentive GNN to tackle these challenges, by incorporating a triple-attention mechanism, \ie node self-attention, neighborhood attention, and layer memory attention. We explain why the proposed attentive modules can improve GNN for few-shot learning with theoretical analysis and illustrations. Extensive experiments show that the proposed Attentive GNN outperforms the state-of-the-art GNN-based methods for few-shot learning over the mini-ImageNet and Tiered-ImageNet datasets, with both inductive and transductive settings.
Data is used widely by service providers as input to inference systems to perform decision making... more Data is used widely by service providers as input to inference systems to perform decision making for authorized tasks. The raw data however allows a service provider to infer other sensitive information it has not been authorized for. We propose a data-driven inference privacy preserving framework to sanitize data so as to prevent leakage of sensitive information that is present in the raw data, while ensuring that the sanitized data is still compatible with the service provider's legacy inference system. We develop an inference privacy framework based on the variational method and include maximum mean discrepancy and domain adaption as techniques to regularize the domain of the sanitized data to ensure its legacy compatibility. However, the variational method leads to weak privacy in cases where the underlying data distribution is hard to approximate. It may also face difficulties when handling continuous private variables. To overcome this, we propose an alternative formulati...
A continuous-time graph signal can be viewed as a continuous time-series of graph signals. It gen... more A continuous-time graph signal can be viewed as a continuous time-series of graph signals. It generalizes both the classical continuous-time signal and ordinary graph signal. In this paper, we consider the sampling theory of bandlimited continuous-time graph signals. We describe an explicit procedure to determine a discrete sampling set for perfect signal recovery. Moreover, in analogous to the Nyquist-Shannon sampling theorem, we give an explicit formula for the minimal sample rate.
A reconfigurable intelligent surface (RIS) consists of massive meta elements, which can improve t... more A reconfigurable intelligent surface (RIS) consists of massive meta elements, which can improve the performance of future wireless communication systems. Existing RIS-aided channel estimation methods try to estimate the cascaded channel directly, incurring high computational and training overhead especially when the number of elements of RIS is extremely large. In this paper, we propose a cost-efficient channel estimation method via rank-one matrix factorization (MF). Specifically, if the RIS is employed near base station (BS), it is found that the RIS-aided channel can be factorized into a product of low-dimensional matrices. To estimate these factorized matrices, we propose alternating minimization and gradient descent approaches to obtain the near optimal solutions. Compared to directly estimating the cascaded channel, the proposed MF method reduces training overhead substantially. Finally, the numerical simulations show the effectiveness of the proposed MF method.
Graph signal processing (GSP) is a framework to analyze and process graph-structured data. Many r... more Graph signal processing (GSP) is a framework to analyze and process graph-structured data. Many research works focus on developing tools such as Graph Fourier transforms (GFT), filters, and neural network models to handle graph signals. Such approaches have successfully taken care of "signal processing" in many circumstances. In this paper, we want to put emphasis on "graph signals" themselves. Although there are characterizations of graph signals using the notion of bandwidth derived from GFT, we want to argue here that graph signals may contain hidden geometric information of the network, independent of (graph) Fourier theories. We shall provide a framework to understand such information, and demonstrate how new knowledge on "graph signals" can help with "signal processing".
Estimating Kullback-Leibler (KL) divergence from data samples is a strenuous task, with existing ... more Estimating Kullback-Leibler (KL) divergence from data samples is a strenuous task, with existing approaches either imposing restrictive assumptions on the domain knowledge of the underlying model or requiring density approximation like space partitioning. The use of kernel maximum mean discrepancy (MMD) yields an alternative non-parametric approach to compare two populations by finding the maximum mean difference generated by measurable functions in the unit ball in a reproducing kernel Hilbert space (RKHS). Predicated on the universal approximation of universal kernels, we propose two corresponding classes of functions in a RKHS that can bound the KL divergence from below and above, and derive the RKHS representations of these bounds. This allows us to develop asymptotically consistent estimates for the derived bounds. We evaluate the proposed bounds as mutual information proxies on an image dataset, and demonstrate that these bounds can stably track variations in mutual information.
2021 IEEE Statistical Signal Processing Workshop (SSP)
In this paper, we develop a signal processing framework of a network without explicit knowledge o... more In this paper, we develop a signal processing framework of a network without explicit knowledge of the network topology. Instead, we make use of knowledge on the distribution of operators on the network. This makes the framework flexible and useful when accurate knowledge of graph topology is unavailable. Moreover, the usual graph signal processing is a special case of our framework by using the delta distribution. The main elements of the theory include Fourier transform, theory of filtering and sampling.
2017 International Conference on Indoor Positioning and Indoor Navigation (IPIN), 2017
This paper considers the problem of decentralized, cooperative, and dynamic self-localization in ... more This paper considers the problem of decentralized, cooperative, and dynamic self-localization in wireless sensor networks. In particular, we are interested in a restrictive but very realistic scenario where few anchors are deployed and each anchor whose location is priori known may only communicate with very few agents (e.g. just one agent) whose location is unknown and to-be-estimated. The lack of agent-to-anchor communication links renders slow estimation convergence thereby demanding more message exchanges among the nodes i.e. agent-to-agent and agent-to-anchor. This urges us to propose an efficient localization method that needs less iterations (i.e. less message exchanges) to achieve a certain accuracy.
Graph signal processing allows us to analyze a graph signal by transforming it into the frequency... more Graph signal processing allows us to analyze a graph signal by transforming it into the frequency domain. In general, the procedure requires one to know the signal value at every node. In real situations, it is possible that only partial observations are made, called subgraph signals. In this paper, we introduce a subgraph signal processing framework. It allows us to define Fourier transform and the notion of frequency domain with signals available on a subset of nodes. As a consequence, we are able to give meaningful frequency interpretation of subgraph signals and perform standard signal processing tasks.
ICASSP 2021 - 2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2021
A heterogeneous graph consists of different vertices and edges types. Learning on heterogeneous g... more A heterogeneous graph consists of different vertices and edges types. Learning on heterogeneous graphs typically employs meta-paths to deal with the heterogeneity by reducing the graph to a homogeneous network, guide random walks or capture semantics. These methods are however sensitive to the choice of meta-paths, with suboptimal paths leading to poor performance. In this paper, we propose an approach for learning on heterogeneous graphs without using metapaths. Specifically, we decompose a heterogeneous graph into different homogeneous relation-type graphs, which are then combined to create higher-order relation-type representations. These representations preserve the heterogeneity of edges and retain their edge directions while capturing the interaction of different vertex types multiple hops apart. This is then complemented with attention mechanisms to distinguish the importance of the relation-type based neighbors and the relation-types themselves. Experiments demonstrate that our model generally outperforms other state-of-the-art baselines in the vertex classification task on three commonly studied heterogeneous graph datasets.
The goal of an infection source node (e.g., a rumor or computer virus source) in a network is to ... more The goal of an infection source node (e.g., a rumor or computer virus source) in a network is to spread its infection to as many nodes as possible, while remaining hidden from the network administrator. On the other hand, the network administrator aims to identify the source node based on knowledge of which nodes have been infected. We model the infection spreading and source identification problem as a strategic game, where the infection source and the network administrator are the two players. As the Jordan center estimator is a minimax source estimator that has been shown to be robust in recent works, we assume that the network administrator utilizes a source estimation strategy that can probe any nodes within a given radius of the Jordan center. Given any estimation strategy, we design a best-response infection strategy for the source. Given any infection strategy, we design a best-response estimation strategy for the network administrator. We derive conditions under which a Nash equilibrium of the strategic game exists. Simulations in both synthetic and real-world networks demonstrate that our proposed infection strategy infects more nodes while maintaining the same safety margin between the true source node and the Jordan center source estimator.
Proceedings of the AAAI Conference on Artificial Intelligence
Though deep learning has been applied successfully in many scenarios, malicious inputs with human... more Though deep learning has been applied successfully in many scenarios, malicious inputs with human-imperceptible perturbations can make it vulnerable in real applications. This paper proposes an error-correcting neural network (ECNN) that combines a set of binary classifiers to combat adversarial examples in the multi-class classification problem. To build an ECNN, we propose to design a code matrix so that the minimum Hamming distance between any two rows (i.e., two codewords) and the minimum shared information distance between any two columns (i.e., two partitions of class labels) are simultaneously maximized. Maximizing row distances can increase the system fault tolerance while maximizing column distances helps increase the diversity between binary classifiers. We propose an end-to-end training method for our ECNN, which allows further improvement of the diversity between binary classifiers. The end-to-end training renders our proposed ECNN different from the traditional error-co...
IEEE Transactions on Knowledge and Data Engineering
The problem of estimating event truths from conflicting agent opinions in a social network is inv... more The problem of estimating event truths from conflicting agent opinions in a social network is investigated. An autoencoder learns the complex relationships between event truths, agent reliabilities and agent observations. A Bayesian network model is proposed to guide the learning process by modeling the relationship of the autoencoder's outputs with different variables. At the same time, it also models the social relationships between agents in the network. The proposed approach is unsupervised and is applicable when ground truth labels of events are unavailable. A variational inference method is used to jointly estimate the hidden variables in the Bayesian network and the parameters in the autoencoder. Experiments on three real datasets demonstrate that our proposed approach is competitive with, and in most cases better than, several state-of-the-art benchmark methods.
2019 IEEE Global Conference on Signal and Information Processing (GlobalSIP)
In a linear stochastic bandit model, each arm is a vector in an Euclidean space and the observed ... more In a linear stochastic bandit model, each arm is a vector in an Euclidean space and the observed return at each time step is an unknown linear function of the chosen arm at that time step. In this paper, we investigate the problem of learning the best arm in a linear stochastic bandit model, where each arm's expected reward is an unknown linear function of the projection of the arm onto a subspace. We call this the projection reward. Unlike the classical linear bandit problem in which the observed return corresponds to the reward, the projection reward at each time step is unobservable. Such a model is useful in recommendation applications where the observed return includes corruption by each individual's biases, which we wish to exclude in the learned model. In the case where there are finitely many arms, we develop a strategy to achieve O(|D| log n) regret, where n is the number of time steps and |D| is the number of arms. In the case where each arm is chosen from an infinite compact set, our strategy achieves O(n 2/3 (log n) 1/2) regret. Experiments verify the efficiency of our strategy.
This paper considers Lorden's minimax quickest change detection (QCD) problem with a privacy ... more This paper considers Lorden's minimax quickest change detection (QCD) problem with a privacy constraint. The goal is to sanitize a signal to satisfy inference privacy requirements while being able to detect a change quickly. We show that the Generalized Likelihood Ratio (GLR) CuSum achieves asymptotic optimality with a properly designed sanitization channel. We formulate the design of this sanitization channel as an optimization problem, which is however challenging to solve. We propose relaxations to the optimization problem and develop algorithms to obtain a solution. We also consider the privacy-aware QCD problem under a decentralized framework and propose algorithms to solve the relaxed channel design problem under this framework.
We investigate the problem of truth discovery based on opinions from multiple agents who may be u... more We investigate the problem of truth discovery based on opinions from multiple agents who may be unreliable or biased. We consider the case where agents' reliabilities or biases are correlated if they belong to the same community, which defines a group of agents with similar opinions regarding a particular event. An agent can belong to different communities for different events, and these communities are unknown a priori. We incorporate knowledge of the agents' social network in our truth discovery framework and develop Laplace variational inference methods to estimate agents' reliabilities, communities, and the event states. We also develop a stochastic variational inference method to scale our model to large social networks. Simulations and experiments on real data suggest that when observations are sparse, our proposed methods perform better than several other inference methods, including majority voting, TruthFinder, AccuSim, the Confidence-Aware Truth Discovery metho...
In a linear stochastic bandit model, each arm is a vector in an Euclidean space and the observed ... more In a linear stochastic bandit model, each arm is a vector in an Euclidean space and the observed return at each time step is an unknown linear function of the chosen arm at that time step. In this paper, we investigate the problem of learning the best arm in a linear stochastic bandit model, where each arm's expected reward is an unknown linear function of the projection of the arm onto a subspace. We call this the projection reward. Unlike the classical linear bandit problem in which the observed return corresponds to the reward, the projection reward at each time step is unobservable. Such a model is useful in recommendation applications where the observed return includes corruption by each individual's biases, which we wish to exclude in the learned model. In the case where there are finitely many arms, we develop a strategy to achieve $O(|\bbD|\log n)$ regret, where $n$ is the number of time steps and $|\bbD|$ is the number of arms. In the case where each arm is chosen f...
Graph sampling approach allows a multidimensional signal generated on a graph to be represented b... more Graph sampling approach allows a multidimensional signal generated on a graph to be represented by the signal at a smaller set of sampled nodes. Currently, self-reset analog-to-digital converters (ADCs) are used to sample high dynamic range signals resulting in modulo-operation based folded signal at the sampled nodes. In this paper, we study the problem of signal recovery from the folded samples of a graph signal. We present a theoretical graph sampling rate that is sufficient and necessary for successful reconstruction of the graph signals from the folded samples. It is shown that the entire signal can be recovered by using an additional sampling node, with a different folding rate, while using the Shannon's rate for the signal at each node. An integer programming based formulation has been proposed to recover the lost information on the folding number at the sampled nodes. Furthermore, we propose a scalable sparse optimization based recovery method for graph signals satisfyin...
Deep neural networks (DNNs) are well-known to be vulnerable to adversarial attacks, where malicio... more Deep neural networks (DNNs) are well-known to be vulnerable to adversarial attacks, where malicious human-imperceptible perturbations are included in the input to the deep network to fool it into making a wrong classification. Recent studies have demonstrated that neural Ordinary Differential Equations (ODEs) are intrinsically more robust against adversarial attacks compared to vanilla DNNs. In this work, we propose a stable neural ODE with Lyapunov-stable equilibrium points for defending against adversarial attacks (SODEF). By ensuring that the equilibrium points of the ODE solution used as part of SODEF is Lyapunov-stable, the ODE solution for an input with a small perturbation converges to the same solution as the unperturbed input. We provide theoretical results that give insights into the stability of SODEF as well as the choice of regularizers to ensure its stability. Our analysis suggests that our proposed regularizers force the extracted feature points to be within a neighbo...
Graph Neural Networks (GNN) has demonstrated the superior performance in many challenging applica... more Graph Neural Networks (GNN) has demonstrated the superior performance in many challenging applications, including the few-shot learning tasks. Despite its powerful capacity to learn and generalize from few samples, GNN usually suffers from severe over-fitting and over-smoothing as the model becomes deep, which limit the model scalability. In this work, we propose a novel Attentive GNN to tackle these challenges, by incorporating a triple-attention mechanism, \ie node self-attention, neighborhood attention, and layer memory attention. We explain why the proposed attentive modules can improve GNN for few-shot learning with theoretical analysis and illustrations. Extensive experiments show that the proposed Attentive GNN outperforms the state-of-the-art GNN-based methods for few-shot learning over the mini-ImageNet and Tiered-ImageNet datasets, with both inductive and transductive settings.
Data is used widely by service providers as input to inference systems to perform decision making... more Data is used widely by service providers as input to inference systems to perform decision making for authorized tasks. The raw data however allows a service provider to infer other sensitive information it has not been authorized for. We propose a data-driven inference privacy preserving framework to sanitize data so as to prevent leakage of sensitive information that is present in the raw data, while ensuring that the sanitized data is still compatible with the service provider's legacy inference system. We develop an inference privacy framework based on the variational method and include maximum mean discrepancy and domain adaption as techniques to regularize the domain of the sanitized data to ensure its legacy compatibility. However, the variational method leads to weak privacy in cases where the underlying data distribution is hard to approximate. It may also face difficulties when handling continuous private variables. To overcome this, we propose an alternative formulati...
A continuous-time graph signal can be viewed as a continuous time-series of graph signals. It gen... more A continuous-time graph signal can be viewed as a continuous time-series of graph signals. It generalizes both the classical continuous-time signal and ordinary graph signal. In this paper, we consider the sampling theory of bandlimited continuous-time graph signals. We describe an explicit procedure to determine a discrete sampling set for perfect signal recovery. Moreover, in analogous to the Nyquist-Shannon sampling theorem, we give an explicit formula for the minimal sample rate.
A reconfigurable intelligent surface (RIS) consists of massive meta elements, which can improve t... more A reconfigurable intelligent surface (RIS) consists of massive meta elements, which can improve the performance of future wireless communication systems. Existing RIS-aided channel estimation methods try to estimate the cascaded channel directly, incurring high computational and training overhead especially when the number of elements of RIS is extremely large. In this paper, we propose a cost-efficient channel estimation method via rank-one matrix factorization (MF). Specifically, if the RIS is employed near base station (BS), it is found that the RIS-aided channel can be factorized into a product of low-dimensional matrices. To estimate these factorized matrices, we propose alternating minimization and gradient descent approaches to obtain the near optimal solutions. Compared to directly estimating the cascaded channel, the proposed MF method reduces training overhead substantially. Finally, the numerical simulations show the effectiveness of the proposed MF method.
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