arXiv subjects

Xiaojing Shen

Publications and source records attributed to Xiaojing Shen.

At least 37 records · Page 2Linked to original sources

arXiv2022

Nonlinear Set Membership Filter with State Estimation Constraints via Consensus-ADMM

This paper considers the state estimation problem for nonlinear dynamic systems with unknown but bounded noises. Set membership filter (SMF) is a popular algorithm to solve this problem. In the set membership setting, we investigate the filter problem where the state estimation requires to be constrained by a linear or nonlinear equality. We propose a consensus alternating direction method of multipliers (ADMM) based SMF algorithm for nonlinear dynamic systems. To deal with the difficulty of nonlinearity, instead of linearizing the nonlinear system, a semi-infinite programming (SIP) approach is used to transform the nonlinear system into a linear one, which allows us to obtain a more accurate estimation ellipsoid. For the solution of the SIP, an ADMM algorithm is proposed to handle the state estimation constraints, and each iteration of the algorithm can be solved efficiently. Finally, the proposed filter is applied to typical numerical examples to demonstrate its effectiveness.

math.OC↗

arXiv2022

Seamless Tracking of Group Targets and Ungrouped Targets Using Belief Propagation

This paper considers the problem of tracking a large-scale number of group targets. Usually, multi-target in most tracking scenarios are assumed to have independent motion and are well-separated. However, for group target tracking (GTT), the targets within groups are closely spaced and move in a coordinated manner, the groups can split or merge, and the numbers of targets in groups may be large, which lead to more challenging data association, filtering and computation problems. Within the belief propagation (BP) framework, we propose a scalable group target belief propagation (GTBP) method by jointly inferring target existence variables, group structure, data association and target states. The method can efficiently calculate the approximations of the marginal posterior distributions of these variables by performing belief propagation on the devised factor graph. As a consequence, GTBP is capable of capturing the changes in group structure, e.g., group splitting and merging. Furthermore, we model the evolution of targets as the co-action of the group or single-target motions specified by the possible group structures and corresponding probabilities. This flexible modeling enables seamless and simultaneous tracking of multiple group targets and ungrouped targets. Particularly, GTBP has excellent scalability and low computational complexity. It not only maintains the same scalability as BP, i.e., scaling linearly in the number of sensor measurements and quadratically in the number of targets, but also only scales linearly in the number of preserved group partitions. Finally, numerical experiments are presented to demonstrate the effectiveness and scalability of the proposed GTBP method.

cs.LG↗

arXiv2022

TBraTS: Trusted Brain Tumor Segmentation

Despite recent improvements in the accuracy of brain tumor segmentation, the results still exhibit low levels of confidence and robustness. Uncertainty estimation is one effective way to change this situation, as it provides a measure of confidence in the segmentation results. In this paper, we propose a trusted brain tumor segmentation network which can generate robust segmentation results and reliable uncertainty estimations without excessive computational burden and modification of the backbone network. In our method, uncertainty is modeled explicitly using subjective logic theory, which treats the predictions of backbone neural network as subjective opinions by parameterizing the class probabilities of the segmentation as a Dirichlet distribution. Meanwhile, the trusted segmentation framework learns the function that gathers reliable evidence from the feature leading to the final segmentation results. Overall, our unified trusted segmentation framework endows the model with reliability and robustness to out-of-distribution samples. To evaluate the effectiveness of our model in robustness and reliability, qualitative and quantitative experiments are conducted on the BraTS 2019 dataset.

eess.IV↗

arXiv2022

An Unbiased Symmetric Matrix Estimator for Topology Inference under Partial Observability

Network topology inference is a fundamental problem in many applications of network science, such as locating the source of fake news, brain connectivity networks detection, etc. Many real-world situations suffer from a critical problem that only a limited part of observed nodes are available. This letter considers the problem of network topology inference under the framework of partial observability. Based on the vector autoregressive model, we propose a novel unbiased estimator for the symmetric network topology with the Gaussian noise and the Laplacian combination rule. Theoretically, we prove that it converges to the network combination matrix in probability. Furthermore, by utilizing the Gaussian mixture model algorithm, an effective algorithm called network inference Gauss algorithm is developed to infer the network structure. Finally, compared with the state-of-the-art methods, numerical experiments demonstrate the proposed algorithm enjoys better performance in the case of small sample sizes.

stat.AP↗

arXiv2021

Towards Understanding the Impact of Model Size on Differential Private Classification

Differential privacy (DP) is an essential technique for privacy-preserving. It was found that a large model trained for privacy preserving performs worse than a smaller model (e.g. ResNet50 performs worse than ResNet18). To better understand this phenomenon, we study high dimensional DP learning from the viewpoint of generalization. Theoretically, we show that for the simple Gaussian model with even small DP noise, if the dimension is large enough, then the classification error can be as bad as the random guessing. Then we propose a feature selection method to reduce the size of the model, based on a new metric which trades off the classification accuracy and privacy preserving. Experiments on real data support our theoretical results and demonstrate the advantage of the proposed method.

cs.LG↗

arXiv2021

Randomized Multiple Model Multiple Hypothesis Tracking

This paper considers the data association problem for multi-target tracking. Multiple hypothesis tracking is a popular algorithm for solving this problem but it is NP-hard and is is quite complicated for a large number of targets or for tracking maneuvering targets. To improve tracking performance and enhance robustness, we propose a randomized multiple model multiple hypothesis tracking method, which has three distinctive advantages. First, it yields a randomized data association solution which maximizes the expectation of the logarithm of the posterior probability and can be solved efficiently by linear programming. Next, the state estimation performance is improved by the random coefficient matrices Kalman filter, which mitigates the difficulty introduced by randomized data association, i.e., where the coefficient matrices of the dynamic system are random. Third, the probability that the target follows a specific dynamic model is derived by jointly optimizing the multiple possible models and data association hypotheses, and it does not require prior mode transition probabilities. Thus, it is more robust for tracking multiple maneuvering targets. Simulations demonstrate the efficiency and superior results of the proposed algorithm over interacting multiple model multiple hypothesis tracking.

cs.IT↗

arXiv2020

The Effect of Population Size for Pathogen Transmission on Prediction of COVID-19 Pandemic Spread

Extreme public health interventions play a critical role in mitigating the local and global prevalence and pandemic potential of COVID-19. Here, we use population size for pathogen transmission to measure the intensity of public health interventions, which is a key characteristic variable for nowcasting and forecasting of the epidemic. By formulating a hidden Markov dynamic system and using nonlinear filtering theory, we have developed a stochastic epidemic dynamic model under public health interventions. The model parameters and states are estimated in time from internationally available public data by combining an unscented filter and an interacting multiple model filter. Moreover, we consider the computability of the population size and provide its selection criterion. We estimate the mean of the basic reproductive number of China and the rest of the globe except China (GEC) to be 2.46 (95% CI: 2.41-2.51) and 3.64 (95% CI: (3.55-3.72), respectively. We infer that the number of latent infections of GEC is about 7.47*10^5 (95% CI: 7.32*10^5-7.62*10^5) as of April 2, 2020. We predict that the peak of infections in hospitals of GEC may reach 3.00*10^6 on the present trajectory, i.e., if the population size for pathogen transmission and epidemic parameters remains unchanged. If the control intensity is strengthened, e.g., 50% reduction or 75% reduction of the population size for pathogen transmission, the peak would decline to 1.84*10^6, 1.27*10^6, respectively.

q-bio.PE↗

arXiv2019

Multiple-Source Ellipsoidal Localization Using Acoustic Energy Measurements

In this paper, the multiple-source ellipsoidal localization problem based on acoustic energy measurements is investigated via set-membership estimation theory. When the probability density function of measurement noise is unknown-but-bounded, multiple-source localization is a difficult problem since not only the acoustic energy measurements are complicated nonlinear functions of multiple sources, but also the multiple sources bring about a high-dimensional state estimation problem. First, when the energy parameter and the position of the source are bounded in an interval and a ball respectively, the nonlinear remainder bound of the Taylor series expansion is obtained analytically on-line. Next, based on the separability of the nonlinear measurement function, an efficient estimation procedure is developed. It solves the multiple-source localization problem by using an alternating optimization iterative algorithm, in which the remainder bound needs to be known on-line. For this reason, we first derive the remainder bound analytically. When the energy decay factor is unknown but bounded, an efficient estimation procedure is developed based on interval mathematics. Finally, numerical examples demonstrate the effectiveness of the ellipsoidal localization algorithms for multiple-source localization. In particular, our results show that when the noise is non-Gaussian, the set-membership localization algorithm performs better than the EM localization algorithm.

cs.IT↗

arXiv2019

Dual Set Membership Filter with Minimizing Nonlinear Transformation of Ellipsoid

In this paper, we propose a dual set membership filter for nonlinear dynamic systems with unknown but bounded noises, and it has three distinctive properties. Firstly, the nonlinear system is translated into the linear system by leveraging a semi-infinite programming, rather than linearizing the nonlinear function. In fact, the semi-infinite programming is to find an ellipsoid bounding the nonlinear transformation of an ellipsoid, which aims to compute a tight ellipsoid to cover the state. Secondly, the duality result of the semi-infinite programming is derived by a rigorous analysis, then a first order Frank-Wolfe method is developed to efficiently solve it with a lower computation complexity. Thirdly, the proposed filter can take advantage of the linear set membership filter framework and can work on-line without solving the semidefinite programming problem. Furthermore, we apply the dual set membership filter to a typical scenario of mobile robot localization. Finally, two illustrative examples in the simulations show the advantages and effectiveness of the dual set membership filter.

math.DS↗

arXiv2018

On Equivalence and Computational Efficiency of the Major Relaxation Methods for Minimum Ellipsoid Containing the Intersection of Ellipsoids

This paper investigates the problem on the minimum ellipsoid containing the intersection of multiple ellipsoids, which has been extensively applied to information science, target tracking and data fusion etc. There are three major relaxation methods involving SDP relaxation, S-procedure relaxation and bounding ellipsoid relaxation, which are derived by different ideas or viewpoints. However, it is unclear for the interrelationships among these methods. This paper reveals the equivalence among the three relaxation methods by three stages. Firstly, the SDP relaxation method can be equivalently simplified to a decoupled SDP relaxation method. Secondly, the equivalence between the SDP relaxation method and the S-procedure relaxation method can be obtained by rigorous analysis. Thirdly, we establish the equivalence between the decoupled SDP relaxation method and the bounding ellipsoid relaxation method. Therefore, the three relaxation methods are unified through the decoupled SDP relaxation method. By analysis of the computational complexity, the decoupled SDP relaxation method has the least computational burden among the three methods. The above results are helpful for the research of set-membership filter and distributed estimation fusion. Finally, the performance of each method is evaluated by some typical numerical examples in information fusion and filtering.

math.OC↗

arXiv2017

Set-Membership Information Fusion for Multisensor Nonlinear Dynamic Systems

The set-membership information fusion problem is investigated for general multisensor nonlinear dynamic systems. Compared with linear dynamic systems and point estimation fusion in mean squared error sense, it is a more challenging nonconvex optimization problem. Usually, to solve this problem, people try to find an efficient or heuristic fusion algorithm. It is no doubt that an analytical fusion formula should be much significant for rasing accuracy and reducing computational burden. However, since it is a more complicated than the convex quadratic optimization problem for linear point estimation fusion, it is not easy to get the analytical fusion formula. In order to overcome the difficulty of this problem, two popular fusion architectures are considered: centralized and distributed set-membership information fusion. Firstly, both of them can be converted into a semidefinite programming problem which can be efficiently computed, respectively. Secondly, their analytical solutions can be derived surprisingly by using decoupling technique. It is very interesting that they are quite similar in form to the classic information filter. In the two analytical fusion formulae, the information of each sensor can be clearly characterized, and the knowledge of the correlation among measurement noises across sensors are not required. Finally, multi-algorithm fusion is used to minimize the size of the state bounding ellipsoid by complementary advantages of multiple parallel algorithms. A typical numerical example in target tracking demonstrates the effectiveness of the centralized, distributed, and multi-algorithm set-membership fusion algorithms. In particular, it shows that multi-algorithm fusion performs better than the centralized and distributed fusion.

cs.IT↗

arXiv2016

Monte Carlo Set-Membership Filtering for Nonlinear Dynamic Systems

When underlying probability density functions of nonlinear dynamic systems are unknown, the filtering problem is known to be a challenging problem. This paper attempts to make progress on this problem by proposing a new class of filtering methods in bounded noise setting via set-membership theory and Monte Carlo (boundary) sampling technique, called Monte Carlo set-membership filter. The set-membership prediction and measurement update are derived by recent convex optimization methods based on S-procedure and Schur complement. To guarantee the on-line usage, the nonlinear dynamics are linearized about the current estimate and the remainder terms are then bounded by an optimization ellipsoid, which can be described as a semi-infinite optimization problem. In general, it is an analytically intractable problem when dynamic systems are nonlinear. However, for a typical nonlinear dynamic system in target tracking, we can analytically derive some regular properties for the remainder. Moreover, based on the remainder properties and the inverse function theorem, the semi-infinite optimization problem can be efficiently solved by Monte Carlo boundary sampling technique. Compared with the particle filter, numerical examples show that when the probability density functions of noises are unknown, the performance of the Monte Carlo set-membership filter is better than that of the particle filter.

math.ST↗

arXiv2016

Distributed Detection Fusion via Monte Carlo Importance Sampling

Distributed detection fusion with high-dimension conditionally dependent observations is known to be a challenging problem. When a fusion rule is fixed, this paper attempts to make progress on this problem for the large sensor networks by proposing a new Monte Carlo framework. Through the Monte Carlo importance sampling, we derive a necessary condition for optimal sensor decision rules in the sense of minimizing the approximated Bayesian cost function. Then, a Gauss-Seidel/person-by-person optimization algorithm can be obtained to search the optimal sensor decision rules. It is proved that the discretized algorithm is finitely convergent. The complexity of the new algorithm is $O(LN)$ compared with $O(LN^L)$ of the previous algorithm where $L$ is the number of sensors and $N$ is a constant. Thus, the proposed methods allows us to design the large sensor networks with general high-dimension dependent observations. Furthermore, an interesting result is that, for the fixed AND or OR fusion rules, we can analytically derive the optimal solution in the sense of minimizing the approximated Bayesian cost function. In general, the solution of the Gauss-Seidel algorithm is only local optimal. However, in the new framework, we can prove that the solution of Gauss-Seidel algorithm is same as the analytically optimal solution in the case of the AND or OR fusion rule. The typical examples with dependent observations and large number of sensors are examined under this new framework. The results of numerical examples demonstrate the effectiveness of the new algorithm.

cs.IT↗

arXiv2015

Posterior Cramer-Rao Bounds for Discrete-Time Nonlinear Filtering with Finitely Correlated Noise

In this paper, an approximation recursive formula of the mean-square error lower bound for the discrete-time nonlinear filtering problem when noises of dynamic systems are temporally correlated is derived based on the Van Trees (posterior) version of the Cramer-Rao inequality. The formula is unified in the sense that it can be applied to the multi-step correlated process noise, multi-step correlated measurement noise and multi-step cross-correlated process and measurement noise simultaneously. The lower bound is evaluated by two typical target tracking examples respectively. Both of them show that the new lower bound is significantly different from that of the method which ignores correlation of noises. Thus, when they are applied to sensor selection problems, number of selected sensors becomes very different to obtain a desired estimation performance.

math.DS↗

arXiv2013

Robust Distributed Maximum Likelihood Estimation with Dependent Quantized Data

In this paper, we consider distributed maximum likelihood estimation (MLE) with dependent quantized data under the assumption that the structure of the joint probability density function (pdf) is known, but it contains unknown deterministic parameters. The parameters may include different vector parameters corresponding to marginal pdfs and parameters that describe dependence of observations across sensors. Since MLE with a single quantizer is sensitive to the choice of thresholds due to the uncertainty of pdf, we concentrate on MLE with multiple groups of quantizers (which can be determined by the use of prior information or some heuristic approaches) to fend off against the risk of a poor/outlier quantizer. The asymptotic efficiency of the MLE scheme with multiple quantizers is proved under some regularity conditions and the asymptotic variance is derived to be the inverse of a weighted linear combination of Fisher information matrices based on multiple different quantizers which can be used to show the robustness of our approach. As an illustrative example, we consider an estimation problem with a bivariate non-Gaussian pdf that has applications in distributed constant false alarm rate (CFAR) detection systems. Simulations show the robustness of the proposed MLE scheme especially when the number of quantized measurements is small.

cs.IT↗

arXiv2013

Adaptive Non-myopic Quantizer Design for Target Tracking in Wireless Sensor Networks

In this paper, we investigate the problem of nonmyopic (multi-step ahead) quantizer design for target tracking using a wireless sensor network. Adopting the alternative conditional posterior Cramer-Rao lower bound (A-CPCRLB) as the optimization metric, we theoretically show that this problem can be temporally decomposed over a certain time window. Based on sequential Monte-Carlo methods for tracking, i.e., particle filters, we design the local quantizer adaptively by solving a particlebased non-linear optimization problem which is well suited for the use of interior-point algorithm and easily embedded in the filtering process. Simulation results are provided to illustrate the effectiveness of our proposed approach.

stat.AP↗

arXiv2013

Sensor Selection Based on Generalized Information Gain for Target Tracking in Large Sensor Networks

In this paper, sensor selection problems for target tracking in large sensor networks with linear equality or inequality constraints are considered. First, we derive an equivalent Kalman filter for sensor selection, i.e., generalized information filter. Then, under a regularity condition, we prove that the multistage look-ahead policy that minimizes either the final or the average estimation error covariances of next multiple time steps is equivalent to a myopic sensor selection policy that maximizes the trace of the generalized information gain at each time step. Moreover, when the measurement noises are uncorrelated between sensors, the optimal solution can be obtained analytically for sensor selection when constraints are temporally separable. When constraints are temporally inseparable, sensor selections can be obtained by approximately solving a linear programming problem so that the sensor selection problem for a large sensor network can be dealt with quickly. Although there is no guarantee that the gap between the performance of the chosen subset and the performance bound is always small, numerical examples suggest that the algorithm is near-optimal in many cases. Finally, when the measurement noises are correlated between sensors, the sensor selection problem with temporally inseparable constraints can be relaxed to a Boolean quadratic programming problem which can be efficiently solved by a Gaussian randomization procedure along with solving a semi-definite programming problem. Numerical examples show that the proposed method is much better than the method that ignores dependence of noises.

math.OC↗

arXiv2013

Study of Neutron-Capture Element Abundances in Metal-Poor Stars

This work describes a study of elemental abundances for 30 metal-poor stars whose chemical abundances provide excellent information for setting constraints on models of neutron-capture processes. Based on the abundances of main r- and weak r-process stars, the abundance patterns of main r-process and weak r-process are obtained. The two r-process component coefficients are defined to determine the relative contributions from individual neutron-capture process to abundances of metal-poor stars. Based on the component coefficients, we find that metal-poor stars BD+4 2621 and HD 4306 are also weak r-process stars, which means that the abundance pattern produced by weak r-process is stable. All metal-poor star abundances contain the contributions of both main r-process and weak r-process. The elements produced by weak r-process have increased along with Fe over the polluted history. Most of the metal-poor star abundances do not follow the pattern observed in solar system, but there is a small fraction that do. For the low-[Sr/Fe] star BD-18 5550 ([Sr/Fe]$\lesssim-1$), neutron-capture element abundances can be explained by the mixture of two r-process components. Since lighter elements in this star cannot be fitted by the two components, the abundance pattern of P-component is estimated from those abundances.

astro-ph.SR↗