arXiv subjects

Lintao Ye

Publications and source records attributed to Lintao Ye.

24 records · Page 2Linked to original sources

arXiv2021

Parameter Estimation in Epidemic Spread Networks Using Limited Measurements

We study the problem of estimating the parameters (i.e., infection rate and recovery rate) governing the spread of epidemics in networks. Such parameters are typically estimated by measuring various characteristics (such as the number of infected and recovered individuals) of the infected populations over time. However, these measurements also incur certain costs, depending on the population being tested and the times at which the tests are administered. We thus formulate the epidemic parameter estimation problem as an optimization problem, where the goal is to either minimize the total cost spent on collecting measurements, or to optimize the parameter estimates while remaining within a measurement budget. We show that these problems are NP-hard to solve in general, and then propose approximation algorithms with performance guarantees. We validate our algorithms using numerical examples.

eess.SY↗

arXiv2021

Near-Optimal Data Source Selection for Bayesian Learning

We study a fundamental problem in Bayesian learning, where the goal is to select a set of data sources with minimum cost while achieving a certain learning performance based on the data streams provided by the selected data sources. First, we show that the data source selection problem for Bayesian learning is NP-hard. We then show that the data source selection problem can be transformed into an instance of the submodular set covering problem studied in the literature, and provide a standard greedy algorithm to solve the data source selection problem with provable performance guarantees. Next, we propose a fast greedy algorithm that improves the running times of the standard greedy algorithm, while achieving performance guarantees that are comparable to those of the standard greedy algorithm. The fast greedy algorithm can also be applied to solve the general submodular set covering problem with performance guarantees. Finally, we validate the theoretical results using numerical examples, and show that the greedy algorithms work well in practice.

cs.LG↗

arXiv2020

Distributed Maximization of Submodular and Approximately Submodular Functions

We study the problem of maximizing a submodular function, subject to a cardinality constraint, with a set of agents communicating over a connected graph. We propose a distributed greedy algorithm that allows all the agents to converge to a near-optimal solution to the global maximization problem using only local information and communication with neighbors in the graph. The near-optimal solution approaches the (1-1/e) approximation of the optimal solution to the global maximization problem with an additive factor that depends on the number of communication steps in the algorithm. We then analyze convergence guarantees of the proposed algorithm. This analysis reveals a tradeoff between the number of communication steps and the performance of the algorithm. Finally, we extend our analysis to nonsubmodular settings, using the notion of approximate submodularity.

math.OC↗

arXiv2020

On the Complexity and Approximability of Optimal Sensor Selection and Attack for Kalman Filtering

Given a linear dynamical system affected by stochastic noise, we consider the problem of selecting an optimal set of sensors (at design-time) to minimize the trace of the steady state a priori or a posteriori error covariance of the Kalman filter, subject to certain selection budget constraints. We show the fundamental result that there is no polynomial-time constant-factor approximation algorithm for this problem. This contrasts with other classes of sensor selection problems studied in the literature, which typically pursue constant-factor approximations by leveraging greedy algorithms and submodularity (or supermodularity) of the cost function. Here, we provide a specific example showing that greedy algorithms can perform arbitrarily poorly for the problem of design-time sensor selection for Kalman filtering. We then study the problem of attacking (i.e., removing) a set of installed sensors, under predefined attack budget constraints, to maximize the trace of the steady state a priori or a posteriori error covariance of the Kalman filter. Again, we show that there is no polynomial-time constant-factor approximation algorithm for this problem, and show specifically that greedy algorithms can perform arbitrarily poorly.

math.OC↗

arXiv2020

Resilient Sensor Placement for Kalman Filtering in Networked Systems: Complexity and Algorithms

Given a linear dynamical system affected by noise, we study the problem of optimally placing sensors (at design-time) subject to a sensor placement budget constraint in order to minimize the trace of the steady-state error covariance of the corresponding Kalman filter. While this problem is NP-hard in general, we consider the underlying graph associated with the system dynamics matrix, and focus on the case when there is a single input at one of the nodes in the graph. We provide an optimal strategy (computed in polynomial-time) to place the sensors over the network. Next, we consider the problem of attacking (i.e., removing) the placed sensors under a sensor attack budget constraint in order to maximize the trace of the steady-state error covariance of the resulting Kalman filter. Using the insights obtained for the sensor placement problem, we provide an optimal strategy (computed in polynomial-time) to attack the placed sensors. Finally, we consider the scenario where a system designer places the sensors under a sensor placement budget constraint, and an adversary then attacks the placed sensors subject to a sensor attack budget constraint. The resilient sensor placement problem is to find a sensor placement strategy to minimize the trace of the steady-state error covariance of the Kalman filter corresponding to the sensors that survive the attack. We show that this problem is NP-hard, and provide a pseudo-polynomial-time algorithm to solve it.

math.OC↗

arXiv2018

On the Complexity and Approximability of Optimal Sensor Selection for Kalman Filtering

Given a linear dynamical system, we consider the problem of selecting (at design-time) an optimal set of sensors (subject to certain budget constraints) to minimize the trace of the steady state error covariance matrix of the Kalman filter. Previous work has shown that this problem is NP-hard for certain classes of systems and sensor costs; in this paper, we show that the problem remains NP-hard even for the special case where the system is stable and all sensor costs are identical. Furthermore, we show the stronger result that there is no constant-factor (polynomial-time) approximation algorithm for this problem. This contrasts with other classes of sensor selection problems studied in the literature, which typically pursue constant-factor approximations by leveraging greedy algorithms and submodularity of the cost function. Here, we provide a specific example showing that greedy algorithms can perform arbitrarily poorly for the problem of design-time sensor selection for Kalman filtering.

math.OC↗