arXiv subjects

Brandon Fallin

Publications and source records attributed to Brandon Fallin.

3 recordsLinked to original sources

arXiv2026

Differentially Private Data-Driven Markov Chain Modeling

Markov chains model a wide range of user behaviors. However, generating accurate Markov chain models requires substantial user data, and sharing these models without privacy protections may reveal sensitive information about the underlying user data. We introduce a method for protecting user data used to formulate a Markov chain model. First, we develop a method for privatizing database queries whose outputs are elements of the unit simplex, and we prove that this method is differentially private. We quantify its accuracy by bounding the expected KL divergence between private and non-private queries. We extend this method to privatize stochastic matrices whose rows are each a simplex-valued query of a database, which includes data-driven Markov chain models. To assess their accuracy, we analytically bound the change in the stationary distribution and the change in the convergence rate between a non-private Markov chain model and its private form. Simulations show that under a typical privacy implementation, our method yields less than 2% error in the stationary distribution, indicating that our approach to private modeling faithfully captures the behavior of the systems we study.

cs.CR↗

arXiv2023

Differentially Private Computation of Basic Reproduction Numbers in Networked Epidemic Models

The basic reproduction number of a networked epidemic model, denoted $R_0$, can be computed from a network's topology to quantify epidemic spread. However, disclosure of $R_0$ risks revealing sensitive information about the underlying network, such as an individual's relationships within a social network. Therefore, we propose a framework to compute and release $R_0$ in a differentially private way. First, we provide a new result that shows how $R_0$ can be used to bound the level of penetration of an epidemic within a single community as a motivation for the need of privacy, which may also be of independent interest. We next develop a privacy mechanism to formally safeguard the edge weights in the underlying network when computing $R_0$. Then we formalize tradeoffs between the level of privacy and the accuracy of values of the privatized $R_0$. To show the utility of the private $R_0$ in practice, we use it to bound this level of penetration under privacy, and concentration bounds on these analyses show they remain accurate with privacy implemented. We apply our results to real travel data gathered during the spread of COVID-19, and we show that, under real-world conditions, we can compute $R_0$ in a differentially private way while incurring errors as low as $7.6\%$ on average.

cs.SI↗

arXiv2023

Differentially Private Reward Functions in Policy Synthesis for Markov Decision Processes

Markov decision processes often seek to maximize a reward function, but onlookers may infer reward functions by observing the states and actions of such systems, revealing sensitive information. Therefore, in this paper we introduce and compare two methods for privatizing reward functions in policy synthesis for multi-agent Markov decision processes, which generalize Markov decision processes. Reward functions are privatized using differential privacy, a statistical framework for protecting sensitive data. The methods we develop perturb either (1) each agent's individual reward function or (2) the joint reward function shared by all agents. We show that approach (1) provides better performance. We then develop a polynomial-time algorithm for the numerical computation of the performance loss due to privacy on a case-by-case basis. Next, using approach (1), we develop guidelines for selecting reward function values to preserve ``goal" and ``avoid" states while still remaining private, and we quantify the increase in computational complexity needed to compute policies from privatized rewards. Numerical simulations are performed on three classes of systems and they reveal a surprising compatibility with privacy: using reasonably strong privacy ($\epsilon =1.3$) on average induces as little as a~$5\%$ decrease in total accumulated reward and a $0.016\%$ increase in computation time.

eess.SY↗