arXiv subjects

Do Young Eun

Publications and source records attributed to Do Young Eun.

21 records · Page 2Linked to original sources

arXiv2019

Non-Markovian Monte Carlo on Directed Graphs

Markov Chain Monte Carlo (MCMC) has been the de facto technique for sampling and inference of large graphs such as online social networks. At the heart of MCMC lies the ability to construct an ergodic Markov chain that attains any given stationary distribution $\boldsymbolπ$, often in the form of random walks or crawling agents on the graph. Most of the works around MCMC, however, presume that the graph is undirected or has reciprocal edges, and become inapplicable when the graph is directed and non-reciprocal. Here we develop a similar framework for directed graphs, which we call Non-Markovian Monte Carlo (NMMC), by establishing a mapping to convert $\boldsymbolπ$ into the quasi-stationary distribution of a carefully constructed transient Markov chain on an extended state space. As applications, we demonstrate how to achieve any given distribution $\boldsymbolπ$ on a directed graph and estimate the eigenvector centrality using a set of non-Markovian, history-dependent random walks on the same graph in a distributed manner. We also provide numerical results on various real-world directed graphs to confirm our theoretical findings, and present several practical enhancements to make our NMMC method ready for practical use in most directed graphs. To the best of our knowledge, the proposed NMMC framework for directed graphs is the first of its kind, unlocking all the limitations set by the standard MCMC methods for undirected graphs.

math.ST↗

arXiv2013

Exploiting the Past to Reduce Delay in CSMA Scheduling: A High-order Markov Chain Approach

Recently several CSMA algorithms based on the Glauber dynamics model have been proposed for multihop wireless scheduling, as viable solutions to achieve the throughput optimality, yet are simple to implement. However, their delay performances still remain unsatisfactory, mainly due to the nature of the underlying Markov chains that imposes a fundamental constraint on how the link state can evolve over time. In this paper, we propose a new approach toward better queueing and delay performance, based on our observation that the algorithm needs not be Markovian, as long as it can be implemented in a distributed manner, achieve the same throughput optimality, while offering far better delay performance for general network topologies. Our approach hinges upon utilizing past state information observed by local link and then constructing a high-order Markov chain for the evolution of the feasible link schedules. We show in theory and simulation that our proposed algorithm, named delayed CSMA, adds virtually no additional overhead onto the existing CSMA-based algorithms, achieves the throughput optimality under the usual choice of link weight as a function of local queue length, and also provides much better delay performance by effectively `de-correlating' the link state process (thus removing link starvation) under any arbitrary network topology. From our extensive simulations we observe that the delay under our algorithm can be often reduced by a factor of 20 over a wide range of scenarios, compared to the standard Glauber-dynamics-based CSMA algorithm.

cs.NI↗

arXiv2012

Beyond Random Walk and Metropolis-Hastings Samplers: Why You Should Not Backtrack for Unbiased Graph Sampling

Graph sampling via crawling has been actively considered as a generic and important tool for collecting uniform node samples so as to consistently estimate and uncover various characteristics of complex networks. The so-called simple random walk with re-weighting (SRW-rw) and Metropolis-Hastings (MH) algorithm have been popular in the literature for such unbiased graph sampling. However, an unavoidable downside of their core random walks -- slow diffusion over the space, can cause poor estimation accuracy. In this paper, we propose non-backtracking random walk with re-weighting (NBRW-rw) and MH algorithm with delayed acceptance (MHDA) which are theoretically guaranteed to achieve, at almost no additional cost, not only unbiased graph sampling but also higher efficiency (smaller asymptotic variance of the resulting unbiased estimators) than the SRW-rw and the MH algorithm, respectively. In particular, a remarkable feature of the MHDA is its applicability for any non-uniform node sampling like the MH algorithm, but ensuring better sampling efficiency than the MH algorithm. We also provide simulation results to confirm our theoretical findings.

stat.ME↗