
Highprecision Estimation of Random Walks in Small Space
In this paper, we provide a deterministic Õ(log N)space algorithm for e...
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Comparing the Switch and Curveball Markov Chains for Sampling Binary Matrices with Fixed Marginals
The Curveball algorithm is a variation on wellknown switchbased Markov...
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Mixing Time on the Kagome Lattice
We consider tilings of a closed region of the Kagome lattice (partition ...
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Utilizing Network Structure to Bound the Convergence Rate in Markov Chain Monte Carlo Algorithms
We consider the problem of estimating the measure of subsets in very lar...
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On the limitations of singlestep drift and minorization in Markov chain convergence analysis
Over the last three decades, there has been a considerable effort within...
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A Unified Markov Chain Approach to Analysing Randomised Search Heuristics
The convergence, convergence rate and expected hitting time play fundame...
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Bioinspired Bipedal Locomotion Control for Humanoid Robotics Based on EACO
To construct a robot that can walk as efficiently and steadily as humans...
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Concentration Bounds for Cooccurrence Matrices of Markov Chains
Cooccurrence statistics for sequential data are common and important data signals in machine learning, which provide rich correlation and clustering information about the underlying object space. We give the first bound on the convergence rate of estimating the cooccurrence matrix of a regular (aperiodic and irreducible) finite Markov chain from a single random trajectory. Our work is motivated by the analysis of a wellknown graph learning algorithm DeepWalk by [Qiu et al. WSDM '18], who study the convergence (in probability) of cooccurrence matrix from random walk on undirected graphs in the limit, but left the convergence rate an open problem. We prove a Chernofftype bound for sums of matrixvalued random variables sampled via an ergodic Markov chain, generalizing the regular undirected graph case studied by [Garg et al. STOC '18]. Using the Chernofftype bound, we show that given a regular Markov chain with n states and mixing time τ, we need a trajectory of length O(τ (log(n)+log(τ))/ϵ^2) to achieve an estimator of the cooccurrence matrix with error bound ϵ. We conduct several experiments and the experimental results are consistent with the exponentially fast convergence rate from theoretical analysis. Our result gives the first sample complexity analysis in graph representation learning.
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