Geometric Random Walks: a Survey

By Santosh Srinivas Vempala. 2007

227 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/a89a8f0b083d9406278bc924b26c18c4dc854bfc

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Citations in the corpus

Fair Algorithms for Infinite and Contextual Bandits (2016, methodology): “Recall that FairGap requires some method of sampling uniformly at random from a given convex body C t , a problem that has attracted extensive attention over the past few decades (see Vempala [2005] for a survey of results).”
Log-concave sampling: Metropolis-Hastings algorithms are fast! (2018, methodology): “For a more rapid introduction to the basics of continuous state-space Markov chains, we refer the reader to the expository paper (Diaconis and Freedman, 1997) or Section 1 and 2 of the papers (Lov´asz and Simonovits, 1993; Vempala, 2005).”
Tractability of Multivariate Problems (2008, background): “This random walk was studied by many authors, see Lovász and Simonovits [179], Vempala [318] and [183].”
Renyi Differential Privacy Mechanisms for Posterior Sampling (2017, methodology): “However, a number of MCMC methods are known to converge in total variational distance in time polynomial in the data dimension for log-concave posteriors (which is the case here) [17].”
Protecting Locations with Differential Privacy under Temporal Correlations (2014, methodology): “We skip the sampling details and refer readers to the survey paper of Santosh Vempala [39] for a complete study.”
Bayesian Inverse Reinforcement Learning (2007, methodology): “The sampling technique we use is an MCMC algorithm GridWalk [Vempala, 2005] that generates a Markov chain on the intersection points of a grid of length δ in the region R (denoted R/δ).”
On the geometry of differential privacy (2009, methodology): “We refer the reader to the survey of Vempala [Vem05] or the original paper of Dyer, Frieze and Kannan [DFK91] for a description of the Grid walk and background information.”
Robust Optimization using Machine Learning for Uncertainty Sets (2014, methodology): “he nite formulation can be solved. 6 Option 2:If Uis not a \nice" set, then do the following: sample Lelements from Uuniformly. For instance, this can be done using geometric random walks [e.g., Vempala, 2005] if Uis convex. Then solve the sampled version of Equation (2) to obtain a robust solu”