Lectures on the Coupling Method

By Torgny Lindvall. 1992

Subfields: Probabilistic & Bayesian Methods

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Citations in the corpus

Unsupervised Image-to-Image Translation Networks (2017, background): “ unsupervised setting, the two sets consist of images from two marginal distributions in two different domains, and the task is to infer the joint distribution using these images. The coupling theory [16] states there exist an inﬁnite set of joint distributions that can arrive the given marginal dis”
The Privacy Blanket of the Shuffle Model (2019, background): “Equation 2 can be derived from the interpretation of the total variation distance in terms of couplings [23].”
Proving Differential Privacy via Probabilistic Couplings (2016, neutral): “Seeking to explain the power of liftings, Barthe et al. [6] establish a tight connection between probabilistic liftings and probabilistic couplings , a basic tool in probability theory [24, 30].”
Hilbert Space Embeddings and Metrics on Probability Measures (2009, methodology): “ws from (52). (iii) The proof of this result was presented in Sriperumbudur et al. (2009b) and is provided here for completeness. To prove the result, we use (57) and the coupling formulation for TV (Lindvall, 1992, p. 19), given as 1 2 TV(P,Q) = inf µ∈L(P,Q) µ(X6= Y), (66) where L(P,Q) is the set o”
On integral probability metrics, φ-divergences and binary classification (2009, methodology): “(ii) To prove (47), we use the coupling formulation for TV [56, p. 19] given by where L ( P , Q ) is the set of all measures on M × M with marginals P and Q .”
On Choosing and Bounding Probability Metrics (2002, background): “(3) Total variation distance has a coupling characterization: (Lindvall 1992, p. 19).”
Achieving Geometric Convergence for Distributed Optimization Over Time-Varying Graphs (2016, background): “…up to a constant, as can be seen by observing that it can take two random walks at least Ω( n 2 ) steps to intersect on these graphs, and thus the spectral gap has to be at least that much (for more details on making such arguments rigorous, we refer the reader to the introductory chapter of [30]).”
Essential spectral radius for Markov semigroups (I): discrete time case (2004, methodology): “Coupling technique was used by Nummelin and Tuominen [35], [36], Lindvall [28] (see also [31], Chap.”
The stability of conditional Markov processes and Markov chains in random environments (2008, methodology): “We can therefore apply the maximal coupling theorem [24], Theorem III.”
QUANTITATIVE CONVERGENCE RATES OF MARKOV CHAINS: A SIMPLE ACCOUNT (2002, background): “These investigations have been motivated largely by interest in Markov chain Monte Carlo (MCMC) algorithms including the Gibbs sampler and the Metropolis-Hastings algorithm (see e.g. Gilks et al., 1996), where convergence bounds provide useful information about how long the algorithms must be run to”
Characterization results and Markov chain Monte Carlo algorithms including exact simulation for some spatial point processes (1999, background): “…2 A - valued random elements ( X , Y ) and ( X 9 , Y 9 ) satisfy ( X , Y ) (cid:22) d ( X 9 , Y 9 ) if there exists a coupling of ( X , Y ) and ( X 9 , Y 9 ) such that ( X , Y ) (cid:22) (X 9 , Y 9 ) almost surely (for a general discussion of coupling and stochastic domination, see Lindvall 1992).”
Learning with Similarity Functions on Graphs using Matchings of Geometric Embeddings (2015, background): “…setting, the connection also opens up the opportunity to draw upon the theory and methods of optimal transport, including optimal couplings [38, 27] to prove rigorous results, in particular to verify the properties of a “good” similarity measure – which, as noted above, can often be quite…”
Random periodic processes, periodic measures and ergodicity (2014, background): “is the so called “coupling”. It says that trajectories with independent noise samples from two diﬀerent points will meet sometimes and a coupled process with the same distribution can be constructed ([41],[49]). However, this crucial phenomena does not hold any more when periodicity exists. It is no”
Probability Theory : The Coupling Method (2012, methodology): “Standard references for coupling are Lindvall [11] and Thorisson [15].”