Strong Data Processing Inequalities: Applications to MCMC and Graphical Models
summary
Defines a pointwise strong data processing inequality (SDPI) for phi‑divergences, proves a general lower bound eta_phi(mu,K) ≥ eta_chi^2(mu,K) (chi^2 SDPI equals squared maximal correlation), and recalls Ahlswede–Gács 1976 exact value 1−2ε^2 for Bernoulli(½) through a BSC(ε). Introduces a comparison principle: if K̄/Y ratios are uniformly bounded by A then eta_phi(K) ≤ 1−(1/A)(1−eta_phi(K̄)). Applies this to bound Swendsen–Wang vs. Heat‑Bath contraction constants, improving Ulrich 2012 with explicit dependence on Q, Δ and e^{βΔ}.
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chapters (9)
- 0:00Introduction to SDPI
- 1:15Defining strong SDPI
- 4:37Phi-divergences and history
- 7:18SDPI constant properties
- 11:23Proof of simulation bounds
- 15:23Coloring problems application
- 18:40Markov chain algorithms
- 22:17Comparison principle proof
- 27:35Q&A and concluding remarks
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