Summary of Deep Learning For Computing Convergence Rates Of Markov Chains, by Yanlin Qu et al.
Deep Learning for Computing Convergence Rates of Markov Chains
by Yanlin Qu, Jose Blanchet, Peter Glynn
First submitted to arxiv on: 30 May 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Probability (math.PR); Machine Learning (stat.ML)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary This paper proposes the Deep Contractive Drift Calculator (DCDC), a general-purpose sample-based algorithm for bounding the convergence of Markov chains to stationarity in Wasserstein distance. The DCDC consists of two components: the Contractive Drift Equation (CDE) and an efficient neural-network-based CDE solver. The authors introduce the CDE, which provides an explicit convergence bound when solved. They also analyze the sample complexity of the algorithm and demonstrate its effectiveness by generating convergence bounds for realistic Markov chains. The DCDC is particularly useful in areas such as Markov chain Monte Carlo and algorithmic analysis. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper helps us understand how to calculate the speed at which Markov chains reach a state of balance. This is important because it can help us make predictions about complex systems. The researchers developed an algorithm called the Deep Contractive Drift Calculator (DCDC) that can do this calculation. They also tested their algorithm on some real-world problems and showed that it works well. |
Keywords
» Artificial intelligence » Neural network
