Mixing Time Estimation in Reversible Markov Chains from a Single Sample Path
Authors: Daniel J. Hsu, Aryeh Kontorovich, Csaba Szepesvari
NeurIPS 2015 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | This article provides the first procedure for computing a fully data-dependent interval that traps the mixing time tmix of a finite reversible ergodic Markov chain at a prescribed confidence level. The interval is computed from a single finite-length sample path from the Markov chain, and does not require the knowledge of any parameters of the chain. This stands in contrast to previous approaches, which either only provide point estimates, or require a reset mechanism, or additional prior knowledge. The interval is constructed around the relaxation time trelax, which is strongly related to the mixing time, and the width of the interval converges to zero roughly at a n rate, where n is the length of the sample path. Upper and lower bounds are given on the number of samples required to achieve constant-factor multiplicative accuracy. The lower bounds indicate that, unless further restrictions are placed on the chain, no procedure can achieve this accuracy level before seeing each state at least Ω(trelax) times on the average. Finally, future directions of research are identified. |
| Researcher Affiliation | Academia | Daniel Hsu Columbia University djhsu@cs.columbia.edu Aryeh Kontorovich Ben-Gurion University karyeh@cs.bgu.ac.il Csaba Szepesv ari University of Alberta szepesva@cs.ualberta.ca |
| Pseudocode | Yes | Algorithm 1 Empirical confidence intervals |
| Open Source Code | No | The paper does not provide any statement or link indicating the availability of open-source code for the described methodology. |
| Open Datasets | No | The paper is theoretical in nature and focuses on statistical procedures and bounds for Markov chains, rather than empirical evaluation on specific datasets. Therefore, it does not mention public datasets or provide access information for them. |
| Dataset Splits | No | The paper is theoretical and focuses on mathematical proofs and algorithms for estimating mixing times. It does not describe experiments with dataset splits for training, validation, or testing. |
| Hardware Specification | No | The paper is theoretical and focuses on mathematical proofs and algorithms. It does not describe any experimental setup that would require hardware specifications. |
| Software Dependencies | No | The paper is theoretical and focuses on mathematical concepts and algorithms. It does not mention any specific software dependencies with version numbers. |
| Experiment Setup | No | The paper focuses on theoretical analysis and algorithm design for estimating mixing times. It does not describe any empirical experimental setup with hyperparameters or training settings. |