# Improved Estimation of Relaxation Time in Non-reversible Markov Chains

@inproceedings{Wolfer2022ImprovedEO, title={Improved Estimation of Relaxation Time in Non-reversible Markov Chains}, author={Geoffrey Wolfer and Aryeh Kontorovich}, year={2022} }

We show that the minimax sample complexity for estimating the pseudo-spectral gap γ ps of an ergodic Markov chain in constant multiplicative error is of the order of

## References

SHOWING 1-10 OF 52 REFERENCES

### Computationally Efficient Estimation of the Spectral Gap of a Markov Chain

- Mathematics, Computer ScienceProc. ACM Meas. Anal. Comput. Syst.
- 2019

The UCPI (Upper Confidence Power Iteration) algorithm is proposed, a low-complexity algorithm which estimates the spectral gap in time O(n) and memory space O ((łn n)^2) given n samples, in stark contrast with most known methods which require at least memoryspace O(|Ω|), so that they cannot be applied to large state spaces.

### Statistical estimation of ergodic Markov chain kernel over discrete state space

- Mathematics
- 2018

We investigate the statistical complexity of estimating the parameters of a discrete-state Markov chain kernel from a single long sequence of state observations. In the finite case, we characterize…

### Improving the Asymptotic Performance of Markov Chain Monte-Carlo by Inserting Vortices

- MathematicsNIPS
- 2010

It is confirmed that non-reversible chains are fundamentally better than reversible ones in terms of asymptotic performance, and suggests interesting directions for further improving MCMC.

### Estimating the spectral gap of a trace-class Markov operator

- MathematicsElectronic Journal of Statistics
- 2019

The utility of a Markov chain Monte Carlo algorithm is, in large part, determined by the size of the spectral gap of the corresponding Markov operator. However, calculating (and even approximating)…

### Estimating the Spectral Gap of a Reversible Markov Chain from a Short Trajectory

- Mathematics
- 2016

The spectral gap $\gamma$ of an ergodic and reversible Markov chain is an important parameter measuring the asymptotic rate of convergence. In applications, the transition matrix $P$ may be unknown,…

### Mixing Time Estimation in Reversible Markov Chains from a Single Sample Path

- MathematicsNIPS
- 2015

This article provides the first procedure for computing a fully data-dependent interval that traps the mixing time of a finite reversible ergodic Markov chain at a prescribed confidence level, and does not require the knowledge of any parameters of the chain.

### Accelerated Sampling on Discrete Spaces with Non-Reversible Markov Processes

- Computer Science, Mathematics
- 2019

A class of efficient continuous-time, non-reversible algorithms which make active use of the structure of the underlying space and place particular emphasis on how symmetries and other group-theoretic notions can be used to improve exploration of the space.

### Improving Asymptotic Variance of MCMC Estimators: Non-reversible Chains are Better

- Mathematics
- 2004

I show how any reversible Markov chain on a finite state space that is irreducible, and hence suitable for estimating expectations with respect to its invariant distribution, can be used to construct…

### Empirical and Instance-Dependent Estimation of Markov Chain and Mixing Time

- Mathematics
- 2019

We tackle the fundamental problem of estimating the mixing time of a Markov chain from a single trajectory of observations. In contrast with previous works which considered Hilbert space methods to…