# Heavy-tailed Sampling via Transformed Unadjusted Langevin Algorithm

@inproceedings{He2022HeavytailedSV, title={Heavy-tailed Sampling via Transformed Unadjusted Langevin Algorithm}, author={Ye He and Krishnakumar Balasubramanian and Murat A. Erdogdu}, year={2022} }

We analyze the oracle complexity of sampling from polynomially decaying heavy-tailed target densities based on running the Unadjusted Langevin Algorithm on certain transformed versions of the target density. The specific class of closed-form transformation maps that we construct are shown to be diffeomorphisms, and are particularly suited for developing efficient diffusion-based samplers. We characterize the precise class of heavy-tailed densities for which polynomial-order oracle complexities…

## 2 Citations

### Towards a Theory of Non-Log-Concave Sampling: First-Order Stationarity Guarantees for Langevin Monte Carlo

- Computer Science, MathematicsCOLT
- 2022

It is proved that averaged Langevin Monte Carlo outputs a sample with ε -relative Fisher information after O ( L 2 d 2 /ε 2 ) iterations, which constitutes a first step towards the general theory of non-log-concave sampling.

### Fisher information lower bounds for sampling

- Computer ScienceArXiv
- 2022

We prove two lower bounds for the complexity of non-log-concave sampling within the framework of Balasubramanian et al. (2022), who introduced the use of Fisher information ( FI ) bounds as a notion…

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