# Fractional Langevin Monte Carlo: Exploring L\'{e}vy Driven Stochastic Differential Equations for Markov Chain Monte Carlo

@inproceedings{cSimcsekli2017FractionalLM, title={Fractional Langevin Monte Carlo: Exploring L\'\{e\}vy Driven Stochastic Differential Equations for Markov Chain Monte Carlo}, author={Umut cSimcsekli}, year={2017} }

Along with the recent advances in scalable Markov Chain Monte Carlo methods, sampling techniques that are based on Langevin diffusions have started receiving increasing attention. These so called Langevin Monte Carlo (LMC) methods are based on diffusions driven by a Brownian motion, which gives rise to Gaussian proposal distributions in the resulting algorithms. Even though these approaches have proven successful in many applications, their performance can be limited by the light-tailed nature…

## 2 Citations

### A Tail-Index Analysis of Stochastic Gradient Noise in Deep Neural Networks

- Computer ScienceICML
- 2019

It is argued that the Gaussianity assumption might fail to hold in deep learning settings and hence render the Brownian motion-based analyses inappropriate and open up a different perspective and shed more light on the belief that SGD prefers wide minima.

### On the Heavy-Tailed Theory of Stochastic Gradient Descent for Deep Neural Networks

- Computer ScienceArXiv
- 2019

It is argued that the Gaussianity assumption might fail to hold in deep learning settings and hence render the Brownian motion-based analyses inappropriate and establish an explicit connection between the convergence rate of SGD to a local minimum and the tail-index $\alpha$.

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