Timezone: »

 
Poster
Rapid Convergence of the Unadjusted Langevin Algorithm: Isoperimetry Suffices
Santosh Vempala · Andre Wibisono

Wed Dec 11 05:00 PM -- 07:00 PM (PST) @ East Exhibition Hall B + C #181
We study the Unadjusted Langevin Algorithm (ULA) for sampling from a probability distribution $\nu = e^{-f}$ on $\R^n$. We prove a convergence guarantee in Kullback-Leibler (KL) divergence assuming $\nu$ satisfies log-Sobolev inequality and $f$ has bounded Hessian. Notably, we do not assume convexity or bounds on higher derivatives. We also prove convergence guarantees in R\'enyi divergence of order $q > 1$ assuming the limit of ULA satisfies either log-Sobolev or Poincar\'e inequality.

Author Information

Santosh Vempala (Georgia Tech)
Andre Wibisono (Georgia Tech)

More from the Same Authors

  • 2022 Poster: Sampling with Riemannian Hamiltonian Monte Carlo in a Constrained Space »
    Yunbum Kook · Yin-Tat Lee · Ruoqi Shen · Santosh Vempala
  • 2021 : An Interactive Tool for Computation with Assemblies of Neurons »
    Seung Je Jung · Christos Papadimitriou · Santosh Vempala
  • 2019 : Poster Session »
    Pravish Sainath · Mohamed Akrout · Charles Delahunt · Nathan Kutz · Guangyu Robert Yang · Joseph Marino · L F Abbott · Nicolas Vecoven · Damien Ernst · andrew warrington · Michael Kagan · Kyunghyun Cho · Kameron Harris · Leopold Grinberg · John J. Hopfield · Dmitry Krotov · Taliah Muhammad · Erick Cobos · Edgar Walker · Jacob Reimer · Andreas Tolias · Alexander Ecker · Janaki Sheth · Yu Zhang · Maciej Wołczyk · Jacek Tabor · Szymon Maszke · Roman Pogodin · Dane Corneil · Wulfram Gerstner · Baihan Lin · Guillermo Cecchi · Jenna M Reinen · Irina Rish · Guillaume Bellec · Darjan Salaj · Anand Subramoney · Wolfgang Maass · Yueqi Wang · Ari Pakman · Jin Hyung Lee · Liam Paninski · Bryan Tripp · Colin Graber · Alex Schwing · Luke Prince · Gabriel Ocker · Michael Buice · Benjamin Lansdell · Konrad Kording · Jack Lindsey · Terrence Sejnowski · Matthew Farrell · Eric Shea-Brown · Nicolas Farrugia · Victor Nepveu · Jiwoong Im · Kristin Branson · Brian Hu · Ramakrishnan Iyer · Stefan Mihalas · Sneha Aenugu · Hananel Hazan · Sihui Dai · Tan Nguyen · Doris Tsao · Richard Baraniuk · Anima Anandkumar · Hidenori Tanaka · Aran Nayebi · Stephen Baccus · Surya Ganguli · Dean Pospisil · Eilif Muller · Jeffrey S Cheng · Gaël Varoquaux · Kamalaker Dadi · Dimitrios C Gklezakos · Rajesh PN Rao · Anand Louis · Christos Papadimitriou · Santosh Vempala · Naganand Yadati · Daniel Zdeblick · Daniela M Witten · Nicholas Roberts · Vinay Prabhu · Pierre Bellec · Poornima Ramesh · Jakob H Macke · Santiago Cadena · Guillaume Bellec · Franz Scherr · Owen Marschall · Robert Kim · Hannes Rapp · Marcio Fonseca · Oliver Armitage · Jiwoong Im · Thomas Hardcastle · Abhishek Sharma · Wyeth Bair · Adrian Valente · Shane Shang · Merav Stern · Rutuja Patil · Peter Wang · Sruthi Gorantla · Peter Stratton · Tristan Edwards · Jialin Lu · Martin Ester · Yurii Vlasov · Siavash Golkar
  • 2019 Poster: Multi-Criteria Dimensionality Reduction with Applications to Fairness »
    Uthaipon Tantipongpipat · Samira Samadi · Mohit Singh · Jamie Morgenstern · Santosh Vempala
  • 2019 Spotlight: Multi-Criteria Dimensionality Reduction with Applications to Fairness »
    Uthaipon Tantipongpipat · Samira Samadi · Mohit Singh · Jamie Morgenstern · Santosh Vempala
  • 2019 Poster: Accelerating Rescaled Gradient Descent: Fast Optimization of Smooth Functions »
    Ashia Wilson · Lester Mackey · Andre Wibisono
  • 2018 Poster: Smoothed Analysis of Discrete Tensor Decomposition and Assemblies of Neurons »
    Nima Anari · Constantinos Daskalakis · Wolfgang Maass · Christos Papadimitriou · Amin Saberi · Santosh Vempala
  • 2018 Poster: The Price of Fair PCA: One Extra dimension »
    Samira Samadi · Uthaipon Tantipongpipat · Jamie Morgenstern · Mohit Singh · Santosh Vempala
  • 2017 Poster: On the Complexity of Learning Neural Networks »
    Le Song · Santosh Vempala · John Wilmes · Bo Xie
  • 2017 Spotlight: On the Complexity of Learning Neural Networks »
    Le Song · Santosh Vempala · John Wilmes · Bo Xie
  • 2015 Poster: Subsampled Power Iteration: a Unified Algorithm for Block Models and Planted CSP's »
    Vitaly Feldman · Will Perkins · Santosh Vempala