341 citations · 852 across the 28 of their papers we have counts for
17 papers · 1 filter
Scaling Up Bayesian Neural Networks with Neural Networks
Zahra Moslemi, Yang Meng, Shiwei Lan +1
Bayesian Neural Networks (BNNs) offer a principled and natural framework for proper uncertainty quantification in the context of deep learning. They address the typical challenges…
Sampling Constrained Continuous Probability Distributions: A Review
Shiwei Lan, Lulu Kang
The problem of sampling constrained continuous distributions has frequently appeared in many machine/statistical learning models. Many Monte Carlo Markov Chain (MCMC) sampling meth…
Scaling Up Bayesian Uncertainty Quantification for Inverse Problems using Deep Neural Networks
Shiwei Lan, Shuyi Li, Babak Shahbaba
Due to the importance of uncertainty quantification (UQ), Bayesian approach to inverse problems has recently gained popularity in applied mathematics, physics, and engineering. How…
Calibrate, Emulate, Sample
Emmet Cleary, Alfredo Garbuno-Inigo, Shiwei Lan +2
Many parameter estimation problems arising in applications are best cast in the framework of Bayesian inversion. This allows not only for an estimate of the parameters, but also fo…
Deep Markov Chain Monte Carlo
Babak Shahbaba, Luis Martinez Lomeli, Tian Chen +1
We propose a new computationally efficient sampling scheme for Bayesian inference involving high dimensional probability distributions. Our method maps the original parameter space…
Adaptive Dimension Reduction to Accelerate Infinite-Dimensional Geometric Markov Chain Monte Carlo
Shiwei Lan
Bayesian inverse problems highly rely on efficient and effective inference methods for uncertainty quantification (UQ). Infinite-dimensional MCMC algorithms, directly defined on fu…
Geodesic Lagrangian Monte Carlo over the space of positive definite matrices: with application to Bayesian spectral density estimation
Andrew Holbrook, Shiwei Lan, Alexander Vandenberg-Rodes +1
We extend the application of Hamiltonian Monte Carlo to allow for sampling from probability distributions defined over symmetric or Hermitian positive definite matrices. To do so,…
Geometric MCMC for Infinite-Dimensional Inverse Problems
Alexandros Beskos, Mark Girolami, Shiwei Lan +2
Bayesian inverse problems often involve sampling posterior distributions on infinite-dimensional function spaces. Traditional Markov chain Monte Carlo (MCMC) algorithms are charact…
Emulation of Higher-Order Tensors in Manifold Monte Carlo Methods for Bayesian Inverse Problems
Shiwei Lan, Tan Bui-Thanh, Mike Christie +1
The Bayesian approach to Inverse Problems relies predominantly on Markov Chain Monte Carlo methods for posterior inference. The typical nonlinear concentration of posterior measure…
Sampling constrained probability distributions using Spherical Augmentation
Shiwei Lan, Babak Shahbaba
Statistical models with constrained probability distributions are abundant in machine learning. Some examples include regression models with norm constraints (e.g., Lasso), probit,…
An Efficient Bayesian Inference Framework for Coalescent-Based Nonparametric Phylodynamics
Shiwei Lan, Julia A. Palacios, Michael Karcher +2
Phylodynamics focuses on the problem of reconstructing past population size dynamics from current genetic samples taken from the population of interest. This technique has been ext…
Discussion of "Geodesic Monte Carlo on Embedded Manifolds"
Simon Byrne, Mark Girolami, Persi Diaconis +9
Contributed discussion and rejoinder to "Geodesic Monte Carlo on Embedded Manifolds" (arXiv:1301.6064)
Spherical Hamiltonian Monte Carlo for Constrained Target Distributions
Shiwei Lan, Bo Zhou, Babak Shahbaba
We propose a new Markov Chain Monte Carlo (MCMC) method for constrained target distributions. Our method first maps the -dimensional constrained domain of parameters to the unit…
Wormhole Hamiltonian Monte Carlo
Shiwei Lan, Jeffrey Streets, Babak Shahbaba
In machine learning and statistics, probabilistic inference involving multimodal distributions is quite difficult. This is especially true in high dimensional problems, where most…
Lagrangian Dynamical Monte Carlo
Shiwei Lan, Vassilios Stathopoulos, Babak Shahbaba +1
Hamiltonian Monte Carlo (HMC) improves the computational efficiency of the Metropolis algorithm by reducing its random walk behavior. Riemannian Manifold HMC (RMHMC) further improv…
Split HMC for Gaussian Process Models
Shiwei Lan, Babak Shahbaba
In this paper, we discuss an extension of the Split Hamiltonian Monte Carlo (Split HMC) method for Gaussian process model (GPM). This method is based on splitting the Hamiltonian i…
Split Hamiltonian Monte Carlo
Babak Shahbaba, Shiwei Lan, Wesley O. Johnson +1
We show how the Hamiltonian Monte Carlo algorithm can sometimes be speeded up by "splitting" the Hamiltonian in a way that allows much of the movement around the state space to be…