Sampling with Mirrored Stein Operators
- URL: http://arxiv.org/abs/2106.12506v1
- Date: Wed, 23 Jun 2021 16:23:34 GMT
- Title: Sampling with Mirrored Stein Operators
- Authors: Jiaxin Shi, Chang Liu, Lester Mackey
- Abstract summary: We introduce a new family of particle evolution samplers suitable for constrained domains and non-Euclidean geometries.
New samplers yield accurate approximations to distributions on the simplex, deliver valid confidence intervals in post-selection inference, and converge more rapidly than prior methods.
- Score: 36.37460207707895
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We introduce a new family of particle evolution samplers suitable for
constrained domains and non-Euclidean geometries. Stein Variational Mirror
Descent and Mirrored Stein Variational Gradient Descent minimize the
Kullback-Leibler (KL) divergence to constrained target distributions by
evolving particles in a dual space defined by a mirror map. Stein Variational
Natural Gradient exploits non-Euclidean geometry to more efficiently minimize
the KL divergence to unconstrained targets. We derive these samplers from a new
class of mirrored Stein operators and adaptive kernels developed in this work.
We demonstrate that these new samplers yield accurate approximations to
distributions on the simplex, deliver valid confidence intervals in
post-selection inference, and converge more rapidly than prior methods in
large-scale unconstrained posterior inference. Finally, we establish the
convergence of our new procedures under verifiable conditions on the target
distribution.
Related papers
- Theory on Score-Mismatched Diffusion Models and Zero-Shot Conditional Samplers [49.97755400231656]
We present the first performance guarantee with explicit dimensional general score-mismatched diffusion samplers.
We show that score mismatches result in an distributional bias between the target and sampling distributions, proportional to the accumulated mismatch between the target and training distributions.
This result can be directly applied to zero-shot conditional samplers for any conditional model, irrespective of measurement noise.
arXiv Detail & Related papers (2024-10-17T16:42:12Z) - Through the Looking Glass: Mirror Schrödinger Bridges [16.05211717546091]
Resampling from a target measure whose density is unknown is a fundamental problem in mathematical statistics and machine learning.
We propose a new model for conditional resampling called mirror Schr"odinger bridges.
arXiv Detail & Related papers (2024-10-09T15:48:56Z) - Statistically Optimal Generative Modeling with Maximum Deviation from the Empirical Distribution [2.1146241717926664]
We show that the Wasserstein GAN, constrained to left-invertible push-forward maps, generates distributions that avoid replication and significantly deviate from the empirical distribution.
Our most important contribution provides a finite-sample lower bound on the Wasserstein-1 distance between the generative distribution and the empirical one.
We also establish a finite-sample upper bound on the distance between the generative distribution and the true data-generating one.
arXiv Detail & Related papers (2023-07-31T06:11:57Z) - Metropolis Sampling for Constrained Diffusion Models [11.488860260925504]
Denoising diffusion models have recently emerged as the predominant paradigm for generative modelling on image domains.
We introduce an alternative, simple noretisation scheme based on the reflected Brownian motion.
arXiv Detail & Related papers (2023-07-11T17:05:23Z) - Bayesian Pseudo-Coresets via Contrastive Divergence [5.479797073162603]
We introduce a novel approach for constructing pseudo-coresets by utilizing contrastive divergence.
It eliminates the need for approximations in the pseudo-coreset construction process.
We conduct extensive experiments on multiple datasets, demonstrating its superiority over existing BPC techniques.
arXiv Detail & Related papers (2023-03-20T17:13:50Z) - Sampling with Mollified Interaction Energy Descent [57.00583139477843]
We present a new optimization-based method for sampling called mollified interaction energy descent (MIED)
MIED minimizes a new class of energies on probability measures called mollified interaction energies (MIEs)
We show experimentally that for unconstrained sampling problems our algorithm performs on par with existing particle-based algorithms like SVGD.
arXiv Detail & Related papers (2022-10-24T16:54:18Z) - Posterior Coreset Construction with Kernelized Stein Discrepancy for
Model-Based Reinforcement Learning [78.30395044401321]
We develop a novel model-based approach to reinforcement learning (MBRL)
It relaxes the assumptions on the target transition model to belong to a generic family of mixture models.
It can achieve up-to 50 percent reduction in wall clock time in some continuous control environments.
arXiv Detail & Related papers (2022-06-02T17:27:49Z) - Minibatch vs Local SGD with Shuffling: Tight Convergence Bounds and
Beyond [63.59034509960994]
We study shuffling-based variants: minibatch and local Random Reshuffling, which draw gradients without replacement.
For smooth functions satisfying the Polyak-Lojasiewicz condition, we obtain convergence bounds which show that these shuffling-based variants converge faster than their with-replacement counterparts.
We propose an algorithmic modification called synchronized shuffling that leads to convergence rates faster than our lower bounds in near-homogeneous settings.
arXiv Detail & Related papers (2021-10-20T02:25:25Z) - Variational Refinement for Importance Sampling Using the Forward
Kullback-Leibler Divergence [77.06203118175335]
Variational Inference (VI) is a popular alternative to exact sampling in Bayesian inference.
Importance sampling (IS) is often used to fine-tune and de-bias the estimates of approximate Bayesian inference procedures.
We propose a novel combination of optimization and sampling techniques for approximate Bayesian inference.
arXiv Detail & Related papers (2021-06-30T11:00:24Z) - Annealed Stein Variational Gradient Descent [4.020523898765405]
Stein variational gradient descent has gained attention in the approximate literature inference for its flexibility and accuracy.
We empirically explore the ability of this method to sample from multi-modal distributions and focus on two important issues: (i) the inability of the particles to escape from local modes and (ii) the inefficacy in reproducing the density of the different regions.
arXiv Detail & Related papers (2021-01-24T22:18:30Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.