Path Integral Sampler: a stochastic control approach for sampling
- URL: http://arxiv.org/abs/2111.15141v1
- Date: Tue, 30 Nov 2021 05:50:12 GMT
- Title: Path Integral Sampler: a stochastic control approach for sampling
- Authors: Qinsheng Zhang, Yongxin Chen
- Abstract summary: We present Path Integral Sampler(PIS), a novel algorithm to draw samples from unnormalized probability density functions.
The PIS draws samples from the initial distribution and then propagates the samples through the Schr"odinger bridge to reach the terminal distribution.
We provide theoretical justification of the sampling quality of PIS in terms of Wasserstein distance when sub-optimal control is used.
- Score: 4.94950858749529
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We present Path Integral Sampler~(PIS), a novel algorithm to draw samples
from unnormalized probability density functions. The PIS is built on the
Schr\"odinger bridge problem which aims to recover the most likely evolution of
a diffusion process given its initial distribution and terminal distribution.
The PIS draws samples from the initial distribution and then propagates the
samples through the Schr\"odinger bridge to reach the terminal distribution.
Applying the Girsanov theorem, with a simple prior diffusion, we formulate the
PIS as a stochastic optimal control problem whose running cost is the control
energy and terminal cost is chosen according to the target distribution. By
modeling the control as a neural network, we establish a sampling algorithm
that can be trained end-to-end. We provide theoretical justification of the
sampling quality of PIS in terms of Wasserstein distance when sub-optimal
control is used. Moreover, the path integrals theory is used to compute
importance weights of the samples to compensate for the bias induced by the
sub-optimality of the controller and time-discretization. We experimentally
demonstrate the advantages of PIS compared with other start-of-the-art sampling
methods on a variety of tasks.
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) - Harmonic Path Integral Diffusion [0.4527270266697462]
We present a novel approach for sampling from a continuous multivariate probability distribution, which may either be explicitly known (up to a normalization factor) or represented via empirical samples.
Our method constructs a time-dependent bridge from a delta function centered at the origin of the state space at $t=0$, transforming it into the target distribution at $t=1$.
We contrast these algorithms with other sampling methods, particularly simulated and path integral sampling, highlighting their advantages in terms of analytical control, accuracy, and computational efficiency.
arXiv Detail & Related papers (2024-09-23T16:20:21Z) - Amortized Posterior Sampling with Diffusion Prior Distillation [55.03585818289934]
We propose a variational inference approach to sample from the posterior distribution for solving inverse problems.
We show that our method is applicable to standard signals in Euclidean space, as well as signals on manifold.
arXiv Detail & Related papers (2024-07-25T09:53:12Z) - Dynamical Measure Transport and Neural PDE Solvers for Sampling [77.38204731939273]
We tackle the task of sampling from a probability density as transporting a tractable density function to the target.
We employ physics-informed neural networks (PINNs) to approximate the respective partial differential equations (PDEs) solutions.
PINNs allow for simulation- and discretization-free optimization and can be trained very efficiently.
arXiv Detail & Related papers (2024-07-10T17:39:50Z) - Sampling for Model Predictive Trajectory Planning in Autonomous Driving using Normalizing Flows [1.2972104025246092]
This paper investigates several sampling approaches for trajectory generation.
normalizing flows originating from the field of variational inference are considered.
Learning-based normalizing flow models are trained for a more efficient exploration of the input domain.
arXiv Detail & Related papers (2024-04-15T10:45:12Z) - Soft-constrained Schrodinger Bridge: a Stochastic Control Approach [4.922305511803267]
Schr"odinger bridge can be viewed as a continuous-time control problem where the goal is to find an optimally controlled diffusion process.
We propose to generalize this problem by allowing the terminal distribution to differ from the target but penalizing the Kullback-Leibler divergence between the two distributions.
One application is the development of robust generative diffusion models.
arXiv Detail & Related papers (2024-03-04T04:10:24Z) - Distributed Markov Chain Monte Carlo Sampling based on the Alternating
Direction Method of Multipliers [143.6249073384419]
In this paper, we propose a distributed sampling scheme based on the alternating direction method of multipliers.
We provide both theoretical guarantees of our algorithm's convergence and experimental evidence of its superiority to the state-of-the-art.
In simulation, we deploy our algorithm on linear and logistic regression tasks and illustrate its fast convergence compared to existing gradient-based methods.
arXiv Detail & Related papers (2024-01-29T02:08:40Z) - Adaptive Annealed Importance Sampling with Constant Rate Progress [68.8204255655161]
Annealed Importance Sampling (AIS) synthesizes weighted samples from an intractable distribution.
We propose the Constant Rate AIS algorithm and its efficient implementation for $alpha$-divergences.
arXiv Detail & Related papers (2023-06-27T08:15:28Z) - Plug-and-Play split Gibbs sampler: embedding deep generative priors in
Bayesian inference [12.91637880428221]
This paper introduces a plug-and-play sampling algorithm that leverages variable splitting to efficiently sample from a posterior distribution.
It divides the challenging task of posterior sampling into two simpler sampling problems.
Its performance is compared to recent state-of-the-art optimization and sampling methods.
arXiv Detail & Related papers (2023-04-21T17:17:51Z) - Unrolling Particles: Unsupervised Learning of Sampling Distributions [102.72972137287728]
Particle filtering is used to compute good nonlinear estimates of complex systems.
We show in simulations that the resulting particle filter yields good estimates in a wide range of scenarios.
arXiv Detail & Related papers (2021-10-06T16:58:34Z)
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.