Polynomial-Chaos-Based Decentralized DynamicParameter Estimation Using Langevin MCMC
Explore the source record for details and available documents.
Mathematics and Computing↗
SEARCH · Search NASA
Results for “Langevin MCMC”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
A Bayesian Approach to Real-Time Dynamic Parameter Estimation Using Phasor Measurement Unit Measurement
Here, we develop a polynomial-chaos-expansion (PCE)-based approach for decentralized dynamic parameter estimation through Bayesian inference. Using this approach, the non-Gaussian distribution of the inverted parameters is obtained. More specifically, we first represent the decentralized generator model with the PCE-based surrogate. This surrogate allows us to efficiently evaluate the time-consuming dynamic solver at parameter values through Metropolis-Hastings (M-H)-based Markov chain Monte Carlo (MCMC). Then, we propose a two-stage hybrid Markov chain Monte Carlo (MCMC) to recover a posteriori distribution of the decentralized generator model parameters. In the first stage, we use the gradient-enhanced Langevin MCMC algorithm to characterize an intermediate posterior parameter distribution. This algorithm is computationally scalable to the high-dimensional parameter space. Based on the intermediate posterior distribution, during the second stage, we use the adaptive MCMC algorithm to fine-tune the strong correlations between the parameters. Finally, the fully recovered a posterior distribution is obtained in the end. The simulation results show that the proposed PCE-based hybrid MCMC algorithm can accurately and efficiently estimate the high-dimensional generator dynamic model parameters with full probabilistic distribution provided.
42 ENGINEERING↗
Ensemble preconditioning for Markov chain Monte Carlo simulation
Not Available
97 MATHEMATICS AND COMPUTING↗
eeyore
The software "eeyore" solves the problem of running Markov chain Monte Carlo (MCMC) algorithms on Bayesian neural networks. There is software for MCMC algorithms and software for neural network (such as PyTorch and TensorFlow), but there are limited solutions for combining the two. The main idea is to create a subclass of the 'torch.nn.Module' for defining Bayesian neural networks with the desired functionality required by MCMC taking the form of additional methods in that sub-class. This way, neural network functionality of PyTorch is exposed to the developer and user, allowing to develop MCMC methods on top of it through a simple API. The code implements Langevin Monte Carlo algorithms and population MCMC algorithms, as well as combinations of these, for Bayesian neural networks. This kind of functionality is not available elsewhere, to the best of the authors' knowledge. Moreover, a simple API is available that allows to implement new MCMC algorithms in the future.
Papamarkou, Theodore↗
Laplacian Smoothing Stochastic Gradient Markov Chain Monte Carlo
As an important Markov chain Monte Carlo (MCMC) method, the stochastic gradient Langevin dynamics (SGLD) algorithm has achieved great success in Bayesian learning and posterior sampling. Furthermore, SGLD typically suffers from a slow convergence rate due to its large variance caused by the stochastic gradient. In order to alleviate these drawbacks, we leverage the recently developed Laplacian smoothing technique and propose a Laplacian smoothing stochastic gradient Langevin dynamics (LS-SGLD) algorithm. We prove that for sampling from both log-concave and non-log-concave densities, LS-SGLD achieves strictly smaller discretization error in 2-Wasserstein distance, although its mixing rate can be slightly slower. Experiments on both synthetic and real datasets verify our theoretical results and demonstrate the superior performance of LS-SGLD on different machine learning tasks including posterior sampling, Bayesian logistic regression, and training Bayesian convolutional neural networks.
97 MATHEMATICS AND COMPUTING↗
DNA Dynamics Is Likely to Be a Factor in the Genomic Nucleotide Repeats Expansions Related to Diseases
Trinucleotide repeats sequences (TRS) represent a common type of genomic DNA motif whose expansion is associated with a large number of human diseases. The driving molecular mechanisms of the TRS ongoing dynamic expansion across generations and within tissues and its influence on genomic DNA functions are not well understood. Here we report results for a novel and notable collective breathing behavior of genomic DNA of tandem TRS, leading to propensity for large local DNA transient openings at physiological temperature. Our Langevin molecular dynamics (LMD) and Markov Chain Monte Carlo (MCMC) simulations demonstrate that the patterns of openings of various TRSs depend specifically on their length. The collective propensity for DNA strand separation of repeated sequences serves as a precursor for outsized intermediate bubble states independently of the G/C-content. We report that repeats have the potential to interfere with the binding of transcription factors to their consensus sequence by altered DNA breathing dynamics in proximity of the binding sites. These observations might influence ongoing attempts to use LMD and MCMC simulations for TRS–related modeling of genomic DNA functionality in elucidating the common denominators of the dynamic TRS expansion mutation with potential therapeutic applications.
59 BASIC BIOLOGICAL SCIENCES↗
Bayesian sparse learning with preconditioned stochastic gradient MCMC and its applications
Deep neural networks have been successfully employed in an extensive variety of research areas, including solving partial differential equations. Despite its significant success, there are some challenges in effectively training DNN, such as avoiding overfitting in over-parameterized DNNs and accelerating the optimization in DNNs with pathological curvature. Here, we propose a Bayesian type sparse deep learning algorithm. The algorithm utilizes a set of spike-and-slab priors for the parameters in the deep neural network. The hierarchical Bayesian mixture will be trained using an adaptive empirical method. That is, one will alternatively sample from the posterior using preconditioned stochastic gradient Langevin Dynamics (PSGLD), and optimize the latent variables via stochastic approximation. The sparsity of the network is achieved while optimizing the hyperparameters with adaptive searching and penalizing. A popular SG-MCMC approach is Stochastic gradient Langevin dynamics (SGLD). However, considering the complex geometry in the model parameter space in nonconvex learning, updating parameters using a universal step size in each component as in SGLD may cause slow mixing. To address this issue, we apply a computationally manageable preconditioner in the updating rule, which provides a step-size parameter to adapt to local geometric properties. Moreover, by smoothly optimizing the hyperparameter in the preconditioning matrix, our proposed algorithm ensures a decreasing bias, which is introduced by ignoring the correction term in the preconditioned SGLD. According to the existing theoretical framework, we show that the proposed algorithm can asymptotically converge to the correct distribution with a controllable bias under mild conditions. Numerical tests are performed on both synthetic regression problems and learning solutions of elliptic PDE, which demonstrate the accuracy and efficiency of the present work.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Dimension-independent likelihood-informed MCMC
Many Bayesian inference problems require exploring the posterior distribution of high-dimensional parameters that represent the discretization of an underlying function. This work introduces a family of Markov chain Monte Carlo (MCMC) samplers that can adapt to the particular structure of a posterior distribution over functions. Two distinct lines of research intersect in the methods developed here. First, we introduce a general class of operator-weighted proposal distributions that are well defined on function space, such that the performance of the resulting MCMC samplers is independent of the discretization of the function. Second, by exploiting local Hessian information and any associated low-dimensional structure in the change from prior to posterior distributions, we develop an inhomogeneous discretization scheme for the Langevin stochastic differential equation that yields operator-weighted proposals adapted to the non-Gaussian structure of the posterior. The resulting dimension-independent and likelihood-informed (DILI) MCMC samplers may be useful for a large class of high-dimensional problems where the target probability measure has a density with respect to a Gaussian reference measure. Two nonlinear inverse problems are used to demonstrate the efficiency of these DILI samplers: an elliptic PDE coefficient inverse problem and path reconstruction in a conditioned diffusion.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Bayesian Static Parameter Estimation for Partially Observed Diffusions via Multilevel Monte Carlo
In this article we consider static Bayesian parameter estimation for partially observed diffusions that are discretely observed. We work under the assumption that one must resort to discretizing the underlying diffusion process, for instance, using the Euler--Maruyama method. Given this assumption, we show how one can use Markov chain Monte Carlo (MCMC) and particularly particle MCMC [C. Andrieu, A. Doucet, and R. Holenstein, J. R. Stat. Soc. Ser. B Stat. Methodol., 72 (2010), 269--342] to implement a new approximation of the multilevel (ML) Monte Carlo (MC) collapsing sum identity. Our approach comprises constructing an approximate coupling of the posterior density of the joint distribution over parameter and hidden variables at two different discretization levels and then correcting by an importance sampling method. The variance of the weights are independent of the length of the observed data set. The utility of such a method is that, for a prescribed level of mean square error, the cost of this MLMC method is provably less than i.i.d. sampling from the posterior associated to the most precise discretization. However the method here comprises using only known and efficient simulation methodologies. Finally, the theoretical results are illustrated by inference of the parameters of two prototypical processes given noisy partial observations of the process: the first is an Ornstein--Uhlenbeck process and the second is a more general Langevin equation.
97 MATHEMATICS AND COMPUTING↗