Markov Chain Monte Carlo for Continuous-Time Switching Dynamical Systems

• URL: http://arxiv.org/abs/2205.08803v1
• Date: Wed, 18 May 2022 09:03:00 GMT
• Title: Markov Chain Monte Carlo for Continuous-Time Switching Dynamical Systems
• Authors: Lukas K\"ohs and Bastian Alt and Heinz Koeppl
• Abstract summary: We propose a novel inference algorithm utilizing a Markov Chain Monte Carlo approach. The presented Gibbs sampler allows to efficiently obtain samples from the exact continuous-time posterior processes.
• Score: 26.744964200606784
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Switching dynamical systems are an expressive model class for the analysis of time-series data. As in many fields within the natural and engineering sciences, the systems under study typically evolve continuously in time, it is natural to consider continuous-time model formulations consisting of switching stochastic differential equations governed by an underlying Markov jump process. Inference in these types of models is however notoriously difficult, and tractable computational schemes are rare. In this work, we propose a novel inference algorithm utilizing a Markov Chain Monte Carlo approach. The presented Gibbs sampler allows to efficiently obtain samples from the exact continuous-time posterior processes. Our framework naturally enables Bayesian parameter estimation, and we also include an estimate for the diffusion covariance, which is oftentimes assumed fixed in stochastic differential equation models. We evaluate our framework under the modeling assumption and compare it against an existing variational inference approach.

Related papers

• Fusion of Gaussian Processes Predictions with Monte Carlo Sampling [61.31380086717422]
  In science and engineering, we often work with models designed for accurate prediction of variables of interest. Recognizing that these models are approximations of reality, it becomes desirable to apply multiple models to the same data and integrate their outcomes.
  arXiv  Detail & Related papers  (2024-03-03T04:21:21Z)
• Logistic-beta processes for dependent random probabilities with beta marginals [58.91121576998588]
  We propose a novel process called the logistic-beta process, whose logistic transformation yields a process with common beta marginals. It can model dependence on both discrete and continuous domains, such as space or time, and has a flexible dependence structure through correlation kernels. We illustrate the benefits through nonparametric binary regression and conditional density estimation examples, both in simulation studies and in a pregnancy outcome application.
  arXiv  Detail & Related papers  (2024-02-10T21:41:32Z)
• Cheap and Deterministic Inference for Deep State-Space Models of Interacting Dynamical Systems [38.23826389188657]
  We present a deep state-space model which employs graph neural networks in order to model the underlying interacting dynamical system. The predictive distribution is multimodal and has the form of a Gaussian mixture model, where the moments of the Gaussian components can be computed via deterministic moment matching rules. Our moment matching scheme can be exploited for sample-free inference, leading to more efficient and stable training compared to Monte Carlo alternatives.
  arXiv  Detail & Related papers  (2023-05-02T20:30:23Z)
• Score-based Continuous-time Discrete Diffusion Models [102.65769839899315]
  We extend diffusion models to discrete variables by introducing a Markov jump process where the reverse process denoises via a continuous-time Markov chain. We show that an unbiased estimator can be obtained via simple matching the conditional marginal distributions. We demonstrate the effectiveness of the proposed method on a set of synthetic and real-world music and image benchmarks.
  arXiv  Detail & Related papers  (2022-11-30T05:33:29Z)
• DynaConF: Dynamic Forecasting of Non-Stationary Time Series [4.286546152336783]
  We propose a new method to model non-stationary conditional distributions over time. We show that our model can adapt to non-stationary time series better than state-of-the-art deep learning solutions.
  arXiv  Detail & Related papers  (2022-09-17T21:40:02Z)
• Learning continuous models for continuous physics [94.42705784823997]
  We develop a test based on numerical analysis theory to validate machine learning models for science and engineering applications. Our results illustrate how principled numerical analysis methods can be coupled with existing ML training/testing methodologies to validate models for science and engineering applications.
  arXiv  Detail & Related papers  (2022-02-17T07:56:46Z)
• Variational Inference for Continuous-Time Switching Dynamical Systems [29.984955043675157]
  We present a model based on an Markov jump process modulating a subordinated diffusion process. We develop a new continuous-time variational inference algorithm. We extensively evaluate our algorithm under the model assumption and for real-world examples.
  arXiv  Detail & Related papers  (2021-09-29T15:19:51Z)
• Anomaly Detection of Time Series with Smoothness-Inducing Sequential Variational Auto-Encoder [59.69303945834122]
  We present a Smoothness-Inducing Sequential Variational Auto-Encoder (SISVAE) model for robust estimation and anomaly detection of time series. Our model parameterizes mean and variance for each time-stamp with flexible neural networks. We show the effectiveness of our model on both synthetic datasets and public real-world benchmarks.
  arXiv  Detail & Related papers  (2021-02-02T06:15:15Z)
• The Connection between Discrete- and Continuous-Time Descriptions of Gaussian Continuous Processes [60.35125735474386]
  We show that discretizations yielding consistent estimators have the property of invariance under coarse-graining' This result explains why combining differencing schemes for derivatives reconstruction and local-in-time inference approaches does not work for time series analysis of second or higher order differential equations.
  arXiv  Detail & Related papers  (2021-01-16T17:11:02Z)

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.