Inference on the Change Point for High Dimensional Dynamic Graphical Models

• URL: http://arxiv.org/abs/2005.09711v3
• Date: Sun, 21 Feb 2021 05:30:44 GMT
• Title: Inference on the Change Point for High Dimensional Dynamic Graphical Models
• Authors: Abhishek Kaul, Hongjin Zhang, Konstantinos Tsampourakis and George Michailidis
• Abstract summary: We develop an estimator for the change point parameter for a dynamically evolving graphical model. It retains sufficient adaptivity against plug-in estimates of the graphical model parameters. It is illustrated on RNA-sequenced data and their changes between young and older individuals.
• Score: 9.74000189600846
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We develop an estimator for the change point parameter for a dynamically evolving graphical model, and also obtain its asymptotic distribution under high dimensional scaling. To procure the latter result, we establish that the proposed estimator exhibits an $O_p(\psi^{-2})$ rate of convergence, wherein $\psi$ represents the jump size between the graphical model parameters before and after the change point. Further, it retains sufficient adaptivity against plug-in estimates of the graphical model parameters. We characterize the forms of the asymptotic distribution under the both a vanishing and a non-vanishing regime of the magnitude of the jump size. Specifically, in the former case it corresponds to the argmax of a negative drift asymmetric two sided Brownian motion, while in the latter case to the argmax of a negative drift asymmetric two sided random walk, whose increments depend on the distribution of the graphical model. Easy to implement algorithms are provided for estimating the change point and their performance assessed on synthetic data. The proposed methodology is further illustrated on RNA-sequenced microbiome data and their changes between young and older individuals.

Related papers

• von Mises Quasi-Processes for Bayesian Circular Regression [57.88921637944379]
  We explore a family of expressive and interpretable distributions over circle-valued random functions. The resulting probability model has connections with continuous spin models in statistical physics. For posterior inference, we introduce a new Stratonovich-like augmentation that lends itself to fast Markov Chain Monte Carlo sampling.
  arXiv  Detail & Related papers  (2024-06-19T01:57:21Z)
• Inferring Change Points in High-Dimensional Regression via Approximate Message Passing [9.660892239615366]
  We propose an Approximate Message Passing (AMP) algorithm for estimating both the signals and the change point locations. We rigorously characterize its performance in the high-dimensional limit where the number of parameters $p$ is proportional to the number of samples $n$. We show how our AMP iterates can be used to efficiently compute a Bayesian posterior distribution over the change point locations in the high-dimensional limit.
  arXiv  Detail & Related papers  (2024-04-11T15:57:12Z)
• Asymptotics of Bayesian Uncertainty Estimation in Random Features Regression [1.170951597793276]
  We focus on the variance of the posterior predictive distribution (Bayesian model average) and compare itss to that of the risk of the MAP estimator. They also agree with each other when the number of samples grow faster than any constant multiple of model dimensions.
  arXiv  Detail & Related papers  (2023-06-06T15:36:15Z)
• Modeling the space-time correlation of pulsed twin beams [68.8204255655161]
  Entangled twin-beams generated by parametric down-conversion are among the favorite sources for imaging-oriented applications. We propose a semi-analytic model which aims to bridge the gap between time-consuming numerical simulations and the unrealistic plane-wave pump theory.
  arXiv  Detail & Related papers  (2023-01-18T11:29:49Z)
• Symmetries in the dynamics of wide two-layer neural networks [0.0]
  We consider the idealized setting of gradient flow on the population risk for infinitely wide two-layer ReLU neural networks (without bias) We first describe a general class of symmetries which, when satisfied by the target function $f*$ and the input distribution, are preserved by the dynamics.
  arXiv  Detail & Related papers  (2022-11-16T08:59:26Z)
• A Model for Multi-View Residual Covariances based on Perspective Deformation [88.21738020902411]
  We derive a model for the covariance of the visual residuals in multi-view SfM, odometry and SLAM setups. We validate our model with synthetic and real data and integrate it into photometric and feature-based Bundle Adjustment.
  arXiv  Detail & Related papers  (2022-02-01T21:21:56Z)
• Inverting brain grey matter models with likelihood-free inference: a tool for trustable cytoarchitecture measurements [62.997667081978825]
  characterisation of the brain grey matter cytoarchitecture with quantitative sensitivity to soma density and volume remains an unsolved challenge in dMRI. We propose a new forward model, specifically a new system of equations, requiring a few relatively sparse b-shells. We then apply modern tools from Bayesian analysis known as likelihood-free inference (LFI) to invert our proposed model.
  arXiv  Detail & Related papers  (2021-11-15T09:08:27Z)
• Moment evolution equations and moment matching for stochastic image EPDiff [68.97335984455059]
  Models of image deformation allow study of time-continuous effects transforming images by deforming the image domain. Applications include medical image analysis with both population trends and random subject specific variation. We use moment approximations of the corresponding Ito diffusion to construct estimators for statistical inference in the parameters full model.
  arXiv  Detail & Related papers  (2021-10-07T11:08:11Z)
• Segmentation of high dimensional means over multi-dimensional change points and connections to regression trees [1.0660480034605242]
  This article provides a new analytically tractable and fully frequentist framework to characterize and implement regression trees. The connection to regression trees is made by a high dimensional model with dynamic mean vectors over multi-dimensional change axes. Results are obtained under a high dimensional scaling $slog2 p=o(T_wT_h), where $p$ is the response dimension, $s$ is a sparsity parameter, and $T_w,T_h$ are sampling periods along change axes.
  arXiv  Detail & Related papers  (2021-05-20T20:29:48Z)
• Bayesian multiscale deep generative model for the solution of high-dimensional inverse problems [0.0]
  A novel multiscale Bayesian inference approach is introduced based on deep probabilistic generative models. The method allows high-dimensional parameter estimation while exhibiting stability, efficiency and accuracy.
  arXiv  Detail & Related papers  (2021-02-04T11:47:21Z)
• Probabilistic Circuits for Variational Inference in Discrete Graphical Models [101.28528515775842]
  Inference in discrete graphical models with variational methods is difficult. Many sampling-based methods have been proposed for estimating Evidence Lower Bound (ELBO) We propose a new approach that leverages the tractability of probabilistic circuit models, such as Sum Product Networks (SPN) We show that selective-SPNs are suitable as an expressive variational distribution, and prove that when the log-density of the target model is aweighted the corresponding ELBO can be computed analytically.
  arXiv  Detail & Related papers  (2020-10-22T05:04:38Z)

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.