A Bayesian Take on Gaussian Process Networks

• URL: http://arxiv.org/abs/2306.11380v4
• Date: Fri, 24 Nov 2023 09:52:49 GMT
• Title: A Bayesian Take on Gaussian Process Networks
• Authors: Enrico Giudice, Jack Kuipers, Giusi Moffa
• Abstract summary: This work implements Monte Carlo and Markov Chain Monte Carlo methods to sample from the posterior distribution of network structures. We show that our method outperforms state-of-the-art algorithms in recovering the graphical structure of the network.
• Score: 1.7188280334580197
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Gaussian Process Networks (GPNs) are a class of directed graphical models which employ Gaussian processes as priors for the conditional expectation of each variable given its parents in the network. The model allows the description of continuous joint distributions in a compact but flexible manner with minimal parametric assumptions on the dependencies between variables. Bayesian structure learning of GPNs requires computing the posterior over graphs of the network and is computationally infeasible even in low dimensions. This work implements Monte Carlo and Markov Chain Monte Carlo methods to sample from the posterior distribution of network structures. As such, the approach follows the Bayesian paradigm, comparing models via their marginal likelihood and computing the posterior probability of the GPN features. Simulation studies show that our method outperforms state-of-the-art algorithms in recovering the graphical structure of the network and provides an accurate approximation of its posterior distribution.

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)
• Joint Bayesian Inference of Graphical Structure and Parameters with a Single Generative Flow Network [59.79008107609297]
  We propose in this paper to approximate the joint posterior over the structure of a Bayesian Network. We use a single GFlowNet whose sampling policy follows a two-phase process. Since the parameters are included in the posterior distribution, this leaves more flexibility for the local probability models.
  arXiv  Detail & Related papers  (2023-05-30T19:16:44Z)
• Variational EP with Probabilistic Backpropagation for Bayesian Neural Networks [0.0]
  I propose a novel approach for nonlinear Logistic regression using a two-layer neural network (NN) model structure with hierarchical priors on the network weights. I derive a computationally efficient algorithm, whose complexity scales similarly to an ensemble of independent sparse logistic models.
  arXiv  Detail & Related papers  (2023-03-02T19:09:47Z)
• Distributed Bayesian Learning of Dynamic States [65.7870637855531]
  The proposed algorithm is a distributed Bayesian filtering task for finite-state hidden Markov models. It can be used for sequential state estimation, as well as for modeling opinion formation over social networks under dynamic environments.
  arXiv  Detail & Related papers  (2022-12-05T19:40:17Z)
• B\'ezier Curve Gaussian Processes [8.11969931278838]
  This paper proposes a new probabilistic sequence model building on probabilistic B'ezier curves. Combined with a Mixture Density network, Bayesian conditional inference can be performed without the need for mean field variational approximation. The model is used for pedestrian trajectory prediction, where a generated prediction also serves as a GP prior.
  arXiv  Detail & Related papers  (2022-05-03T19:49:57Z)
• A new perspective on probabilistic image modeling [92.89846887298852]
  We present a new probabilistic approach for image modeling capable of density estimation, sampling and tractable inference. DCGMMs can be trained end-to-end by SGD from random initial conditions, much like CNNs. We show that DCGMMs compare favorably to several recent PC and SPN models in terms of inference, classification and sampling.
  arXiv  Detail & Related papers  (2022-03-21T14:53:57Z)
• Bayesian Structure Learning with Generative Flow Networks [85.84396514570373]
  In Bayesian structure learning, we are interested in inferring a distribution over the directed acyclic graph (DAG) from data. Recently, a class of probabilistic models, called Generative Flow Networks (GFlowNets), have been introduced as a general framework for generative modeling. We show that our approach, called DAG-GFlowNet, provides an accurate approximation of the posterior over DAGs.
  arXiv  Detail & Related papers  (2022-02-28T15:53:10Z)
• Kalman Bayesian Neural Networks for Closed-form Online Learning [5.220940151628734]
  We propose a novel approach for BNN learning via closed-form Bayesian inference. The calculation of the predictive distribution of the output and the update of the weight distribution are treated as Bayesian filtering and smoothing problems. This allows closed-form expressions for training the network's parameters in a sequential/online fashion without gradient descent.
  arXiv  Detail & Related papers  (2021-10-03T07:29:57Z)
• What Are Bayesian Neural Network Posteriors Really Like? [63.950151520585024]
  We show that Hamiltonian Monte Carlo can achieve significant performance gains over standard and deep ensembles. We also show that deep distributions are similarly close to HMC as standard SGLD, and closer than standard variational inference.
  arXiv  Detail & Related papers  (2021-04-29T15:38:46Z)

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.