Scalable Bayesian Network Structure Learning with Splines

• URL: http://arxiv.org/abs/2110.14626v1
• Date: Wed, 27 Oct 2021 17:54:53 GMT
• Title: Scalable Bayesian Network Structure Learning with Splines
• Authors: Charupriya Sharma, Peter van Beek
• Abstract summary: A Bayesian Network (BN) is a probabilistic graphical model consisting of a directed acyclic graph (DAG) We present a novel approach capable of learning the global DAG structure of a BN and modelling linear and non-linear local relationships between variables.
• Score: 2.741266294612776
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: A Bayesian Network (BN) is a probabilistic graphical model consisting of a directed acyclic graph (DAG), where each node is a random variable represented as a function of its parents. We present a novel approach capable of learning the global DAG structure of a BN and modelling linear and non-linear local relationships between variables. We achieve this by a combination of feature selection to reduce the search space for local relationships, and extending the widely used score-and-search approach to support modelling relationships between variables as Multivariate Adaptive Regression Splines (MARS). MARS are polynomial regression models represented as piecewise spline functions - this lets us model non-linear relationships without the risk of overfitting that a single polynomial regression model would bring. The combination allows us to learn relationships in all bnlearn benchmark instances within minutes and enables us to scale to networks of over a thousand nodes

Related papers

• SMART: A Flexible Approach to Regression using Spline-Based Multivariate Adaptive Regression Trees [0.0]
  Decision trees are powerful for predictive modeling but often suffer from high variance when modeling continuous relationships. We introduce Spline-based Multivariate Adaptive Regression Trees (MARS), which uses a decision tree to identify subsets of data with distinct continuous relationships. MARS's native ability to handle higher-order terms allows the tree to focus solely on identifying discontinuities in the relationship.
  arXiv  Detail & Related papers  (2024-10-08T01:18:08Z)
• Variational Interpretable Learning from Multi-view Data [2.687817337319978]
  DICCA is designed to disentangle both the shared and view-specific variations for multi-view data. Empirical results on real-world datasets show that our methods are competitive across domains.
  arXiv  Detail & Related papers  (2022-02-28T01:56:44Z)
• Hierarchical Infinite Relational Model [3.731168012111833]
  The hierarchical infinite relational model (HIRM) is a new probabilistic generative model for noisy, sparse, and heterogeneous relational data. We present new algorithms for fully Bayesian posterior inference via Gibbs sampling.
  arXiv  Detail & Related papers  (2021-08-16T16:32:13Z)
• Improving the Reconstruction of Disentangled Representation Learners via Multi-Stage Modeling [54.94763543386523]
  Current autoencoder-based disentangled representation learning methods achieve disentanglement by penalizing the ( aggregate) posterior to encourage statistical independence of the latent factors. We present a novel multi-stage modeling approach where the disentangled factors are first learned using a penalty-based disentangled representation learning method. Then, the low-quality reconstruction is improved with another deep generative model that is trained to model the missing correlated latent variables.
  arXiv  Detail & Related papers  (2020-10-25T18:51:15Z)
• 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)
• Estimation of Switched Markov Polynomial NARX models [75.91002178647165]
  We identify a class of models for hybrid dynamical systems characterized by nonlinear autoregressive (NARX) components. The proposed approach is demonstrated on a SMNARX problem composed by three nonlinear sub-models with specific regressors.
  arXiv  Detail & Related papers  (2020-09-29T15:00:47Z)
• Identification of Probability weighted ARX models with arbitrary domains [75.91002178647165]
  PieceWise Affine models guarantees universal approximation, local linearity and equivalence to other classes of hybrid system. In this work, we focus on the identification of PieceWise Auto Regressive with eXogenous input models with arbitrary regions (NPWARX) The architecture is conceived following the Mixture of Expert concept, developed within the machine learning field.
  arXiv  Detail & Related papers  (2020-09-29T12:50:33Z)
• Model Fusion with Kullback--Leibler Divergence [58.20269014662046]
  We propose a method to fuse posterior distributions learned from heterogeneous datasets. Our algorithm relies on a mean field assumption for both the fused model and the individual dataset posteriors.
  arXiv  Detail & Related papers  (2020-07-13T03:27:45Z)
• Flexible Bayesian Nonlinear Model Configuration [10.865434331546126]
  Linear, or simple parametric, models are often not sufficient to describe complex relationships between input variables and a response. We introduce a flexible approach for the construction and selection of highly flexible nonlinear parametric regression models. A genetically modified mode jumping chain Monte Carlo algorithm is adopted to perform Bayesian inference.
  arXiv  Detail & Related papers  (2020-03-05T21:20:55Z)
• Struct-MMSB: Mixed Membership Stochastic Blockmodels with Interpretable Structured Priors [13.712395104755783]
  Mixed membership blockmodel (MMSB) is a popular framework for community detection and network generation. We present a flexible MMSB model, textitStruct-MMSB, that uses a recently developed statistical relational learning model, hinge-loss Markov random fields (HL-MRFs) Our model is capable of learning latent characteristics in real-world networks via meaningful latent variables encoded as a complex combination of observed features and membership distributions.
  arXiv  Detail & Related papers  (2020-02-21T19:32:32Z)
• Model Fusion via Optimal Transport [64.13185244219353]
  We present a layer-wise model fusion algorithm for neural networks. We show that this can successfully yield "one-shot" knowledge transfer between neural networks trained on heterogeneous non-i.i.d. data.
  arXiv  Detail & Related papers  (2019-10-12T22:07:15Z)

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.