Using Mixed-Effect Models to Learn Bayesian Networks from Related Data Sets

• URL: http://arxiv.org/abs/2206.03743v1
• Date: Wed, 8 Jun 2022 08:32:32 GMT
• Title: Using Mixed-Effect Models to Learn Bayesian Networks from Related Data Sets
• Authors: Marco Scutari, Christopher Marquis, Laura Azzimonti
• Abstract summary: We provide an analogous solution for learning a Bayesian network from continuous data using mixed-effects models. We study its structural, parametric, predictive and classification accuracy. The improvement is marked for low sample sizes and for unbalanced data sets.
• Score: 0.04297070083645048
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We commonly assume that data are a homogeneous set of observations when learning the structure of Bayesian networks. However, they often comprise different data sets that are related but not homogeneous because they have been collected in different ways or from different populations. In our previous work (Azzimonti, Corani and Scutari, 2021), we proposed a closed-form Bayesian Hierarchical Dirichlet score for discrete data that pools information across related data sets to learn a single encompassing network structure, while taking into account the differences in their probabilistic structures. In this paper, we provide an analogous solution for learning a Bayesian network from continuous data using mixed-effects models to pool information across the related data sets. We study its structural, parametric, predictive and classification accuracy and we show that it outperforms both conditional Gaussian Bayesian networks (that do not perform any pooling) and classical Gaussian Bayesian networks (that disregard the heterogeneous nature of the data). The improvement is marked for low sample sizes and for unbalanced data sets.

Related papers

• Context-Specific Refinements of Bayesian Network Classifiers [1.9136291802656262]
  We study the relationship between our novel classes of classifiers and Bayesian networks. We introduce and implement data-driven learning routines for our models. The study demonstrates that models embedding asymmetric information can enhance classification accuracy.
  arXiv  Detail & Related papers  (2024-05-28T15:50:50Z)
• Neural network reconstruction of cosmology using the Pantheon compilation [0.0]
  We reconstruct the Hubble diagram using various data sets, including correlated ones. Using ReFANN, that was built for data sets with independent uncertainties, we expand it to include non-Guassian data points.
  arXiv  Detail & Related papers  (2023-05-24T18:42:21Z)
• Rethinking Data Heterogeneity in Federated Learning: Introducing a New Notion and Standard Benchmarks [65.34113135080105]
  We show that not only the issue of data heterogeneity in current setups is not necessarily a problem but also in fact it can be beneficial for the FL participants. Our observations are intuitive. Our code is available at https://github.com/MMorafah/FL-SC-NIID.
  arXiv  Detail & Related papers  (2022-09-30T17:15:19Z)
• How to Combine Variational Bayesian Networks in Federated Learning [0.0]
  Federated learning enables multiple data centers to train a central model collaboratively without exposing any confidential data. deterministic models are capable of performing high prediction accuracy, their lack of calibration and capability to quantify uncertainty is problematic for safety-critical applications. We study the effects of various aggregation schemes for variational Bayesian neural networks.
  arXiv  Detail & Related papers  (2022-06-22T07:53:12Z)
• 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)
• NOTMAD: Estimating Bayesian Networks with Sample-Specific Structures and Parameters [70.55488722439239]
  We present NOTMAD, which learns to mix archetypal networks according to sample context. We demonstrate the utility of NOTMAD and sample-specific network inference through analysis and experiments, including patient-specific gene expression networks.
  arXiv  Detail & Related papers  (2021-11-01T17:17:34Z)
• Semiparametric Bayesian Networks [5.205440005969871]
  We introduce semiparametric Bayesian networks that combine parametric and nonparametric conditional probability distributions. Their aim is to incorporate the bounded complexity of parametric models and the flexibility of nonparametric ones.
  arXiv  Detail & Related papers  (2021-09-07T11:47:32Z)
• Evaluating State-of-the-Art Classification Models Against Bayes Optimality [106.50867011164584]
  We show that we can compute the exact Bayes error of generative models learned using normalizing flows. We use our approach to conduct a thorough investigation of state-of-the-art classification models.
  arXiv  Detail & Related papers  (2021-06-07T06:21:20Z)
• Deep Archimedean Copulas [98.96141706464425]
  ACNet is a novel differentiable neural network architecture that enforces structural properties. We show that ACNet is able to both approximate common Archimedean Copulas and generate new copulas which may provide better fits to data.
  arXiv  Detail & Related papers  (2020-12-05T22:58:37Z)
• A Bayesian Hierarchical Score for Structure Learning from Related Data Sets [0.7240563090941907]
  We propose a new Bayesian Dirichlet score, which we call Bayesian Hierarchical Dirichlet (BHD) BHD is based on a hierarchical model that pools information across data sets to learn a single encompassing network structure. We find that BHD outperforms the Bayesian Dirichlet equivalent uniform (BDeu) score in terms of reconstruction accuracy as measured by the Structural Hamming distance.
  arXiv  Detail & Related papers  (2020-08-04T16:41:05Z)
• 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)

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.