Bayesian stochastic blockmodeling

• URL: http://arxiv.org/abs/1705.10225v9
• Date: Wed, 22 Mar 2023 15:39:51 GMT
• Title: Bayesian stochastic blockmodeling
• Authors: Tiago P. Peixoto
• Abstract summary: This chapter provides a self-contained introduction to the use of Bayesian inference to extract large-scale modular structures from network data. We focus on nonparametric formulations that allow their inference in a manner that prevents overfitting, and enables model selection. We show how inferring the blockmodel can be used to predict missing and spurious links, and shed light on the fundamental limitations of the detectability of modular structures in networks.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-sa/4.0/
• Abstract: This chapter provides a self-contained introduction to the use of Bayesian inference to extract large-scale modular structures from network data, based on the stochastic blockmodel (SBM), as well as its degree-corrected and overlapping generalizations. We focus on nonparametric formulations that allow their inference in a manner that prevents overfitting, and enables model selection. We discuss aspects of the choice of priors, in particular how to avoid underfitting via increased Bayesian hierarchies, and we contrast the task of sampling network partitions from the posterior distribution with finding the single point estimate that maximizes it, while describing efficient algorithms to perform either one. We also show how inferring the SBM can be used to predict missing and spurious links, and shed light on the fundamental limitations of the detectability of modular structures in networks.

Related papers

• Influence Functions for Scalable Data Attribution in Diffusion Models [52.92223039302037]
  Diffusion models have led to significant advancements in generative modelling. Yet their widespread adoption poses challenges regarding data attribution and interpretability. In this paper, we aim to help address such challenges by developing an textitinfluence functions framework.
  arXiv  Detail & Related papers  (2024-10-17T17:59:02Z)
• Bayesian Model Selection via Mean-Field Variational Approximation [10.433170683584994]
  We study the non-asymptotic properties of mean-field (MF) inference under the Bayesian framework. We show a Bernstein von-Mises (BvM) theorem for the variational distribution from MF under possible model mis-specification.
  arXiv  Detail & Related papers  (2023-12-17T04:48:25Z)
• Amortizing intractable inference in large language models [56.92471123778389]
  We use amortized Bayesian inference to sample from intractable posterior distributions. We empirically demonstrate that this distribution-matching paradigm of LLM fine-tuning can serve as an effective alternative to maximum-likelihood training. As an important application, we interpret chain-of-thought reasoning as a latent variable modeling problem.
  arXiv  Detail & Related papers  (2023-10-06T16:36:08Z)
• 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)
• Bayesian Hierarchical Models for Counterfactual Estimation [12.159830463756341]
  We propose a probabilistic paradigm to estimate a diverse set of counterfactuals. We treat the perturbations as random variables endowed with prior distribution functions. A gradient based sampler with superior convergence characteristics efficiently computes the posterior samples.
  arXiv  Detail & Related papers  (2023-01-21T00:21:11Z)
• 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)
• DiBS: Differentiable Bayesian Structure Learning [38.01659425023988]
  We propose a general, fully differentiable framework for Bayesian structure learning (DiBS) DiBS operates in the continuous space of a latent probabilistic graph representation. Contrary to existing work, DiBS is agnostic to the form of the local conditional distributions.
  arXiv  Detail & Related papers  (2021-05-25T11:23:08Z)
• Likelihoods and Parameter Priors for Bayesian Networks [7.005458308454871]
  We introduce several assumptions that permit the construction of likelihoods and parameter priors for a large number of Bayesian-network structures. We present a method for directly computing the marginal likelihood of a random sample with no missing observations.
  arXiv  Detail & Related papers  (2021-05-13T12:45:44Z)
• A Bayesian Approach to Block-Term Tensor Decomposition Model Selection and Computation [10.91885508254207]
  The so-called block-term decomposition (BTD) tensor model, especially in its rank-$(L_r,L_r,1)$ version, has been recently receiving increasing attention. The challenge of estimating the BTD model structure, namely the number of block terms and their individual ranks, has only recently started to attract significant attention. A Bayesian approach is taken to addressing the problem of rank-$(L_r,L_r,1)$ BTD model selection and computation, based on the idea of imposing column sparsity emphjointly on the
  arXiv  Detail & Related papers  (2021-01-08T09:37:21Z)
• Slice Sampling for General Completely Random Measures [74.24975039689893]
  We present a novel Markov chain Monte Carlo algorithm for posterior inference that adaptively sets the truncation level using auxiliary slice variables. The efficacy of the proposed algorithm is evaluated on several popular nonparametric models.
  arXiv  Detail & Related papers  (2020-06-24T17:53:53Z)
• Bayesian Deep Learning and a Probabilistic Perspective of Generalization [56.69671152009899]
  We show that deep ensembles provide an effective mechanism for approximate Bayesian marginalization. We also propose a related approach that further improves the predictive distribution by marginalizing within basins of attraction.
  arXiv  Detail & Related papers  (2020-02-20T15:13:27Z)

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.