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Bayesian inference with sources of uncertainty: from confidence modelling to sparse estimation

arXiv stat.ML / 5/6/2026

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Key Points

  • The paper proposes a general extension to Bayesian inference that lets researchers explicitly model confidence for each source of uncertainty inside the model.
  • This confidence-encoding mechanism is positioned as a new design control knob that improves how regularization can be managed.
  • The authors develop a method to induce sparsity in statistical models using the proposed framework.
  • The approach is demonstrated across linear regression, logistic regression, and Bayesian neural networks, showing broad applicability of the technique.

Abstract

We introduce a general framework that extends Bayesian inference by allowing the researcher to explicitly encode confidence in each source of uncertainty within the model. This mechanism provides a new handle for model design and regularisation control. Building on this framework, we develop a general approach for inducing sparsity in statistical models and illustrate its use in linear and logistic regression, as well as in Bayesian neural networks.

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