# Belief Propagation and Locally Bayesian Learning

- Adam Sanborn,
*University College London*
- Ricardo Silva,
*University College London*

## Abstract

Highlighting, a conditioning effect, consists of both primacy-like
and recency-like effects in human subjects. This combination of effects are
notoriously difficult for Bayesian models to produce. An approximation to
probabilistic inference, Locally Bayesian learning (LBL), can predict
highlighting by partitioning the model into regions during learning and passing
messages between these regions. While the approximation matches behavior in this
task, it is unclear how LBL compares to other approximations used in Bayesian
models, and what behaviors this approximations will predict in other paradigms.
Our contribution is to show LBL is closely related to the statistical algorithms
of Assumed Density Filtering (ADF), which simplifies calculations by assuming
independence, and belief propagation, which identifies how to make these
calculations through message passing. We propose that people use ADF to learn and
show how this model can produce highlighting behavior. In addition, we
demonstrate how the degrees of approximation used in LBL and ADF cause the models
to make very different predictions in a proposed experimental design.

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