kalman_filter: Kalman filter associative model

In XSLmodels: Run and Optimize Cross-Situational Word Learning Models

Kalman filter associative model

Description

A Kalman-filter generalization of rescorla_wagner()'s error-driven update rule (Dayan & Kakade, 2000; Kruschke, 2008; Gershman, 2015): each word-object association is tracked as a Gaussian belief (mean mu and variance sigma2), and each trial's update is scaled by that pair's own Kalman gain, sigma2 / (sigma2 + sigma2_obs). This makes the effective learning rate adaptive rather than fixed – large (fast learning) while an association is still uncertain, and automatically shrinking as confidence accumulates – and it emerges from three interpretable parameters rather than being hand-set. Between observations, every association's variance grows by tau2 (the model assumes true associations drift slowly over time), which keeps the model able to revise a belief rather than converging to a fixed point.

Usage

kalman_filter(tau2, sigma2_obs, sigma2_0)

Arguments

tau2	Process (diffusion) noise: how much uncertainty about every association grows per trial, whether or not it was observed
sigma2_obs	Observation noise: how uninformative a single co-occurrence observation is (larger = slower learning per trial)
sigma2_0	Initial (prior) uncertainty about every association, before any training

Details

Note that the three parameters share a scale redundancy: multiplying tau2, sigma2_obs and sigma2_0 together by any constant leaves every Kalman gain – and hence the learned matrix – unchanged. Only two of the three are identifiable; when fitting, hold one fixed (conventionally sigma2_obs).

Value

An object of class xslMod

Examples

mod <- kalman_filter(tau2 = .01, sigma2_obs = .5, sigma2_0 = 1)
xsl_run(mod, get_example_ambiguous_condition())

XSLmodels documentation built on Oct. 18, 2026, 5:08 p.m.