Predict referent selection for a single trial from an association matrix

Given a model's word-object association matrix, returns the probability distribution over a trial's candidate objects for one heard word – the quantity to compare against a participant's choice on a referent-selection (m-alternative forced choice) trial. This is model-agnostic: it works on the matrix of any xslFit (or any word-by-object matrix), reading each entry as an association strength / meaning weight.

Usage

predict_referent(
  m,
  word,
  objects,
  prior = NULL,
  pragmatic = FALSE,
  threshold = NULL,
  rsa_alpha = 3,
  depth = 1,
  d = NULL
)

Arguments

m: A word-by-object association matrix (e.g. xsl_run(mod, data)$fits[[1]]$matrix). Assumed non-negative; negative entries are clamped to 0. dimnames are used to resolve character word/objects.
word: The heard word: a row name of m, or a positive integer row index. A value not present in m is treated as a novel word.
objects: The candidate objects present on the trial: column names of m, or positive integer column indices. An entry not present in m is treated as an unnamed (novel) object.
prior: Optional prior over objects (length length(objects), non-negative). Defaults to uniform. Set an entry to 0 to remove that object from consideration entirely (e.g. an object the speaker has no epistemic access to).
pragmatic: If TRUE, use the RSA pragmatic listener instead of the literal one.
threshold: Optional; binarize m at this value (m >= threshold) before predicting. The RSA layer is sharpest on a binary lexicon.
rsa_alpha, depth: Speaker rationality and recursion depth for the RSA listener (only used when pragmatic = TRUE).
d: Optional exponent for an exponentiated (power) choice rule: the (clamped, possibly thresholded) associations are raised to d before choice, as in get_perf(). NULL (the default) leaves them unchanged. xsl_run() passes a model's ch_dec parameter here, so that bayesian_decay() scores test trials with the same decision rule it uses elsewhere.

Value

A numeric vector of probabilities over objects, in the given order, summing to 1.

Details

The literal rule is Bayes' rule on the word's row, P(object | word) proportional to m[word, object] * prior(object), normalized over the objects present. With pragmatic = TRUE the objects are instead resolved by a one-step Rational Speech Act pragmatic listener (rsa_listener()), which additionally reasons that the speaker could have used a different word – this is what yields strong mutual exclusivity when a heard word is lexically ambiguous and a competitor word names one of the candidates. A truly novel (unseen) word carries no lexical evidence and returns the prior in either mode.

Examples

m <- xsl_run(fgt2009(alpha = 1), get_example_unambiguous_condition())$fits[[1]]$matrix
predict_referent(m, 1, c(1, 2, 3))
#> [1] 0.4637596 0.2893341 0.2469063
predict_referent(m, 1, c(1, 2, 3), prior = c(1, 0, 1)) # object 2 unavailable
#> [1] 0.6525705 0.0000000 0.3474295