catlearn (version 1.0)

slpDGCM: Similarity-Dissimilarity Generalized Context Model (DGCM)

Description

Stewart and Morin (2007)'s extension to Nosofsky's (1984, 2011) Exemplar-based Generalized Context Model. The implementation also contains O'Bryan et al. (2018)'s version of the Similarity-Dissimilarity Generalized Context Model, see Note 1.

Usage

slpDGCM(st, test, dec = "BIAS", exemplar_mute = FALSE, exemplar_decay = TRUE)

Value

If exemplar_decay = FALSE, returns a list of the following matrices:

v A matrix of evidence accumulated for each category (columns) on each trial (rows) as output by Equation 3 in Stewart and Morin (2007).

p A matrix of response probabilities. Category responses (columns) for each trial (rows).

If exemplar_decay = TURE, the function also returns memory decay for each trial, decay.

Arguments

st

List of model parameters

test

Test matrix.

dec

Decision mechanism. If NOISE, use O'Bryan et al. (2018)'s background-noise decision rule. If BIAS (default), use Stewart and Morin (2007)'s category-bias decision rule.

exemplar_mute

If TRUE, only those exemplars contribute evidence to the decision rule, which have at least one feature common with the current stimuli (O'Bryan et al., 2018). If FALSE (default), all exemplars contribute.

exemplar_decay

If TRUE (default), exemplar weightings decay as specified by Stewart and Morin (2007). If FALSE, exemplar weightings are static.

Author

Lenard Dome, Andy Wills

Details

This implementation houses the two version of DGCM. In order to use the instantiation of DGCM described in O'Bryan et al. (2018), set exemplar_decay = FALSE and exemplar_mute = TRUE. The default settings of the function will run the model that corresponds to Stewart and Morin (2007).

The functions works as a stateful list processor. Specifically, it takes a data frame as an argument, where each row is one trial for the model, and the columns specify the input representation, teaching signals, and other control signals. It returns two matrices containing, for each trial, response probabilities and the accumulated evidence for each category. It also returns the final state of the network (e.g. memory decay), hence its description as a 'stateful' list processor, see Note 1.

This implementation took the assumption that when exemplar_decay = TRUE, memory strengths for exemplar are equal to each other at the beginning of the test phase. In future releases, we plan to implement a feature that allows initial memory strengths to be treated as freely varying parameters.

st must be a list containing the following items:

attentional_weights - vector of attentional weights, where sum of all elements equal to 1.

c - generalization constant.

r - The Minkowski metric parameter r gives a city block metric when r = 1 (used for separable-dimension stimuli) and a Euclidean metric when r = 2 (used for integral-dimension stimuli).

s - similarity and dissimilarity weighting. If 0, evidence for a category will be purely based on the dissimilarity between current input vector and all exemplars from the other categories. If it is 1, evidence for a given category will be solely based on similarity to its own exemplars.

t - exemplar weighting. If memory_decay = FALSE, it is a vector of exemplar-specific memory strength. If memory_decay = TRUE (default), it is a vector of exemplar-specific memory strengths that will update according to the function as specified in Equation 4 in Stewart and Morin (2007).

beta - category bias vector. Only used when dec set to BIAS, otherwise ignored. Currently, there is no restriction in place on what values are allowed in this implementation, but Stewart and Morin (2007) specifies that elements of beta should sum to 1.

base - a vector of baseline level of similarity. This parameter will control how much noise will spread over all categories in the background-noise decision rule. It is only used if dec is set to NOISE.

gamma - decision scaling constant. Only used when dec is set to BIAS.

theta - decay rate. If exemplar_decay = FALSE, theta is ignored.

colskip - the number of optional columns to skip in test plus one. If you have no optional columns, set it to one.

outcomes - the number of categories.

exemplars - a matrix of exemplars and their corresponding category indicated by a single integer.

test must be a data.matix with the following columns:

opt1, opt2, ... - any number of optional columns, the names of which can be chosen by the user. These optional columns are ignored by the slpDGCM function, but you may wish to use them for readability.

x1, x2, x3, ...- input to the model, there must be one column for each input unit. Each row is one trial. DGCM uses a nominal stimulus representation, which means that features are coded as either 0 (absent) or 1 (present).

References

Nosofsky, R. M. (1984). Choice, similarity, and the context theory of classification. Journal of Experimental Psychology: Learning, memory, and cognition, 10, 104.

O'Bryan, Sean R., et al. (2018). Model-based fMRI reveals dissimilarity processes underlying base rate neglect. ELife 7: e36395.

Stewart, N., & Morin, C. (2007). Dissimilarity is used as evidence of category membership in multidimensional perceptual categorization: A test of the similarity–dissimilarity generalized context model. Quarterly Journal of Experimental Psychology, 60, 1337-1346.

Examples

  ## Replicate O'Bryan et al. (2018)
  # Exemplars
  stim = matrix(c(
                1,1,0,0,0,0, 1,
                1,0,1,0,0,0, 2,
                0,0,0,1,1,0, 3,
                0,0,0,1,0,1, 4), ncol = 7, byrow = TRUE)

  # Transfer/test stimuli
  # This is a row for each unique transfer stimulus
  tr = matrix(c(
               1, 1, 0, 0, 0, 0, #0,1,2
               1, 0, 1, 0, 0, 0, #3
               0, 0, 0, 1, 1, 0, #4,5,6
               0, 0, 0, 1, 0, 1, #7
               1, 0, 0, 0, 0, 0, #8
               0, 0, 0, 1, 0, 0, #9
               0, 1, 0, 0, 0, 0, #10
               0, 0, 1, 0, 0, 0, #11
               0, 0, 0, 0, 1, 0, #12
               0, 0, 0, 0, 0, 1, #13
               0, 1, 1, 0, 0, 0, #14, 15
               0, 0, 0, 0, 1, 1, #16, 17
               1, 0, 0, 0, 1, 0, #18
               1, 0, 0, 0, 0, 1, #19
               0, 1, 0, 1, 0, 0, #20
               0, 0, 1, 1, 0, 0, #21
               0, 0, 1, 0, 1, 0, #22, 23
               0, 1, 0, 0, 0, 1 #24, 25
               ),
               ncol = 6,
               byrow = TRUE)

  # parameters from paper
  aweights = c(0.27692188, 0.66524089, 0.88723335, 0.16967400, 0.71206208,
               0.87939732)

  st <- list(attentional_weights = aweights/sum(abs(aweights)),
             c = 9.04906080,
             s = 0.94614863,
             b = 0.02250668,
             t = c(3, 1, 3, 1),
             beta = c(1, 1, 1, 1)/4,
             gamma = 1,
             theta = 0.4,
             r = 1,
             colskip = 1,
             outcomes = 4,
             exemplars = stim)

  slpDGCM(st, tr, exemplar_decay = FALSE, exemplar_mute = TRUE, dec = "NOISE")