slpLMSnet: Gluck & Bower (1988) network model

In catlearn: Formal Psychological Models of Categorization and Learning

Gluck & Bower (1988) network model

Description

Gluck and Bower (1988) adaptive least-mean-square (LMS) network

Usage

slpLMSnet(st, tr, xtdo = FALSE, dec = "logistic")

Arguments

st	List of model parameters
tr	Numerical matrix of training items, use data.matrix() if matrix is not numeric.
xtdo	Boolean specifying whether to include extended information in the output (see below)
dec	Specify what response rule to use. logistic, Equation 7 in Gluck and Bower (1988), which will output probability ratings for each outcome (these will not necessary sum to one). softmax, Footnote 2 in Gluck and Bower (1988), which will output response probabilities for each outcome (these will sum to one).

Details

The function operates as a stateful list processor (slp; see Wills et al., 2017). Specifically, it takes a matrix as an argument. Each row represents a single trial. Each column represents different types of information required by the implementation of the model, such as the elemental representation of stimuli, teaching signals, and other variables specifying the model's behaviour (e.g. freezing learning).

Argument st must be a list containing the following items:

beta - the learning rate (fixed for a given simulation) for the LMS learning rule. The upper bound of this parameter is not specified, but we suggest 0 < beta \le 1.

theta - is a positive scaling constant. When theta rises, the logistic choice function will become less linear. When theta is high, the logistic function will approximate the behaviour of a step function.

bias - is a bias parameter. It is the value of the output activation that results in an output probability rating of P = 0.5. For example, if you wish an output activation of 0.4 to produce a rated probability of 0.5, set beta to 0.4. If you are not sure what to use here, set it to 0. The bias parameter is not part of the original Gluck and Bower (1988) LMS network, see Note 1.

w - is a matrix of initial connection weights, where each row is an outcome, and each column is a feature or cue. If you are not sure what to use here, set all values to 0.

outcomes - is the number of possible categories or outcomes.

colskip - the number of optional columns to be skipped in the tr matrix. colskip should be set to the number of optional columns PLUS ONE. So, if you have added no extra columns, colskip = 1.

Argument tr must be a matrix, where each row is one trial presented to the model. Trials are always presented in the order specified. The columns must be as described below, in the order described below:

ctrl - a vector of control codes. Available codes are: 0 = normal trial; 1 = reset model (i.e. set associative strengths (weights) back to their initial values as specified in w (see above)); 2 = Freeze learning. Control codes are actioned before the trial is processed.

opt1, opt2, ... - any number of preferred optional columns, the names of which can be chosen by the user. It is important that these columns are placed after the control column, and before the remaining columns (see below). These optional columns are ignored by the slpLMSnet function, but you may wish to use them for readability. For example, you might choose to include columns such as block number, trial number and condition. The argument colskip (see above) must be set to the number of optional columns plus one.

x1, x2, ... - activation of input nodes of corresponding features. Feature patterns usually represented as a bit array. Each element in the bit array encodes the activations of the input nodes given the presence or absence of the corresponding features. These activations can take on either 1 or 0, present and absent features respectively. For example, Medin and Edelson's (1988) inverse base-rate effect with stimuli AB and AC can be represented as [1 1 0] and [1 0 1] respectively. In a more unconventional scenario, you can set activation to vary between present 1 and absent -1, see Note 2. slpLMSnet can also support any positive or negative real number for activations, e.g. one might use values between 0 and 1 to represent the salience of the features.

d1, d2, ... - teaching input signals indicating the category feedback on the current trial. It is a bit array, similar to the activations of input nodes. If there are two categories and the stimuli on the current trial belongs to the first, then this would be represented in tr as [1 0], on edge cases see Note 3. The length of this array must be provided via outcomes in st.

Value

Returns a list with the following items if xtdo = FALSE:

p	A matrix with either the probability rating for each outcome on each trial if dec = "logistic", or response probabilities for each outcome on each trial if dec = "softmax".
nodeActivation	Output node activations on each trial, as output by Equation 3 in Gluck and Bower (1988).
connectionWeightMatrix	A connection weight matrix, W, where each row represents the corresponding element in the teaching signals array in tr, while each column represents the corresponding element from the input activation array from tr. So cell w_12 would be the connection weight between the second stimulus and the first category.

If xtdo = TRUE, the following item also returned:

squaredDifferences

The least mean squeared differences between desired and actual activations of output nodes on each trial (Eq. 4 in Gluck and Bower, 1988). This metric is an indicator of the network's performance, which is measured by its accuracy.

Note

1. The bias parameter is not part of the original Gluck and Bower (1988) model. bias in the current implementation helps comparisons between simulations using the act2probrat logistic choice function. Set bias to 0 for operation as specified in Gluck & Bower (1988). Also note that, where there is more than one output node, the same bias value is subtracted from the output of each node. This form of decision mechanism is not present in the literature as far as we are aware, although using a negative bias value would, in multi-outcome cases, approximate a 'background noise' decision rule, as used in, for example, Nosofsky et al. (1994).

2. slpLMSnet can support both positive and negative real numbers as input node activations. For example, one might wish to follow Markman's (1989) suggestion that the absence of a feature element is encoded as -1 instead of 0.

3. slpLMSnet can process a bit array of teaching signals, where the model is told that the stimulus belongs to more than one category. slpLMSnet uses matrix operations to update weights, so it can encode and update multiple teaching signals on the same trial.

Author(s)

Lenard Dome, Andy Wills

References

Gluck, M. A., & Bower, G. H. (1988). From conditioning to category learning: An adaptive network model. Journal of Experimental Psychology: General, 117, 227-247.

Markman, A. B. (1989). LMS rules and the inverse base-rate effect: Comment on Gluck and Bower (1988). Journal of Experimental Psychology: General, 118, 417-421.

Medin, D. L., & Edelson, S. M. (1988). Problem structure and the use of base-rate information from experience. Journal of Experimental Psychology: General, 117, 68-85.

Nosofsky, R.M., Gluck, M.A., Plameri, T.J., McKinley, S.C. and Glauthier, P. (1994). Comparing models of rule-based classification learning: A replication and extension of Shepard, Hovland, and Jenkins (1961). Memory and Cognition, 22, 352-369.

Wills, A.J., O'Connell, G., Edmunds, C.E.R., & Inkster, A.B.(2017). Progress in modeling through distributed collaboration: Concepts, tools, and category-learning examples. Psychology of Learning and Motivation, 66, 79-115.

Examples

## load catlearn
library(catlearn)

## create st with initial state
st <- list(beta = 0.025, # learning rate
           theta = 1, # decision scaling parameter
           bias = 0, # decision bias parameter
           # initial weight matrix, 
           # row = number of categories,
           # col = number of cues
           w = matrix(rep(0, 6*4), nrow = 4, ncol = 6),
           outcomes = 4, # number of possible outcomes
           colskip = 3)

## create inverse base-rate effect tr for 1 subject and without bias cue
tr <- krus96train(subjs = 1, ctxt = FALSE)

# run simulation and store output
out <- slpLMSnet(st, data.matrix(tr))

out$connectionWeightMatrix

catlearn documentation built on April 4, 2023, 5:12 p.m.