Gluck and Bower (1988) adaptive least-mean-square (LMS) network
slpLMSnet(st, tr, xtdo = FALSE)List of model parameters
Numerical matrix of training items, use data.matrix() if
matrix is not numeric.
Boolean specifying whether to include extended information in the output (see below)
Returns a list with the following items if xtdo = FALSE:
Probabilites of responses on each trial, as output by the logistic choice function (Eq. 7, and Footnote 2, in Gluck and Bower, 1988).
Output node activations on each trial, as output by Equation 3 in Gluck and Bower (1988).
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:
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.
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 bounds 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 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.
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 Shepaard, 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.
# NOT RUN {
## 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
# }
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