DOI: 10.5061/dryad.34pb0
title: Data from: Probability matching in perceptrons: effects of conditional dependence and linear nonseparability

description: Probability matching occurs when the behavior of an agent matches the
 likelihood of occurrence of events in the agent's environment. For
 instance, when artificial neural networks match probability, the activity
 in their output unit equals the past probability of reward in the presence
 of a stimulus. Our previous research demonstrated that simple artificial
 neural networks (perceptrons, which consist of a set of input units
 directly connected to a single output unit) learn to match probability
 when presented different cues in isolation. The current paper extends this
 research by showing that perceptrons can match probabilities when
 presented simultaneous cues, with each cue signaling different reward
 likelihoods. In our first simulation, we presented up to four different
 cues simultaneously; the likelihood of reward signaled by the presence of
 one cue was independent of the likelihood of reward signaled by other
 cues. Perceptrons learned to match reward probabilities by treating each
 cue as an independent source of information about the likelihood of
 reward. In a second simulation, we violated the independence between cues
 by making some reward probabilities depend upon cue interactions. We did
 so by basing reward probabilities on a logical combination (AND or XOR) of
 two of the four possible cues. We also varied the size of the reward
 associated with the logical combination. We discovered that this latter
 manipulation was a much better predictor of perceptron performance than
 was the logical structure of the interaction between cues. This indicates
 that when perceptrons learn to match probabilities, they do so by assuming
 that each signal of a reward is independent of any other; the best
 predictor of perceptron performance is a quantitative measure of the
 independence of these input signals, and not the logical structure of the
 problem being learned.
description: Network responses and
 training sets for Dawson/Gupta paperThe directories included
 in the zip file provide the training files and the results for the PLOS
 ONE manuscript “Probability matching in perceptrons: Effects of
 conditional dependence and linear nonseparability” by Michael Dawson and
 Maya Gupta. The responses of the various networks in the two simulations
 that are reported are given in the two Excel spreadsheets. Each
 spreadsheet provides details about the training patterns, the likelihood
 of each pattern type being rewarded in a training set, and the responses
 of networks to patterns after training in separate worksheets. Comments
 are provided on each worksheet to explain the numbers that it contains.
 The other two directories provide the raw training sets used in each
 simulation; there are 5 for Simulation 1 and there are 20 for Simulation
 2. To be run with the software they need the .net extension; however they
 are all simply text files. The simulations were conducted using the
 Rosenblatt program, which implements gradient descent training of
 perceptrons. Detailed descriptions of the mathematics of this program, and
 accounts of using the software, have been previously published (Dawson,
 2004, 2005). The program itself is available as freeware from this
 location:
 http://www.bcp.psych.ualberta.ca/~mike/Software/Rosenblatt/index.html
 References Dawson, M. R. W. (2004). Minds And Machines: Connectionism And
 Psychological Modeling. Malden, MA: Blackwell Pub. Dawson, M. R. W.
 (2005). Connectionism : A Hands-on Approach (1st ed.). Oxford, UK ;
 Malden, MA: Blackwell Pub.DawsonGupta.zip