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---------------------------------- How to use bp-ct (October 1999) ---------------------------------- This HOWTO is maintained by Pietro Terna, University of Torino, Department of economics and finance, <terna@econ.unito.it> bp-ct is a Swarm (version 1.3.1 or 1.4.1 or 2.0.1) code, handling simple artificial neural networks, trained with the error backpropagation (BP) technique. The code applies the Environment- Rules-Agents (ERA) scheme and it is also capable of generating automatically the neural network inputs and targets, mainly to apply the Cross Target (CT) technique. A general introduction to bp-ct, and to the ideas behind it (with ERA and CT frameworks), is contained in: Terna, P. (1999), Economic Experiments with Swarm: a Neural Network Approach to the Self-Development of Consistency in Agents' Behavior, in F. Luna and B. Stefansson (eds.), Economic Simulations in Swarm: Agent- Based Modelling and Object Oriented Programming. Dordrecht and London: Kluwer Academic. ------------------------ A few words introduction ------------------------ The CT method has the goal of building agents based upon artificial neural networks (that self develop their rules while acting and learning). Anyway, adopting the ERA scheme we can interchange the techniques in an easy way, so we are planning for the future to use Production Systems, Classifier Systems, Genetic Algorithms. With the ERA protocol, we use a specialized class of objects, named RuleMaster, to manage the behavior of the agents. A ruleMaster (ruleMaster = an instance of RuleMaster) receives all the necessary data from each agent, which owns a dataWarehouse object. To allow agent heterogeneity, we can have several ruleMaster objects. To simplify the code design, the interaction with the environment is allowed only to the agents. Another specialized class of objects (the RuleMaker class) handles the development of the rules. The code allows us to use simultaneously any number of agents (an agent = a neural network) and can be used: (i) as a simple BP artificial neural networks training program; (ii) as a BP program using internally generated inputs and targets, without a true CT scheme or (iii) with the CT scheme. The bp-ct code shows cases (i) and (ii); the companion ct-hayek code is a true CT application, that shows the (iii) case. ---------------------- How to use the program ---------------------- ------------------------------------------------------------- (i) bp-ct as a BP artificial neural networks training program (Subsection 6.1 of the paper quoted above) ------------------------------------------------------------- In this case we must provide the files containing training and verification data. In the bp-ct package we have, as an example, a data.training file and a data.verification file, both containing four lines with all the possible inputs and desired outputs (targets) of an OrXor function, which uses as input two logical values (0=F; 1=T) and as output the Or and the Xor logical results. In this example the data set and the validation set are exactly coincident, because we are limited to these four possibilities, but normally we are employing a verification set other than the training one (think, as an example, to the case of time series forecasting with neural networks). Using neural networks, if we apply in the output layer a transformation function like the logistic, output and target values must be mapped in the range 0-1 (or, better, 0.1-0.9, to avoid the necessity of huge negative or positive inputs to the function to obtain 0 or 1 as outputs); traditionally this is done also for the input values, as a largely adopted convention (mapping them in the range 0-1). In our package, this modification from the external metrics to the internal one is done via a minmax.data file - also needed in the cases (ii) and (iii) - containing, in each row, four values: rows identify the inputs and then the outputs-targets of the neural network function; the four values in each row are the min and the max in the external metrics and the min and max (normally 0-1 for the input lines and 0.1-0.9 for the output-target lines) in the internal one (see the example in the package: two rows refer to inputs and have the 0 1 0 1 form; two refer to the outputs-targets and have the 0 1 0.1 0.9 form). To begin using the program, run bp-ct and set the probes to ModelSwarm and to ObserverSwarm (the two windows labeled ModelSwarm and ObserverSwarm) in the following way: ModelSwarm useEO_EP 0 agentNumber 2 inputNodeNumber 2 hiddenNodeNumber 4 outputNodeNumber 2 patternNumberInVerificationSet 4 patternNumberInTrainingSet 4 epochNumberInEachTrainingCycle 100 epochGroups 0 agentsAreDisplayingData 0 readWeightsFromFile 0 ObserverSwarm displayErrorGraphInVerificationSet 1 displayErrorGraphInTrainingSet 1 numberOfTheAgentA_ToBeObservedDirectly 1 stopAtEpochGroupNumber 10 Explanations: NB if you change a value in a box displayed in a probe window, remember to 'enter' it, by pressing the enter button on the keyboard. (a) useEO_EP can be used only in the (iii) case; see the paper cited above to read about the use of this switch in the ct-hayek companion code; (b) agentNumber can be 1 or > 1; in our case we train simultaneously two neural networks on the specific task of approximating the OrXor function; being the initial parameters (the weights, in the neural networks jargon) randomly chosen, the results can be slightly different; the possibility of using several agent/neural networks is mainly important in type (iii) applications; (c) inputNodeNumber, is here set to 2 as required by the OrXor problem; we suggest not to use this setting interactively, but to modify it in modelSwarm.m; (d) hiddenNodeNumber, is here set to 4 to allow more flexibility to the neural network (the choice of the right number of hidden nodes is always a puzzle); the same suggestion presented above applies here; (e) outputNodeNumber, see (c); (f) patternNumberInVerificationSet, is here set to 4, accordingly to the data.verification file content; (g) patternNumberInTrainingSet, is here set to 4, accordingly to the data.training file content; (h) epochNumberInEachTrainingCycle is the number of learning steps for each cycle run of the program; an epoch is a learning run upon the complete training set (with four patterns in our example); choosing here epochNumberInEachTrainingCycle = 100 we obtain 100*4 training steps in each cycle (a cycle is reported as an Epoch Group in the label of the X axis of the graphic windows); (i) epochGroups is set by the program, to display the number of epoch groups done until now; (j) agentsAreDisplayingData, if set to 1 it produces a report on the active window; set to 0 to avoid the report; (k) readWeightsFromFile, if 1 the program reads previously generated weights from files (see below); set to 0 to avoid reading. (l) displayErrorGraphInVerificationSet (0 = no; 1 = yes); (m) displayErrorGraphInTrainingSet (0 = no; 1 = yes); [The program generates two windows that report error measures, one related to training data and the other related to verification data; the errors reported are: (1) the conventional backpropagation error (sum of the errors in all the output units in all the patterns, i.e. epoch error, divided by the number of patterns; this measure is also conventionally divided by 2), labeled as Mean/Min/Max bp error; (2) the proportional error (this error is the ratio obtained dividing the absolute value of the difference between each target and each output by half the difference between the max potential value and the min potential value; this is a raw measure of the error as a proportion of half the range of the output values; we have