LCS Case Studies BRANDEN PAPALIA, JAMES PATRICK, MICHAEL STEWART FACULTY OF ENGINEERING, COMPUTING AND MATHEMATICS

The University of Western Australia Mining Imbalanced Data

The University of Western Australia XCS Overview  XCS evolves a population of classifiers P  Each classifier is a rule where condition -> action  Rule also contains a set of parameters: Prediction pthe payoff prediction Prediction error eestimate the error between p and payoff Fitness Fevaluates the classifier’s accuracy Numerosity num the number of copies of this classifier in the population

The University of Western Australia Procedure  At each iteration the XCS builds the match set M  M contains all classifiers in P that match the input  Two types of selection regimes may be applied: Pure-explore regime selects action with highest prediction p Pure-exploit regime selects action with highest fitness F  Pure-explore is typically used during training, whereas pure-exploit is used when the system predicts new unknown instances  The final selected classifiers form the action set A

The University of Western Australia  The chosen action from A is sent to the environment  Environment returns a reward R that the XCS uses to update the parameters of the classifiers in the population  The prediction p, error e, and fitness F is updated in each iteration Updating Parameters

The University of Western Australia 1. Prediction  The prediction is adjusted using the formula: p = p + β( R – p) Where: p is the prediction β is the learning rate (0 < β < 1) R is the reward 2. Error  The prediction is adjusted using the formula: e = e + β(|R – p| - e) Where: e is the error β is the learning rate (0 < β < 1) R is the reward p is the prediction

The University of Western Australia 3. Accuracy  XCS first computes accuracy k: Where: Ɛ 0 is the maximum error that the classifier can take to be considered accurate a and v control the rate and decline in accuracy 4. Fitness  The accuracy k is used to determine the relative accuracy k’ of the classifier in A  Fitness is updated using k’: F = F + β( k’ – F)

The University of Western Australia Discovery Component  A genetic algorithm (GA) is applied to the action set  The GA selects two parents from A, and copies them to create two new classifiers  These new classifiers are introduced into the population

The University of Western Australia Multiplexer  Orriols-Puig & Ester Bernado-Mansilla used an imbalanced multiplexer to investigate how class imbalances affect XCS  Multiplexer: Binary string of size L First log 2 L bits are address bits Remaining bits are position bits Output is the value of the position bit indicated by the decimal value of the address bits

The University of Western Australia XCS on Imbalanced Multiplexer  This case study ran an XCS on an 11-bit multiplexer  This imbalanced multiplexer deliberately undersamples the class labeled as ‘1’.  Imbalance ratio ir refers to the ratio between the number of instances sampled of the majority class TN and minority class TP  Correct classification of the majority class (TN rate) quickly raised to 100% for any imbalance ratio tested  Correct classification of the minority class (TP rate) is only 100% for ir < 16  After ir > 64, the XCS classifies all inputs as if they were in the majority class

The University of Western Australia Modelling Parameter’s Bounds  Orriols-Puig & Ester Bernado-Mansilla sought to derive a bound on ir, whereby the XCS will consider overgeneral classifiers as accurate  Overgeneral classifiers have a high error in inbalanced datasets, as they will often incorrectly classify each class  However, as ir increases, the proportion of minority class decreases, causing overgeneral classifiers to have a lower error  The case study finds that the bound on ir scales proportionally to the maximum reward, and inversely proportional to the max error to be considered accurate

The University of Western Australia Online Configuration of XCS  Case study uses an online adaption algorithm to automatically tune the XCS parameters

The University of Western Australia β Adaption  β (learning rate) adapted in order to align the prediction value of the overgeneral classifier to the theoretical prediction  Consider worst case (classifier receives 1 minority class instance and ir n instances of the majority class) and compute the error  Calculates a new learning rate based on this error

The University of Western Australia Using LCS to Mine Imbalanced Datasets  Case study looked at 25 real-world two-class problems, each with different imbalance ratios and characteristics

The University of Western Australia Results  Results show that XCS outperformed other methods in twelve occasions

The University of Western Australia Results (contd)

The University of Western Australia Summary  This case study showed that XCS can solve the multiplexer problem for ir < 32  Also presented an algorithm that modified the parameters of an XCS during runtime to provide a significant improvement to classification in imbalanced datasets  XCS is comparable with other learning algorithms in the realm of imbalanced data mining

The University of Western Australia Foreign Exchange Trading

The University of Western Australia Foreign Exchange Trading  Price prediction Technical (Not featured in our case study) Historical  Tracding method Long position Short position

The University of Western Australia The Data Set  Six sets of financial time series  5 Currencies United States Dollar (USD) German Deutsche Mark (DEM) British Pound (GBP) Japanese Yen (JPY) Swiss Franc (CHF)  A set contains 3 daily data elements and span Jan 1,1974 to Oct 11, 1995  The three elements: Daily interest rates for the base currency Daily exchange rate Interest rates for the counter currencies

The University of Western Australia Foreign exchange Trading – LC System introduction  Implementation set out to prove LCS’ competitiveness versus Genetic Programing  Utilises NewBoole, a LCS technique similar to Zeroth level Classifier System (ZCS)  NewBoole learning and reward strategy Supervised online learning Symmetrical penalty-payoff strategy  NewBoole Key parameters N – Classifier Population Size Ρ – Genetic Algorithm request rate µ – Mutation rate x – crossover rate m – mutation range β – learning rate

The University of Western Australia Learning Classifier Implementation  Time based trading indicators  Each classifier can either advocate a long or a short action for a currency for each time, t  At time t+1 the excess return (the interest that could have been earnt it no trade was made) that could have been made is compared with the chosen outcome Excess for long position Excess for a short position

The University of Western Australia Learning Classifier implementation continued  After excess return is calculated, transaction costs are subtracted  After the comparison is made the correctness of the position is established  Classifiers are categorised based on the profit they would have generated for the single transaction instance being considered  Rewards are distributed Transaction cost

The University of Western Australia Results Learning classifier system performance (Jan 1, 1981 to Sep 30, 1995) Genetic Programming (Jan 1, 1981 to Sep 30, 1995)

The University of Western Australia Notable Observations  LCS results, while not as good as GP results, did not require offline learning to be achieved  Lower rule evaluations under LCS (1,000 Million to 26 Million)  LCS can suffer quick fitness delay following incorrect trades  LCS had a tendency to advocate the same trade after many trials

The University of Western Australia References Albert Orriols-Puig, E. B.-M. (2008). Mining Imbalanced Data with Learning Classifier Systems. In L. Bull, E. Bernado-Mansilla, & J. Holmes, Learning Classifier Systems in Data Mining (pp ). Springer-Verlag Berlin Heidelberg. Chawla, N. V. (2005). Data Mining For Imbalanced Datasets: An Overview. In O. Maimon, & L. Rokach, The Data Mining and Knowledge Discovery Handbook (pp ). Springer US. Stone, C., & Bull, L. (2008). Foreign Exchange Trading Using a Learning Classifier System. In L. Bull, J. Holmes, & E. Bernado-Mansilla, Learning Classifier Systems in Data Mining (pp ). Springer Berlin Heidelberg.