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  • 1. Copyright © 2013 Geoffrey I WebbFundamental and Advanced Machine Learning Methods for Big Data Applications Geoffrey I Webb, Ana Martinez, Nayyar Zaidi, Shenglei Chen Monash University http://www.csse.monash.edu.au/~webb
  • 2. Copyright © 2013 Geoffrey I Webb
  • 3. Copyright © 2013 Geoffrey I Webb Overview• Big data• Classification learning• Sampling• Dimensionality reduction• Scaling-up existing algorithms• Stream learning• Bias and variance and big data• Selective KDB• Incremental Bayesian Network Classifiers
  • 4. Copyright © 2013 Geoffrey I Webb Big data • Can mean many things – Complex integration of many heterogeneous data sources – Very large/streaming data Name (SI Value Binary usage decimal prefixes) kilobyte (kB) megabyte (MB) gigabyte (GB) terabyte (TB) petabyte (PB) exabyte (EB) zettabyte (ZB) yottabyte (YB)Big data | Class learning | Sampling | Dimensionality red’n | Scaling-up | Streams | Bias/variance | Selective KDB | Incremental BNC
  • 5. Copyright © 2013 Geoffrey I Webb What is ‘big’? • Number of – instances – dimensions – classes • Big data usually includes data sets with sizes beyond the ability of commonly used software tools to capture, curate, manage, and process the data within a tolerable elapsed time. Big data sizes are a constantly moving target, as of 2012 ranging from a few dozen terabytes to many petabytes of data in a single data set. – Wikipedia • Machine learning research usually treats more than 1 million examples as very large.Big data | Class learning | Sampling | Dimensionality red’n | Scaling-up | Streams | Bias/variance | Selective KDB | Incremental BNC
  • 6. Copyright © 2013 Geoffrey I Webb Examples • Spelling correction • Translation • Farecast • Recommender systems • Electoral outcomesWhitelaw, C, B Hutchinson, GY Chung, & G Ellis. "Using the web for language independent spellchecking and autocorrection." In Proceedings of the 2009 Conferenceon Empirical Methods in Natural Language Processing: Volume 2, pp. 890-899. Association for Computational Linguistics, 2009.Silver, Nate. The Signal and the Noise: Why So Many Predictions Fail-but Some Dont. Penguin Press, 2012.Big data | Class learning | Sampling | Dimensionality red’n | Scaling-up | Streams | Bias/variance | Selective KDB | Incremental BNC
  • 7. Copyright © 2013 Geoffrey I Webb Not a universal panacea • Jeopardy but not chess • Spelling correction and translation but not comprehension http://www.engadget.com/2011/02/15/watson-soundly-beats-the-humans-in-first-round-of-jeopardy/Big data | Class learning | Sampling | Dimensionality red’n | Scaling-up | Streams | Bias/variance | Selective KDB | Incremental BNC
  • 8. Copyright © 2013 Geoffrey I Webb Classification learningBig data | Class learning | Sampling | Dimensionality red’n | Scaling-up | Streams | Bias/variance | Selective KDB | Incremental BNC
  • 9. Copyright © 2013 Geoffrey I Webb Evolving distributions • Key issue – Is the distribution from which the data are drawn static or dynamic? – Concept drift • class membership changes, eg rich – Concept evolution • new classes emerge – Distribution drift • probabilities changeBig data | Class learning | Sampling | Dimensionality red’n | Scaling-up | Streams | Bias/variance | Selective KDB | Incremental BNC
  • 10. Copyright © 2013 Geoffrey I Webb Dimension of change • Normally time but may be other such as location • Classifier can only take dimension of change into account if data to be classified will fall within current scope or if it is possible to extrapolate 18 14 16 12 14 10 12 10 8 Training Training 8 6 Testing Testing 6 4 4 2 2 0 0 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28Big data | Class learning | Sampling | Dimensionality red’n | Scaling-up | Streams | Bias/variance | Selective KDB | Incremental BNC
  • 11. Copyright © 2013 Geoffrey I Webb Loss functionsBig data | Class learning | Sampling | Dimensionality red’n | Scaling-up | Streams | Bias/variance | Selective KDB | Incremental BNC
  • 12. Copyright © 2013 Geoffrey I Webb Imbalanced classes • Many big datasets have a rare class of interest and a majority class from which we seek to distinguish it. – Ad click-through – Conversions – Disease – Fraud – Homeland securityBig data | Class learning | Sampling | Dimensionality red’n | Scaling-up | Streams | Bias/variance | Selective KDB | Incremental BNC
  • 13. Copyright © 2013 Geoffrey I Webb Loss functions for imbalanced classesBig data | Class learning | Sampling | Dimensionality red’n | Scaling-up | Streams | Bias/variance | Selective KDB | Incremental BNC
  • 14. Copyright © 2013 Geoffrey I Webb Loss functions for imbalanced classes Predictions Pos Neg Actual Pos TP FN Neg FP TNBig data | Class learning | Sampling | Dimensionality red’n | Scaling-up | Streams | Bias/variance | Selective KDB | Incremental BNC
  • 15. Copyright © 2013 Geoffrey I Webb Loss functions for imbalanced classes • Area under the ROC curve True Positive Rate (TPR) Predictions Pos Neg Actual Pos TP FN Neg FP TN False Positive Rate (FPR) Predictions Pos Neg Actual Pos TP FN Neg FP TN Prof. William H. Press, “Unit 17: Classifier Performance: ROC, Precision-Recall, and All That.” http://www.nr.com/CS395T/lectures2008/17-ROCPrecisionRecall.pdfBig data | Class learning | Sampling | Dimensionality red’n | Scaling-up | Streams | Bias/variance | Selective KDB | Incremental BNC
  • 16. Copyright © 2013 Geoffrey I Webb Loss functions for imbalanced classes • Area under the Precision Recall Curve Recall = True Positive Rate (TPR) Predictions Pos Neg Actual Pos TP FN Neg FP TN Precision Predictions Pos Neg Actual Pos TP FN Neg FP TN Prof. William H. Press, “Unit 17: Classifier Performance: ROC, Precision-Recall, and All That.” http://www.nr.com/CS395T/lectures2008/17-ROCPrecisionRecall.pdfBig data | Class learning | Sampling | Dimensionality red’n | Scaling-up | Streams | Bias/variance | Selective KDB | Incremental BNC
  • 17. Copyright © 2013 Geoffrey I Webb Mutual informationBig data | Class learning | Sampling | Dimensionality red’n | Scaling-up | Streams | Bias/variance | Selective KDB | Incremental BNC
  • 18. Copyright © 2013 Geoffrey I Webb Learning curves 0.7 KDB k=2 0.6 0.5 Root Mean Squared Error 0.4 0.3 0.2 0.1 0 0 100,000 200,000 300,000 400,000 500,000 600,000 700,000 800,000 900,000 1,000,000 Data quantityBig data | Class learning | Sampling | Dimensionality red’n | Scaling-up | Streams | Bias/variance | Selective KDB | Incremental BNC
  • 19. Copyright © 2013 Geoffrey I Webb Sampling • Select s instances from a dataset of size n • Important that sample be selected randomly • Make sure you use a robust random number generatorBig data | Class learning | Sampling | Dimensionality red’n | Scaling-up | Streams | Bias/variance | Selective KDB | Incremental BNC
  • 20. Copyright © 2013 Geoffrey I Webb Ideal Sampling • Select data quantity at which learning curve approaches asymptotic error and learn from sample 0.7 KDB k=2 0.6 0.5 Root Mean Squared Error 0.4 0.3 0.2 0.1 0 0 100,000 200,000 300,000 400,000 500,000 600,000 700,000 800,000 900,000 1,000,000 Data quantityBig data | Class learning | Sampling | Dimensionality red’n | Scaling-up | Streams | Bias/variance | Selective KDB | Incremental BNC
  • 21. Copyright © 2013 Geoffrey I Webb Finding asymptotic error • Progressive sampling 0.7 KDB k=2 0.6 0.5 Root Mean Squared Error 0.4 0.3 0.2 0.1 0 0 100,000 200,000 300,000 400,000 500,000 600,000 700,000 800,000 900,000 1,000,000 Data quantityProvost, F, D Jensen, T Oates. “Efficient progressive sampling.” In Proc 5th ACM SIGKDD international conference on Knowledge Discovery and Data Mining, pp. 23-32. ACM, 1999.Big data | Class learning | Sampling | Dimensionality red’n | Scaling-up | Streams | Bias/variance | Selective KDB | Incremental BNC
  • 22. Copyright © 2013 Geoffrey I Webb Hoeffdings bound Error margin Sample Population mean Sample size meanHulten, G, and P Domingos. "Mining complex models from arbitrarily large databases in constant time." In Proceedings 8th ACM SIGKDD international conference on Knowledge discovery and data mining, pp. 525-531. ACM, 2002.Big data | Class learning | Sampling | Dimensionality red’n | Scaling-up | Streams | Bias/variance | Selective KDB | Incremental BNC
  • 23. Copyright © 2013 Geoffrey I Webb Maximum sample • Take largest sample capacity can handle 0.7 KDB k=2 0.6 0.5 Root Mean Squared Error 0.4 0.3 0.2 0.1 0 0 100,000 200,000 300,000 400,000 500,000 600,000 700,000 800,000 900,000 1,000,000 Data quantityBig data | Class learning | Sampling | Dimensionality red’n | Scaling-up | Streams | Bias/variance | Selective KDB | Incremental BNC
  • 24. Copyright © 2013 Geoffrey I Webb Maximum sample • Take largest sample capacity can handle • Saves overheads of repeated sampling and risk of terminating too soon • Has risk that asymptotic error may not be reached – but alternative techniques wouldn’t be able to handle a larger sample anyway!Big data | Class learning | Sampling | Dimensionality red’n | Scaling-up | Streams | Bias/variance | Selective KDB | Incremental BNC
  • 25. Copyright © 2013 Geoffrey I Webb Sampling with and without replacement • Sampling involves deciding how many times Ki each element i of a collection should occur in the sample • Sampling without replacement restricts Ki to 0 or 1Big data | Class learning | Sampling | Dimensionality red’n | Scaling-up | Streams | Bias/variance | Selective KDB | Incremental BNC
  • 26. Copyright © 2013 Geoffrey I Webb Uniform fixed-sized sampling with replacement for fixed n selected ← 0 while selected < s add a randomly selected instance to the sample increment selectedBig data | Class learning | Sampling | Dimensionality red’n | Scaling-up | Streams | Bias/variance | Selective KDB | Incremental BNC
  • 27. Copyright © 2013 Geoffrey I Webb Uniform sequential variable-sized sampling without replacement i ← 1 while i < n with fixed probability do add the next instance to the sample increment iBig data | Class learning | Sampling | Dimensionality red’n | Scaling-up | Streams | Bias/variance | Selective KDB | Incremental BNC
  • 28. Copyright © 2013 Geoffrey I Webb Uniform sequential fixed-sized sampling without replacement for known n selected ← 0 i ← 1 while selected < s with probability (s - selected )/(n-i+1) do add the next instance to the sample increment selected increment iBig data | Class learning | Sampling | Dimensionality red’n | Scaling-up | Streams | Bias/variance | Selective KDB | Incremental BNC
  • 29. Copyright © 2013 Geoffrey I Webb Uniform sequential fixed-sized sampling without replacement for unknown n count ← 0 while count < s and count < n add the next instance to the sample increment count while more instances remain increment count with probability s/count do add the next instance to the sample replacing an existing instance selected at random else discard the next instance Tille, Yves. Sampling algorithms. Springer, 2006.Big data | Class learning | Sampling | Dimensionality red’n | Scaling-up | Streams | Bias/variance | Selective KDB | Incremental BNC
  • 30. Copyright © 2013 Geoffrey I Webb Dimensionality reduction • Many learning algorithms are super-linear with respect to dimensionality • Dimensionality can be reduced by – feature selection – feature projectionBig data | Class learning | Sampling | Dimensionality red’n | Scaling-up | Streams | Bias/variance | Selective KDB | Incremental BNC
  • 31. Copyright © 2013 Geoffrey I Webb Feature selection • Most powerful techniques are too computationally intensive for big data – Eg wrapper techniques – Best approach varies depending on base learner • Techniques that consider only the relationship between an attribute and the class are efficient – Eg top-k mutual information – However, overlook complex interactions between attributes • May be most effective to use powerful technique on a sampleBig data | Class learning | Sampling | Dimensionality red’n | Scaling-up | Streams | Bias/variance | Selective KDB | Incremental BNC
  • 32. Copyright © 2013 Geoffrey I Webb Feature Projection • Project feature space onto lower dimensional space • Principal Components Analysis • First principal component is the planar projection that maximises variance (= minimises RMSE with respect to original) • Subsequent principal components are those that maximise variance (= minimise RMSE) while being uncorrelated with prior components • First few principal components will capture most of the variation (= information) in the data • Generalisations including principal curves and manifolds project onto manifolds instead of planesBig data | Class learning | Sampling | Dimensionality red’n | Scaling-up | Streams | Bias/variance | Selective KDB | Incremental BNC
  • 33. Copyright © 2013 Geoffrey I Webb Scaling-up existing algorithms • Distributed cloud/cluster computing • Hadoop – Commodity clusters – Map Reduce • Map problem onto sub-problems and distribute these • Assemble solution from solutions to sub-problems White, Tom. Hadoop: The definitive guide. OReilly Media, Inc., 2012Big data | Class learning | Sampling | Dimensionality red’n | Scaling-up | Streams | Bias/variance | Selective KDB | Incremental BNC
  • 34. Copyright © 2013 Geoffrey I Webb Streaming algorithms • Handle data that are too large to retain – computer network/phone traffic, financial transactions, web searches, sensor data • May be difficult to get labelled data • Strong memory and running time constraints – learning rate must be greater than the data rate – only limited data can be retained • Real time accuracy evaluation and formalisation, mainly to adjust the parameters accordingly.Big data | Class learning | Sampling | Dimensionality red’n | Scaling-up | Streams | Bias/variance | Selective KDB | Incremental BNC
  • 35. Copyright © 2013 Geoffrey I Webb Online and incremental learning • Online learning – Data arrives as input stream – Classifier makes prediction – Then correct classification is revealed and classifier updated – Examples • Ad placement, online conversions • Incremental learning – Classifier is updated as input arrives – Classifier is identical to batch classifierAuer, Peter. “Online Learning.” In Encyclopedia of Machine Learning, C. Sammut and G.I. Webb, Editors. 2010, Springer: New York. p. 736-743.Big data | Class learning | Sampling | Dimensionality red’n | Scaling-up | Streams | Bias/variance | Selective KDB | Incremental BNC
  • 36. Copyright © 2013 Geoffrey I Webb Streaming Strategies • Retain samples of data and learn from these – Continually assess current model against incoming data and when models lose accuracy take new samples and relearn • Continually update a model using current data – Refine using new data – Prune elements that decline in accuracy • Create ensemble of classifiers each learned from successive time periods – Retire older classifiers as newer ones are createdBig data | Class learning | Sampling | Dimensionality red’n | Scaling-up | Streams | Bias/variance | Selective KDB | Incremental BNC
  • 37. Copyright © 2013 Geoffrey I Webb Weighted majority algorithm • Each classifier E has a weight wt E • Classification by weighted majority vote • All incorrect classifiers have their weights reduced wt+1 E =wt E , 0<  <1 • Error is bounded to no more than twice the error of the best classifierLittlestone, N, and MK Warmuth. "The weighted majority algorithm." In 30th Annual Symposium on Foundation of Computer Science, pp. 256-261. IEEE, 1989.Big data | Class learning | Sampling | Dimensionality red’n | Scaling-up | Streams | Bias/variance | Selective KDB | Incremental BNC
  • 38. Copyright © 2013 Geoffrey I Webb Winnow Threshold Binary attributes Non-negative real valued weights Prediction Correct xi = 0 xi = 1 1 0 unchanged 0 1 unchangedLittlestone, N. "Learning quickly when irrelevant attributes abound: A new linear-threshold algorithm." Machine Learning 2(4)(1988): 285-318.Big data | Class learning | Sampling | Dimensionality red’n | Scaling-up | Streams | Bias/variance | Selective KDB | Incremental BNC
  • 39. Copyright © 2013 Geoffrey I Webb Stochastic gradient descent • Many classifiers have parameters that are learned by optimisation e.g. logistic regression and SVM – usually requires many passes through the data • For linear classifiers stochastic gradient descent often converges before a single pass is completed. – global gradient approximated by the gradient at each example – performs sequential updates – good step size is essential • learn from an initial sample – must take examples in random orderZhang, Tong. "Solving large scale linear prediction problems using stochastic gradient descent algorithms." In Proceedings 21st International Conference on Machine learning, p. 116. ACM, 2004.Big data | Class learning | Sampling | Dimensionality red’n | Scaling-up | Streams | Bias/variance | Selective KDB | Incremental BNC
  • 40. Copyright © 2013 Geoffrey I Webb Bias and variance • Learning curves are not all equal 0.8 KDB k=2 KDB k=2 KDB k=5 0.7 0.6 Root Mean Squared Error 0.5 0.4 0.3 0.2 0.1 0 0 100,000 200,000 300,000 400,000 500,000 600,000 700,000 800,000 900,000 1,000,000 Data quantityBig data | Class learning | Sampling | Dimensionality red’n | Scaling-up | Streams | Bias/variance | Selective KDB | Incremental BNC
  • 41. Copyright © 2013 Geoffrey I Webb Bias and variance • A major factor in the difference between learning curves • Decomposition of 0-1 loss • Bias and variance relate to the performance of the learner given different training sets “Bias Variance Decomposition.” In Encyclopedia of Machine Learning, C. Sammut and G.I. Webb, Editors. 2010, Springer: New York. p. 100-101.Big data | Class learning | Sampling | Dimensionality red’n | Scaling-up | Streams | Bias/variance | Selective KDB | Incremental BNC
  • 42. Copyright © 2013 Geoffrey I Webb Bias and Variance 1,0,1,1,0,1,0,0,1 1,1,0,1,0,1,1,1,1 0,0,1,1,0,1,0,1,0 1 1,0,1,1,1,0,1,1,0 1 1,0,1,1,0,1,0,0,1 1,1,0,1,0,1,1,1,1 0,0,1,1,0,1,0,1,0 Learner 1,0,1,1,0,1,0,0,? 1 1,1,0,1,0,1,1,1,? 1,0,1,1,1,0,1,1,0 0 1,0,1,1,0,1,0,0,1 1,1,0,1,0,1,1,1,1 0 0,0,1,1,0,1,0,1,0 1,0,1,1,1,0,1,1,0 0Big data | Class learning | Sampling | Dimensionality red’n | Scaling-up | Streams | Bias/variance | Selective KDB | Incremental BNC
  • 43. Copyright © 2013 Geoffrey I Webb Bias and Variance 1,0,1,1,0,1,0,0,1 1,1,0,1,0,1,1,1,1 0,0,1,1,0,1,0,1,0 1 1,0,1,1,1,0,1,1,0 1 1,0,1,1,0,1,0,0,1 1,1,0,1,0,1,1,1,1 0,0,1,1,0,1,0,1,0 Learner 1,0,1,1,0,1,0,0,? 1 1,1,0,1,0,1,1,1,? 1,0,1,1,1,0,1,1,0 0 1,0,1,1,0,1,0,0,1 1,1,0,1,0,1,1,1,1 0 0,0,1,1,0,1,0,1,0 1,0,1,1,1,0,1,1,0 0Big data | Class learning | Sampling | Dimensionality red’n | Scaling-up | Streams | Bias/variance | Selective KDB | Incremental BNC
  • 44. Copyright © 2013 Geoffrey I Webb Bias and Variance 1,0,1,1,0,1,0,0,1 1,1,0,1,0,1,1,1,1 0,0,1,1,0,1,0,1,0 1 1,0,1,1,1,0,1,1,0 1 1,0,1,1,0,1,0,0,1 1,1,0,1,0,1,1,1,1 0,0,1,1,0,1,0,1,0 Learner 1,0,1,1,0,1,0,0,? 1 1,1,0,1,0,1,1,1,? 1,0,1,1,1,0,1,1,0 0 1,0,1,1,0,1,0,0,1 1,1,0,1,0,1,1,1,1 0 0,0,1,1,0,1,0,1,0 1,0,1,1,1,0,1,1,0 0Big data | Class learning | Sampling | Dimensionality red’n | Scaling-up | Streams | Bias/variance | Selective KDB | Incremental BNC
  • 45. Copyright © 2013 Geoffrey I Webb Bias and Variance 1,0,1,1,0,1,0,0,1 1,1,0,1,0,1,1,1,1 0,0,1,1,0,1,0,1,0 1 1,0,1,1,1,0,1,1,0 1X 1,0,1,1,0,1,0,0,1 1,1,0,1,0,1,1,1,1 0,0,1,1,0,1,0,1,0 Learner 1,0,1,1,0,1,0,0,? 1 1,1,0,1,0,1,1,1,? 1,0,1,1,1,0,1,1,0 0 1,0,1,1,0,1,0,0,1 1,1,0,1,0,1,1,1,1 0X 0,0,1,1,0,1,0,1,0 1,0,1,1,1,0,1,1,0 0 Variance ≈ (lower limit on) error due to variability in response to samplingBig data | Class learning | Sampling | Dimensionality red’n | Scaling-up | Streams | Bias/variance | Selective KDB | Incremental BNC
  • 46. Copyright © 2013 Geoffrey I Webb Bias and Variance 1,0,1,1,0,1,0,0,1 1,1,0,1,0,1,1,1,1 0,0,1,1,0,1,0,1,0 1X 1,0,1,1,1,0,1,1,0 1 1,0,1,1,0,1,0,0,1 1,1,0,1,0,1,1,1,1 0,0,1,1,0,1,0,1,0 Learner 1,0,1,1,0,1,0,0,? 1X 1,1,0,1,0,1,1,1,? 1,0,1,1,1,0,1,1,0 0X 1,0,1,1,0,1,0,0,1 1,1,0,1,0,1,1,1,1 0 0,0,1,1,0,1,0,1,0 1,0,1,1,1,0,1,1,0 0X Variance ≈ (lower limit on) error due to variability in response to sampling Bias ≈ error due to central tendency of the learner Bias = error - varianceBig data | Class learning | Sampling | Dimensionality red’n | Scaling-up | Streams | Bias/variance | Selective KDB | Incremental BNC
  • 47. Copyright © 2013 Geoffrey I Webb Bias and variance High bias Low bias High bias Low bias High variance High variance Low variance Low variance Image from Bias Variance Decomposition, in Encyclopedia of Machine Learning, C. Sammut and G.I. Webb, Editors. 2010, Springer: New York. p. 100-101.Big data | Class learning | Sampling | Dimensionality red’n | Scaling-up | Streams | Bias/variance | Selective KDB | Incremental BNC
  • 48. Copyright © 2013 Geoffrey I Webb Intrinsic error • Many bias/variance analyses also include intrinsic error • For our purposes this is included in biasBig data | Class learning | Sampling | Dimensionality red’n | Scaling-up | Streams | Bias/variance | Selective KDB | Incremental BNC
  • 49. Copyright © 2013 Geoffrey I Webb Bias/variance and big data • As data quantity increases, variance should decrease • Low variance important for small data • Low bias important for big dataBig data | Class learning | Sampling | Dimensionality red’n | Scaling-up | Streams | Bias/variance | Selective KDB | Incremental BNC
  • 50. Copyright © 2013 Geoffrey I Webb Low bias important for big data • Low bias requires capacity to describe wide variety of multivariate distributions • Big datasets contain fine detail needed to precisely delineate complex multivariate distributionsBig data | Class learning | Sampling | Dimensionality red’n | Scaling-up | Streams | Bias/variance | Selective KDB | Incremental BNC
  • 51. Copyright © 2013 Geoffrey I Webb Bias/variance and big data 0.8 Naïve Bayes 0.7 KDB k=2 KDB k=5 0.6 Root Mean Squared Error 0.5 0.4 0.3 0.2 0.1 0 0 100,000 200,000 300,000 400,000 500,000 600,000 700,000 800,000 900,000 1,000,000 Data quantityBig data | Class learning | Sampling | Dimensionality red’n | Scaling-up | Streams | Bias/variance | Selective KDB | Incremental BNC
  • 52. Copyright © 2013 Geoffrey I Webb Most machine learning research has used small data 0.8 Naïve Bayes 0.7 KDB k=2 KDB k=5 0.6 Root Mean Squared Error 0.5 0.4 0.3 0.2 0.1 0 0 100,000 200,000 300,000 400,000 500,000 600,000 700,000 800,000 900,000 1,000,000 Data quantityBig data | Class learning | Sampling | Dimensionality red’n | Scaling-up | Streams | Bias/variance | Selective KDB | Incremental BNC
  • 53. Copyright © 2013 Geoffrey I Webb Computational tractability • Error will be minimised by low bias algorithms • Big data require efficient computation – Linear wrt size – Learn in a limited number of passes • Most low-bias learners are compute intensive – super-linear with respect to data quantity – Kernel SVM and Random ForestsBig data | Class learning | Sampling | Dimensionality red’n | Scaling-up | Streams | Bias/variance | Selective KDB | Incremental BNC
  • 54. Copyright © 2013 Geoffrey I Webb k-dependence Bayesian classifier (KDB) • Bayesian network classifier proposed by Sahami (1995). • KDB – the probability of each attribute value is conditioned C by the class and at most k other attributes. A A A A4 – Extends TAN to multiple 1 2 3 parents.Big data | Class learning | Sampling | Dimensionality red’n | Scaling-up | Streams | Bias/variance | Selective KDB | Incremental BNC
  • 55. Copyright © 2013 Geoffrey I Webb k-dependence Bayesian classifier (KDB) • k=0 is Naïve Bayes C • k   variance and  bias • High k with low bias should A1 A2 A3 A4 have low error for big data. 0.8 Naïve Bayes 0.7 KDB k=2 KDB k=5 0.6 Root Mean Squared Error 0.5 0.4 0.3 0.2 0.1 0 0 100,000 200,000 300,000 400,000 500,000 600,000 700,000 800,000 900,000 1,000,000 Data quantityBig data | Class learning | Sampling | Dimensionality red’n | Scaling-up | Streams | Bias/variance | Selective KDB | Incremental BNC
  • 56. Copyright © 2013 Geoffrey I Webb KDB algorithm 1st pass: • Order attributes according to mutual C information (MI) with the class. 2nd pass: • Assign k parents to each attribute A1 A2 A3 A4 according to MI conditioned on the class. • Add the class as parent of all attributesBig data | Class learning | Sampling | Dimensionality red’n | Scaling-up | Streams | Bias/variance | Selective KDB | Incremental BNC
  • 57. Copyright © 2013 Geoffrey I Webb Two pass learning No of instances Av no of values/att No of attributes No of classes No of classes No of attributes Av no of values/attBig data | Class learning | Sampling | Dimensionality red’n | Scaling-up | Streams | Bias/variance | Selective KDB | Incremental BNC
  • 58. Copyright © 2013 Geoffrey I Webb Selective KDB - Motivation • KDB is efficient and effective for large data. • Irrelevant attributes can increase error. • Cannot predetermine the best k for a given data quantity. • Want an efficient way to select attributes and best k.Big data | Class learning | Sampling | Dimensionality red’n | Scaling-up | Streams | Bias/variance | Selective KDB | Incremental BNC
  • 59. Copyright © 2013 Geoffrey I Webb Selective KDB C C C MI(Ai;C) MI(Ai;Aj,C) A1 A2 A3 A4 A1 A2 A3 A1 A2 A3 A4 LF1 LF2 LF3 LF4 best Leave-one-out cv (Pazzani’s trick) Attributes ordered by MI Each alternative model tested is a minor addition to the previousBig data | Class learning | Sampling | Dimensionality red’n | Scaling-up | Streams | Bias/variance | Selective KDB | Incremental BNC
  • 60. Copyright © 2013 Geoffrey I Webb Selective KDB • Loss function can be RMSE, 0-1 loss, Matthews Correlation Coefficient (for unbalanced datasets), etc. • Still the value of k has to be tuned. – Solution: Selective2 KDB: matrix of loss function results kxn . a1 a2 a3 a4 a5 a6 p1 p1 p1 p1 p1 p2 p2 p2 p2 p3 p3 p3Big data | Class learning | Sampling | Dimensionality red’n | Scaling-up | Streams | Bias/variance | Selective KDB | Incremental BNC
  • 61. Copyright © 2013 Geoffrey I Webb Selective KDB • Loss function can be RMSE, 0-1 loss, Matthews Correlation Coefficient (for unbalanced datasets), etc. • Still the value of k has to be tuned. – Solution: Selective2 KDB: matrix of loss function results kxn . KDB Selective KDB Selective2 KDB Training time Test timeBig data | Class learning | Sampling | Dimensionality red’n | Scaling-up | Streams | Bias/variance | Selective KDB | Incremental BNC
  • 62. Copyright © 2013 Geoffrey I Webb Selective KDB – Results (RMSE) • Competitive with KDB in 16 very large datasets (165K- 54.6M examples): KDB selective KDB 8-8-0 5-11-0 5-11-0 6-10-0 6-9-1 k-selective KDB 5-11-0 • Mean best k = 4.11 • Mean % attributes selected = 82.6626.72Big data | Class learning | Sampling | Dimensionality red’n | Scaling-up | Streams | Bias/variance | Selective KDB | Incremental BNC
  • 63. Copyright © 2013 Geoffrey I Webb Selective KDB – Results (RMSE) • Comparison with Random Forest. RF (5EF) RF (Num) Trees = 10 Trees = 100 Trees = 10 Trees = 100 k-selective KDB 6-1-6 4-1-7 5-0-8 4-0-8 • Need to sample in 3/4 (out of 16) datasets to get RF 10/100 results. Mnist MITC Satellite Splice (250K/8.1M) (600K/839K) (2M/8.7M) (10M/54.6M) RF (100) Sample 0.29580.0017 0.05180.0007 0.45680.0006 0.05300.0005 k-selective Sample 0.23240.0029 0.04550.0019 0.45310.0011 0.05210.0006 KDB All data 0.14490.0007 0.04460.0020 0.44480.0004 0.05230.0002Big data | Class learning | Sampling | Dimensionality red’n | Scaling-up | Streams | Bias/variance | Selective KDB | Incremental BNC
  • 64. Copyright © 2013 Geoffrey I Webb Selective KDB – Results (MCC) • Unbalanced datasets: use MCC as loss function. • Splice dataset: 0.32% of positive classes. KDB selective KDB 0.1768 0.1918 0.1855 0.1984 0.1932 0.2043 0.1986 0.2105 0.2061 0.2148 Numeric Discrete • Comparison with Random Forest. attributes attributes MITC Splice (600K/839K) (10M/54.6M) RF (100) Sample 0.9989 0.0950 k-selective Sample 0.9954 0.1963 KDB All data 0.9956 0.2148Big data | Class learning | Sampling | Dimensionality red’n | Scaling-up | Streams | Bias/variance | Selective KDB | Incremental BNC
  • 65. Copyright © 2013 Geoffrey I Webb Incremental Bayesian Network Classifiers y x1 x2 x3 … xnBig data | Class learning | Sampling | Dimensionality red’n | Scaling-up | Streams | Bias/variance | Selective KDB | Incremental BNC
  • 66. Copyright © 2013 Geoffrey I Webb Incremental naïve Bayes • Probability estimates are based on counts of the frequency of each attribute value co-occurring with the class • These can be updated incrementally • Can these desirable features be generalised to more sophisticated learners?Big data | Class learning | Sampling | Dimensionality red’n | Scaling-up | Streams | Bias/variance | Selective KDB | Incremental BNC
  • 67. Copyright © 2013 Geoffrey I Webb Adding edges reduces bias • With additional edges it is possible to exactly represent all naïve Bayes distributions and more – Lower bias – Higher variance – Should be more accurate for bigger data – But which edges should we add? y x1 x2 x3 … xnBig data | Class learning | Sampling | Dimensionality red’n | Scaling-up | Streams | Bias/variance | Selective KDB | Incremental BNC
  • 68. Copyright © 2013 Geoffrey I Webb Averaged n-Dependence Estimators • Develop all of a family of classifiers that each add edges to naïve Bayes • Select order of dependence, n • Each model selects n attributes – All other attributes are independent given these attributes and the class – Each model has lower bias but higher variance than NB – Ensembling reduces the varianceWebb, GI, JR Boughton, FZheng, KM Ting, HSalem. "Learning by extrapolation from marginal to full-multivariate probability distributions: decreasingly naive Bayesian classification." Machine Learning 86(2) (2012): 233-272Big data | Class learning | Sampling | Dimensionality red’n | Scaling-up | Streams | Bias/variance | Selective KDB | Incremental BNC
  • 69. Copyright © 2013 Geoffrey I Webb Averaged n-Dependence Estimators All subsets of n attributesBig data | Class learning | Sampling | Dimensionality red’n | Scaling-up | Streams | Bias/variance | Selective KDB | Incremental BNC
  • 70. Copyright © 2013 Geoffrey I Webb Averaged n-Dependence Estimators • Incremental learning in a single pass through the data • Training time complexity O(man+1) Number of attributes Number of Number • Classification time complexity O(a k) n+1 training examples of classes • Space complexity O(an+1vn+1k) Average number of values per attributeBig data | Class learning | Sampling | Dimensionality red’n | Scaling-up | Streams | Bias/variance | Selective KDB | Incremental BNC
  • 71. Copyright © 2013 Geoffrey I Webb Averaged n-Dependence Estimators • As n increases bias decreases – Good for big data 0.7 0.6 Root Mean Squared Error 0.5 0.4 Naïve Bayes 0.3 A1DE 0.2 A2DE 0.1 A3DE 0 0 100000 200000 300000 400000 500000 600000 700000 800000 900000 1000000Big data | Class learning | Sampling | Dimensionality red’n | Scaling-up | Streams | Bias/variance | Selective KDB | Incremental BNC
  • 72. Copyright © 2013 Geoffrey I Webb Subsumption resolution • If P(x1 | x2) = 1.0 then P(y | x1,x2) = P(y | x2) – Eg P(oedema | female, pregnant) = P(oedema | pregnant) • Subsumption resolution looks for subsuming attributes at classification time and ignores them – Simple correction for extreme form of violation of attribute independence assumption – Very effective in practice – reduce bias at small cost in variance – though not always applicable – For AnDE with n≥1 uses statistics collected already – no learning overhead – often reduces classification timeZheng, F, GI Webb, P Suraweera, L Zhu. "Subsumption resolution: an efficient and effective technique for semi-naive Bayesian learning." Machine Learning 87(1)(2012): 93-125.Big data | Class learning | Sampling | Dimensionality red’n | Scaling-up | Streams | Bias/variance | Selective KDB | Incremental BNC
  • 73. Copyright © 2013 Geoffrey I Webb Weighting Jiang, Liangxiao, and Harry Zhang. "Weightily averaged one-dependence estimators." In PRICAI 2006, pp. 970-974. Springer Berlin, 2006.Big data | Class learning | Sampling | Dimensionality red’n | Scaling-up | Streams | Bias/variance | Selective KDB | Incremental BNC
  • 74. Copyright © 2013 Geoffrey I Webb Weighting • Weighting also reduces bias at the cost of a small increase in variance 0.6 A3DE A3DE W 0.5 Root Mean Squared Error 0.4 0.3 0.2 0.1 0 0 100000 200000 300000 400000 500000 600000 700000 800000 900000 1000000 Data quantityBig data | Class learning | Sampling | Dimensionality red’n | Scaling-up | Streams | Bias/variance | Selective KDB | Incremental BNC
  • 75. Copyright © 2013 Geoffrey I Webb Weighting and subsumption resolution are complementary • When SR is applicable, both in combination have lower bias but slightly higher variance than either alone RMSE Dataset Size A2DE A2DE-SR A2DE-W A2DE-WSR cleveland 303 0.359 0.360 0.361 0.361 small balance-scale 625 0.430 0.430 0.430 0.430 anneal 898 0.118 0.098 0.116 0.096 adult 48,842 0.313 0.306 0.308 0.303 localization 164,860 0.499 0.499 0.498 0.498 large covtype 581,102 0.371 0.349 0.350 0.335 poker-hand 1,025,010 0.496 0.496 0.420 0.420 kddcup 5,209,460 0.044 0.040 0.043 0.039Big data | Class learning | Sampling | Dimensionality red’n | Scaling-up | Streams | Bias/variance | Selective KDB | Incremental BNC
  • 76. Copyright © 2013 Geoffrey I WebbQuestions?
  • 77. Copyright © 2013 Geoffrey I Webb ReferencesSilver, Nate. The Signal and the Noise: Why So Many Predictions Fail-but Some Dont. Penguin Press, 2012.Whitelaw, Casey, Ben Hutchinson, Grace Y. Chung, and Gerard Ellis. "Using the web for language independent spellchecking andautocorrection." In Proceedings of the 2009 Conference on Empirical Methods in Natural Language Processing: Volume 2, pp. 890-899.Association for Computational Linguistics, 2009.Prof. William H. Press, “Unit 17: Classifier Performance: ROC, Precision-Recall, and All That.”http://www.nr.com/CS395T/lectures2008/17-ROCPrecisionRecall.pdfProvost, Foster, David Jensen, and Tim Oates. “Efficient progressive sampling.” In Proceedings 5th ACM SIGKDD internationalconference on Knowledge Discovery and Data Mining, pp. 23-32. ACM, 1999.Hulten, Geoff, and Pedro Domingos. "Mining complex models from arbitrarily large databases in constant time." In Proceedings of theeighth ACM SIGKDD international conference on Knowledge discovery and data mining, pp. 525-531. ACM, 2002.Tille, Yves. Sampling algorithms. Springer, 2006.White, Tom. Hadoop: The definitive guide. OReilly Media, Inc., 2012Auer, Peter. “Online Learning.” In Encyclopedia of Machine Learning, C. Sammut and G.I. Webb, Editors. 2010, Springer: New York. p.736-743.Littlestone, Nick, and Manfred K. Warmuth. "The weighted majority algorithm." In Foundations of Computer Science, 1989., 30th AnnualSymposium on, pp. 256-261. IEEE, 1989.Littlestone, Nick. "Learning quickly when irrelevant attributes abound: A new linear-threshold algorithm." Machine learning 2, no. 4(1988): 285-318.Zhang, Tong. "Solving large scale linear prediction problems using stochastic gradient descent algorithms." In Proceedings 21stInternational Conference on Machine learning, p. 116. ACM, 2004.“Bias Variance Decomposition.” In Encyclopedia of Machine Learning, C. Sammut and G.I. Webb, Editors. 2010, Springer: New York. p.100-101.Sahami, Mehran. "Learning limited dependence Bayesian classifiers." In KDD-96: Proceedings of the Second International Conferenceon Knowledge Discovery and Data Mining, pp. 335-338. 1996.Webb, Geoffrey I., Janice R. Boughton, Fei Zheng, Kai Ming Ting, and Houssam Salem. "Learning by extrapolation from marginal to full-multivariate probability distributions: decreasingly naive Bayesian classification." Machine Learning 86, no. 2 (2012): 233-272.Zheng, Fei, Geoffrey I. Webb, Pramuditha Suraweera, and Liguang Zhu. "Subsumption resolution: an efficient and effective technique forsemi-naive Bayesian learning." Machine Learning 87, no. 1 (2012): 93-125.Jiang, Liangxiao, and Harry Zhang. "Weightily averaged one-dependence estimators." In PRICAI 2006: trends in artificial intelligence, pp.970-974. Springer Berlin Heidelberg, 2006.

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