1. Mining High-Speed Data Streams Presented by: William Kniffin Pedro Domingos Geoff Hulten Sixth ACM SIGKDD International Conference - 2000

2. Outline → Introduction → Hoeffding Trees → The VFDT System → Performance Study → Conclusion / Summary → Test Questions 2

3. Outline → Introduction → Hoeffding Trees → The VFDT System → Performance Study → Conclusion / Summary → Test Questions 3

4. Introduction – System Limitations Knowledge Discovery System limitations: o Time o Memory o Sample Size Traditional Systems: o Amount of available data is small o Systems use a fraction of their computation power to avoid overfitting Current Systems: o Bottleneck is time and memory o Majority of sample data is unused; underfitting issues surface 5

5. Introduction Today’s Algorithms: o Efficient, but cannot handle supermassive databases o Current Data Mining systems are not equipped to handle the exponential increase of data expansion o New examples arrive at a higher rate than they can be mined 6

6. Introduction - Cont. Requirements for ‘Modern’ Algorithms: o Operate continuously and indefinitely o Incorporate new examples as they become available o Never lose potentially valuable information o Build a model using at most one scan of a database or dataset o Use only a fixed amount of main memory o Require small, constant time per record o Make a usable model that can be available at any point during the algorithm’s runtime 7

7. Introduction - Cont. What can fulfill these requirements? o Incremental Learning Methods  Online Methods  Successive Methods  Sequential Methods 8

8. Outline → Introduction → Hoeffding Trees → The VFDT System → Performance Study → Conclusion / Summary → Test Questions 9

9. Hoeffding Trees Classic Decision Tree Learners o Examples: ID3, C4.5, CART o Assumes examples can be stored simultaneously in main memory; loss of learnable examples. Disk-based Decision Tree Learners o Examples: SLIQ, SPRINT o Assumes examples are stored on disk. o Big Datasets easily fill disk and errors occur when the dataset is too large to fit. 10

10. Hoeffding Trees - Cont. A typical type of Classification Problem o Given : N training examples in the form (x,y) o y = discrete class label o x = array of d attributes o Goal: Produce a model, y = f(x), to predict classes y of future examples x with high accuracy. 11

11. Hoeffding Trees - Cont. Challenge : Design a decision tree learner for extremely large (potentially infinite) datasets with high accuracy and low computational cost. Given a stream of examples: o The first ones will be used to choose the root test o Succeeding ones will pass to corresponding leaves o Pick the best attributes at each leaf o Continue process recursively 12

12. Hoeffding Trees - Cont. Hoeffding Bound : o Complicated … basically: o Let G(Xi) be the heuristic measure used to choose test attributes o Like GINI or info-gain in CART and C4.5 respectively) o Our goal is to ensure that, with high probability, the attribute chosen using n examples (where n is as small as possible) is the same that would be chosen using infinite examples 14

13. Hoeffding Tree Algorithm Inputs: o S : sequence of examples o X : set of discrete attributes o G(.) : split evaluation function o δ : desired probability of choosing the correct attribute at any given node Output: o HT : A decision tree (Hoeffding Tree) 16

14. Hoeffding Tree Algorithm 17

15. Outline → Introduction → Hoeffding Trees → The VFDT System → Performance Study → Conclusion / Summary → Test Questions 22

16. The VFDT System Very Fast Decision Tree learner (VFDT) A decision tree learning system Based on the Hoeffding Tree algorithm VFDT allows the use of either information gain or the Gini index as the attribute evaluation measure 23

17. The VFDT System - Cont. Includes a number of refinements to the Hoeffding Tree algorithm: o Ties o G-Computation o Memory o Poor Attributes o Initialization o Rescans 24

18. The VFDT System - Ties Two or more attributes may have similar G’s A large number of examples may be required to decide between them with high confidence In a VFDT, we specify a user-threshold for ties and split 25

19. The VFDT System - G-Computation The most significant part of the time cost per example is recomputing G Computing a G value for every new example is inefficient. In a VFDT, users can specify an n min value n min : Number of new examples that must accumulate at a leaf before recomputing G 26

20. The VFDT System - Memory a VFDT’s memory use is dominated by the memory required to keep counts for all growing leaves. If the maximum available memory is reached, VFDT deactivates the least promising leaves. The least promising leaves are considered to be the ones with the lowest values of p l e l. 27

21. The VFDT System - Poor Attributes a VFDT’s memory usage is also minimized by dropping early on attributes that do not look promising. The memory used to store the corresponding counts can also be freed. 28

22. The VFDT System - Initialization VFDT can be initialized with the tree produced by a conventional RAM-based learner on a small subset of the data. Gives VFDT a “head start” 29

23. The VFDT System - Rescans VFDT can rescan previously-seen examples. Rescans are activated if: o The data arrives slowly enough that time allows for rescans o The dataset is finite and small enough that it is feasible VFDT will never grow a tree smaller than ones produced by other algorithms. 30

24. Outline → Introduction → Hoeffding Trees → The VFDT System → Performance Study → Conclusion / Summary → Test Questions 31

25. Synthetic Data Study Comparing VFDT with C4.5 Restricted Two Systems to using the same amount of RAM (40MB) VFDT used information gain as the G function. o At tree depth of 18, all the nodes were replaced with leaves. o Each leaf was randomly assigned a class. Stream of training examples were then generated o Various levels of class and attribute noise was added. 32

26. Synthetic Data Study - Cont. Accuracy as a function of the number of training examples 33

27. Synthetic Data Study - Cont. Tree Size as a function of the number of training examples 34

28. Synthetic Data Study - Cont. Accuracy as a function of the noise level 35

29. Web Data - Trial Run Application of VFDT to mine the stream of Web Page Requests Test Location : The Entire University of Washington Campus Statistics for mining 1.6 million examples: o VFDT took 1450 seconds to do one pass over the training data o 983 seconds were spent reading data from the disk o C4.5 took 24 hours to mine 1.6 million examples. 37

30. Outline → Introduction → Hoeffding Trees → The VFDT System → Performance Study → Conclusion / Summary → Test Questions 39

31. Conclusion - Hoeffding Trees A method for learning online Learns from the increasingly common high-volume data streams Allows learning in very small constant time per example Strong guarantees of high asymptotic similarities to corresponding batch trees. 40

32. Conclusion - VFDT Systems A high-performance data mining system Based on Hoeffding trees Empirical studies show its effectiveness in taking advantage of massive numbers of examples Practical, efficient, and accurate. 41

33. Outline → Introduction → Hoeffding Trees → The VFDT System → Performance Study → Conclusion / Summary → Test Questions 42

34. Test Questions - 1 of 3 Question: Name four of the challenges that modern algorithms have to overcome today. o Answer: See Slide 6. o Operate continuously and indefinitely o Incorporate new examples as they become available o Never lose potentially valuable information o Build a model using at most one scan of a database or dataset o Use only a fixed amount of main memory. o Require small, constant time per record. o Make a usable model that can be available at any point during the algorithm’s runtime. 43

35. Test Questions - 2 of 3 Question: List the input requirements of the HT-Algorithm, and state what output is generated. o Answer: See Slide 16 o Inputs:  S : sequence of examples  X : set of discrete attributes  G(.) : split evaluation function  δ : desired probability of choosing the wrong attribute at any given node o Output:  HT : A decision tree (Hoeffding Tree) 44

36. Test Questions - 3 of 3 Question: What does VFDT stand for and when does the algorithm rescan? o Answer: See Slide 23. Rescans are activated if: o The data arrives slowly enough that time allows for rescans o The dataset is finite and small enough that it is feasible 45