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Using Qualitative Knowledge in Numerical Learning
- 1. USING QUALITATIVE KNOWLEDGE IN NUMERICAL LEARNING Ivan Bratko Faculty of Computer and Info. Sc. University of Ljubljana Slovenia
- 2. THIS TALK IS ABOUT: AUTOMATED MODELLING FROM DATA WITH MACHINE LEARNING COMBINING NUMERICAL AND QUALITATIVE REPRESENTATIONS
- 8. TIME BEHAVIOUR OF WATER LEVEL Initial_ouflow =12.5
- 9. VARYING INITIAL OUTFLOW Initial_ouflow =12.5 11.25 10.0 8.75 6.25
- 10. PREDICTING WATER LEVEL WITH M5 11.25 10.0 8.75 6.25 7.5 Initial_ouflow =12.5 Qualitatively incorrect – water level cannot increase M5 prediction
- 12. Q 2 LEARNING AIMS AT OVERCOMING THESE DIFFICULTIES
- 18. HOW CAN WE DESCRIBE QUALITATIVE PROPERTIES ? We can use concepts from field of qualitative reasoning in AI Related terms: Qualitative physics, Naive physics, Qualitative modelling
- 26. THIS REASONING IS VALID FOR ALL CONTAINERS OF ANY SHAPE AND SIZE, REGARDLESS OF ACTUAL NUMBERS!
- 29. MONOTONIC FUNCTIONS Y = M + (X) specifies a family of functions X Y
- 33. PROGRAM QUIN INDUCING QUALITATIVE CONSTRAINTS FROM NUMERICAL DATA Šuc 2001 ( PhD Thesis , also as book 2003 ) Šuc and Bratko, ECML ’ 01
- 36. EXAMPLE PROBLEM FOR QUIN In this region: z = M +,+ (x,y)
- 37. INDUCED QUALITATIVE TREE FOR z = x 2 - y 2 + noise z= M -,+ ( x,y) z= M -,- ( x,y) z= M +,+ ( x , y) z= M +,- ( x,y) 0 > 0 > 0 0 > 0 0 y x y
- 39. Q2Q Qualitative to Quantitative Transformation
- 42. RESPECTING MQCs NUMERICALLY z = M +,+ (x,y) requires: If x 1 < x 2 and y 1 < y 2 then z 1 < z 2 (x 2 , y 2 ) (x 1 , y 1 ) x y
- 43. QFILTER AN APPROACH TO Q2Q TRANSFORMATION Šuc and Bratko, ECML ’03
- 47. QFILTER APPLIED TO WATER OUTFLOW Qualitative constraint that applies to water outflow: h = M -,+ (time, InitialOutflow) This could be supplied by domain expert, or induced from data by QUIN
- 48. PREDICTING WATER LEVEL WITH M5 7.5 M5 prediction
- 49. QFILTER’S PREDICTION QFILTER predictions T rue values
- 53. APPROXIMATE QUALITATIVE MODEL OF ZOO CHANGE Induced from data by QUIN
- 54. EXPERIMENT WITH NOISY DATA All results as MSE (Mean Squared Error) 2.269 ; 1.889 0.112 ; 0.102 0.015 ; 0.008 ZooChange 20 % noise LWR; Q 2 5 % noise LWR; Q 2 no noise LWR; Q 2 Domain
- 63. WHEEL MODEL : PREDICTING TOE ANGLE
- 64. WHEEL MODEL : PREDICTING TOE ANGLE
- 65. WHEEL MODEL : PREDICTING TOE ANGLE
- 66. WHEEL MODEL : PREDICTING TOE ANGLE Qualiative errors Q 2 predicted alpha Q 2
- 68. EXAMPLE: GANTRY CRANE Control force Load Carriage
- 69. USE MACHINE LEARNING: BASIC IDEA Controller System Observe Execution trace Learning program Reconstructed controller (“clone”) Actions States
- 72. SKILL RECONSTRUTION IN CRANE Control forces: F x , F L State: X, d X, , d , L, d L
- 73. CARRIAGE CONTROL QUIN: dX des = f(X, , d ) M - ( X ) M + ( ) X < 20.7 X < 60.1 M + ( X ) yes yes no no First the trolley velocity is increasing From about middle distance from the goal until the goal the trolley velocity is decreasing At the goal reduce the swing of the rope (by acceleration of the trolley when the rope angle increases)
- 74. CARRIAGE CONTROL: dX des = f(X, , d ) M - ( X ) M + ( ) X < 20.7 X < 60.1 X < 29.3 M + ( X ) d < -0.02 M - ( X ) M -,+ ( X , ) M +,+,- ( X, , d ) yes yes yes yes no no no no Enables reconstruction of individual differences in control styles Operator S Operator L
- 75. CASE STUDY IN REVERSE ENGINEERING: ANTI-SWAY CRANE
- 80. Robot Arm Domain Y 1 Y 2 Two-link, two-joint robot arm Link 1 extendible: L 1 [2, 10] Y 1 = L 1 sin( 1 ) Y 2 = L 1 sin( 1 ) + 5 sin( 1 + 2 ) 1 2 Four learning problems: A: Y 1 = f(L 1 , 1 ) B: Y 2 = f(L 1 , 1 , 2 , sum , Y 1 ) C: Y 2 = f(L 1 , 1 , 2 , sum ) D: Y 2 = f(L 1 , 1 , 2 ) L 1 Derived attribute sum = 1 + 2 Difficulty for Q 2
- 81. Robot Arm: LWR and Q 2 at different noise levels Q 2 outperforms LWR with all four learning problems (at all three noise levels) A 0, 5, 10% n. | B 0, 5, 10% n. | C 0, 5, 10% n. | D 0, 5, 10% n.
- 83. UCI and Dynamic Domains: LWR compared to Q 2 Similar results with other two base-learners. Q 2 significantly better than base-learners in 18 out of 24 comparisons (24 = 8 datasets * 3 base-learners)
Notes de l'éditeur
- I’ll give an example of the learning problem for QUIN algorithm. The red points on the picture are example points for the fn. z=… And this are noisy example – QUIN has to be able to learn from noisy data. We can see some qualitatively similar regions: there are 4 qual. different regions. This examples are the learning examples for QUIN: Z is the class var., and x and y are the attributes.
- I’ll give an example of the learning problem for QUIN algorithm. The red points on the picture are example points for the fn. z=… And this are noisy example – QUIN has to be able to learn from noisy data. We can see some qualitatively similar regions: there are 4 qual. different regions. This examples are the learning examples for QUIN: Z is the class var., and x and y are the attributes.
- From this learning examples, QUIN induces the following qual.tree that defines the partition of the attribute space into the areas with common behaviour of the class variable. In the leaves are QCFs. For example, the rightmost leaf that applies when x and y are both positive says that z is ... We say that z is …
- A basic alg. for learning of q.trees uses MDL to learn …QCF, that is QCF that fits the examples best. To learn a qual. tree. a top-down greedy alg., that is similar to dec.tree learning algorithms, is used:… QUIN is heuristic improvement of this basic algorithm that considers also the consistency and prox…
- Given results for ZooChange are multiplied by 1000 (actual values are 1000 times smaller)
- The improvements of Q2 are even more obvious on INTEC wheel model. The blue line denotes the time behavior of toe angle alpha on the most difficult test trace.
- The red line is alpha predicted by LWR.
- and the orange line, alpha predicted by M5.
- The green line corresponds to Q2 prediction learned from the same data. Q2 clearly has the best numerical fit. Also with other state-of-the-art numerical predictors qualitative errors are clearly visible.
- To evaluate accuracy benefits of Q2 learning we compared Because Qfilter optimaly adjusts a base-learner’s predictions to be consistent with a qualitative tree, the differences… We experimented with 3 base-learners: {it RRE} is the root mean squared error normalized by the root mean squared error of average class value. Using our implementation of model and regression trees.
- Now I wll describe the experiments with 5 UCI and 3 Dyanmic Domains We used the 5 smallest data sets from the UCI repository with the majority of continuous attributes. A reason for choosing these data sets is also that Quinlan gives results of M5 and several other regression methods on these data sets, which enables a better comparison of $Q^2$ to other methods. The other three data sets are from dynamic domains where QUIN has typically been previously applied to explain the underlying control skill and to use the induced qualitative models to control a dynamic system. Until now, it was not possible to measure the numerical accuracy of the learned qualitative trees or compare it to other learning methods. Data set {em AntiSway} was used in reverse-engineering of an industrial gantry crane controller. This so-called {em anti-sway crane} is used in metallurgical companies to reduce the swing of the load and increase the productivity of transportation of slabs. Data sets {em CraneSkill1} and {em CraneSkill2} are the logged data of two experienced human operators controlling a crane simulator. Such control traces are typically used to reconstruct the underlying operator's control skill. The learning task is to predict the velocity of a crane trolley given the position of the trolley, rope angle and its velocity.
- The graph gives the RREs of LWR and Q2 in these 8 datasets using 10CV. Q 2 is much better in all domains, except in AutoMPG domain.