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USING QUALITATIVE KNOWLEDGE IN NUMERICAL LEARNING Ivan Bratko Faculty of Computer and Info. Sc. University of Ljubljana Slovenia

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THIS TALK IS ABOUT: AUTOMATED MODELLING FROM DATA WITH MACHINE LEARNING COMBINING NUMERICAL AND QUALITATIVE REPRESENTATIONS

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3 BUILING MODELS FROM DATA Observed system Machine learning, numerical regression Model of system Data

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EXAMPLE: POPULATION DYNAMICS A lake with zooplankton, phytoplankton and nutrient nitrogen Variables in system: Nut Phyto Zoo

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POPULATION DYNAMICS Observed behaviour in time Data provided by Todorovski&Džeroski

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PRIOR KNOWLEDGE We would like our modelling methods to make use of expert’s prior knowledge (possibly qualitative) Phytoplankton feeds on Nutrient, Zooplankton feeds on Phytoplankton Nutrient Phyto Zoo

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QUALITATIVE DIFFICULTIES OF NUMERICAL LEARNING Learn time behavior of water level: h = f( t, initial_outflow) Level h outflow t h

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TIME BEHAVIOUR OF WATER LEVEL Initial_ouflow=12.5

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VARYING INITIAL OUTFLOW Initial_ouflow=

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PREDICTING WATER LEVEL WITH M5 Qualitatively incorrect – water level cannot increase M5 prediction Initial_ouflow=12.5

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QUALITATIVE ERRORS OF NUMERICAL LEARNERS Experiments with regression (model) trees (M5; Quinlan 92), LWR (Atkenson et.al. 97) in Weka (Witten & Frank 2000), neural nets,... Qualitative errors: water level should never increase water level should not be negative An expert might accept numerical errors, but such qualitative errors are particularly disturbing

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Q 2 LEARNING AIMS AT OVERCOMING THESE DIFFICULTIES

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Q 2 LEARNING Šuc, Vladušič, Bratko; IJCAI’03, AIJ 2004, IJCAI’05 Aims at overcoming these difficulties of numerical learning Q 2 = Q ualitatively faithful Q uantitative learning Q 2 makes use of qualitative constraints

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QUALITATIVE CONSTRAINTS FOR WATER LEVEL For any initial outflow: Level is always decreasing with time For any time point: Greater the initial outflow, greater the level

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SUMMARY OF Q 2 LEARNING Standard numerical learning approaches make qualitative errors. As a result, numerical predictions are qualitatively inconsistent with expectations Q 2 learning (Qualitatively faithful Quantitative prediction); A method that enforces qualitative consistency Resulting numerical models enable clearer interpretation, and also significantly improve quantitative prediction

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IDEA OF Q 2 First find qualitative laws in data Respect these qualitative laws in numerical learning

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CONTENTS OF REST OF TALK Building blocks of Q 2 learning: Ideas from Qualitative Reasoning, Algorithms QUIN, QFILTER, QCGRID Experimental analysis Applications: Car modelling, ecological modelling, behavioural cloning (operating a crane, flying an aircraft)

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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

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QUALITATIVE MODELLING IN AI Naive physics, as opposed to "proper physics“ Qualitative modelling, as opposed to quantitative modelling

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ESSENCE OF NAIVE PHYSICS Describe physical processes qualitatively, without numbers or exact numerical relations “Naive physics”, as opposed to "proper physics“ Close to common sense descriptions

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EXAMPLE: BATH TUB What will happen? Amount of water will keep increasing, so will level, until the level reaches the top.

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EXAMPLE: U-TUBE What will happen? La Lb Level La will be decreasing, and Lb increasing, until La = Lb.

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QUALITATIVE REASONING ABOUT U-TUBE Total amount of water in system constant If La > Lb then flow from A to B Flow causes amount in A to decrease Flow causes amount in B to increase All changes in time happen continuously and smoothly Level La Level Lb A B

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QUALITATIVE REASONING ABOUT U-TUBE In any container: the greater the amount, the greater the level So, La will keep decreasing, Lb increasing Level La Level Lb

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QUALITATIVE REASONING ABOUT U-TUBE La will keep decreasing, Lb increasing, until they equalise Level La Level Lb La Lb Time

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THIS REASONING IS VALID FOR ALL CONTAINERS OF ANY SHAPE AND SIZE, REGARDLESS OF ACTUAL NUMBERS!

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QHY REASON QUALITATIVELY? Because it is easier than quantitatively Because it is easy to understand - facilitates explanation We want to exploit these advantages in ML

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RELATION BETWEEN AMOUNT AND LEVEL The greater the amount, the greater the level A = M + (L) A is a monotonically increasing function of L

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MONOTONIC FUNCTIONS Y = M + (X) specifies a family of functions X Y

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MONOTONIC QUALITATIVE CONSTRAINTS, MQCs Generalisation of monotonically increasing functions to several arguments Example: Z = M +,- ( X, Y) Z increases with X, and decreases with Y More precisely: if X increases and Y stays unchanged then Z increases

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EXAMPLE: BEHAVIOUR OF GAS Pressure = M +,- (Temperature, Volume) Pressure increases with Temperature Pressure decreases with Volume

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Q 2 LEARNING Induce qualitative constraints (QUIN) Qualitative to Quantitative Transformation (Q2Q) Numerical predictor: respects qualitative constraints fits data numerically Numerical data One possibility: QFILTER

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PROGRAM QUIN INDUCING QUALITATIVE CONSTRAINTS FROM NUMERICAL DATA Šuc 2001 (PhD Thesis, also as book 2003) Šuc and Bratko, ECML’01

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QUIN QUIN = Qualitative Induction Numerical examples QUIN Qualitative tree Qualitative tree: similar to decision tree, qualitative constraints in leaves

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EXAMPLE PROBLEM FOR QUIN Noisy examples: z = x 2 - y 2 + noise(st.dev. 50)

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EXAMPLE PROBLEM FOR QUIN In this region: z = M +,+ (x,y)

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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 y x y

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QUIN ALGORITHM: OUTLINE Top-down greedy algorithm (similar to induction of decision trees) For every possible split, find the “most consistent” MQC (min. error-cost) for each subset of examples Select the best split according to MDL

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Q2Q Qualitative to Quantitative Transformation

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Q2Q EXAMPLE X < 5 y n Y = M + (X) Y = M - (X) 5 X Y

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QUALITATIVE TREES IMPOSE NUMERICAL CONSTRAINTS MQCs impose numerical constraints on class values, between pairs of examples y = M + (x) requires: If x 1 > x 2 then y 1 > y 2

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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

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QFILTER AN APPROACH TO Q2Q TRANSFORMATION Šuc and Bratko, ECML’03

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TASK OF QFILTER Given: qualitative tree points with class predictions by arbitrary numerical learner learning examples (optionally) Modify class predictions to achieve consistency with qualitative tree

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QFILTER IDEA Force numerical predictions to respect qualitative constraints: find minimal changes of predicted values so that qualitative constraints become satisfied “minimal” = min. sum of squared changes a quadratic programming problem

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RESPECTING MQCs NUMERICALLY Y = M + (X) X Y

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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

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PREDICTING WATER LEVEL WITH M5 M5 prediction 7.5

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QFILTER’S PREDICTION QFILTER predictions True values

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POPULATION DYNAMICS Aquatic ecosystem with zooplankton, phytoplankton and nutrient nitrogen Phyto feeds on Nutrient, Zoo feeds on Phyto Nutrient Phyto Zoo

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POPULATION DYNAMICS WITH Q 2 Behaviour in time

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PREDICTION PROBLEM Predict the change in zooplankton population: ZooChange(t) = Zoo(t + 1) - Zoo(t) Biologist’s rough idea: ZooChange = Growth - Mortality M +,+ (Zoo, Phyto) M + (Zoo)

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APPROXIMATE QUALITATIVE MODEL OF ZOO CHANGE Induced from data by QUIN

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EXPERIMENT WITH NOISY DATA Domain no noise LWR; Q 2 5 % noise LWR; Q 2 20 % noise LWR; Q 2 ZooChange0.015 ; ; ; All results as MSE (Mean Squared Error)

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APPLICATIONS OF Q 2 FROM REAL ECOLOGICAL DATA Growth of algae Lagoon of Venice Plankton in Lake Glumsoe

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Lake Glumsø Location and properties: Lake Glumsø is located in a sub-glacial valley in Denmark Average depth 2 m Surface area m 2 Pollution Receives waste water from community with 3000 inhabitants (mainly agricultural) High nitrogen and phosphorus concentration in waste water caused hypereutrophication No submerged vegetation low transparency of water oxygen deficit at the bottom of the lake

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Lake Glumsø – data Relevant variables for modelling are: phytoplankton phyto zooplankton zoo soluble nitrogen ns soluble phosphorus ps water temperature temp

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PREDICTION ACCURACY Over all (40) experiments. Q 2 better than LWR in 75% (M5, 83%) of the test cases The differences were found significant (t-test) at 0.02 significance level

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OTHER ECOLOGICAL MODELLING APPLICATIONS Predicting ozone concentrations in Ljubljana and Nova Gorica Predicting flooding of Savinja river Q2 model by far superior to any predictor so far used in practice

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CASE STUDY INTEC’S CAR SIMULATION MODELS Goal: simplify INTEC’s car models to speed up simulation Context: Clockwork European project (engineering design)

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Intec’s wheel model

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Learning Manouvres Learning manouvres were very simple: Sinus bump Turning left Turning right Road excitation: Steering position

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WHEEL MODEL: PREDICTING TOE ANGLE

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Q2Q2 Qualiative errors Q 2 predicted alpha

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BEHAVIOURAL CLONING Given a skilled operator, reconstruct the human’s sub cognitive skill

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EXAMPLE: GANTRY CRANE Control force Load Carriage

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USE MACHINE LEARNING: BASIC IDEA Controller System Observe Execution trace Learning program Reconstructed controller (“clone”) ActionsStates

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CRITERIA OF SUCCESS Induced controller description has to: Be comprehensible Work as a controller

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WHY COMPREHENSIBILITY? To help the user’s intuition about the essential mechanism and causalities that enable the controller achieve the goal

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SKILL RECONSTRUTION IN CRANE Control forces: F x, F L State: X, dX, , d , L, dL

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CARRIAGE CONTROL QUIN: dX des = f(X, , d ) M-(X)M-(X) M+()M+() X < 20.7 X < 60.1 M+(X)M+(X) yes 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)

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CARRIAGE CONTROL: dX des = f(X, , d ) M-(X)M-(X) M+()M+() X < 20.7 X < 60.1 X < 29.3 M+(X)M+(X) d < M-(X)M-(X) M -,+ ( X, ) M +,+,- ( X, , d ) yes no Enables reconstruction of individual differences in control styles Operator S Operator L

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CASE STUDY IN REVERSE ENGINEERING: ANTI-SWAY CRANE

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ANTI-SWAY CRANE Industrial crane controller minimising load swing, “anti- sway crane” Developed by M. Valasek (Czech Technical University, CTU) Reverse engineering of anti-sway crane: a case study in the Clockwork European project

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ANTI-SWAY CRANE OF CTU Crane parameters: travel distance 100m height 15m, width 30m tons In daily use at Nova Hut metallurgical factory, Ostrava

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EXPLAINING HOW CONTROLLER WORKS Load swinging to right; Accelerate cart to right to reduce swing

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EMPIRICAL EVALUATION Compare errors of base-learners and corresponding Q 2 learners differences btw. a base-learner and a Q 2 learner are only due to the induced qualitative constraints Experiments with three base-learners: Locally Weighted Regression (LWR) Model trees Regression trees

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Y1Y1 Y2Y2 Robot Arm Domain 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 ) 11 22 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 ) L1L1 Derived attribute sum = 1 + 2 Difficulty for Q 2

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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.

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UCI and Dynamic Domains Five smallest regression data sets from UCI Dynamic domains: typical domains where QUIN was applied so far to explain the control skill or control the system until now was not possible to measure accuracy of the learned concepts (qualitative trees) AntiSway logged data from an anti-sway crane controller CraneSkill1, CraneSkill2: logged data of experienced human operators controlling a crane

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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)

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Q 2 - CONCLUSIONS A novel approach to numerical learning Can take into account qualitative prior knowledge Advantages: qualitative consistency of induced models and data – important for interpretation of induced models improved numerical accuracy of predictions

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Q 2 TEAM + ACKNOWLEDGEMENTS Q 2 learning, QUIN, Qfilter, QCGRID (AI Lab, Ljubljana): Dorian Šuc Daniel Vladušič Car modelling data Wolfgan Rulka (INTEC, Munich) Zbinek Šika (Czech Technical Univ.) Population dynamics data Sašo Džeroski, Ljupčo Todorovski (J. Stefan Institute, Ljubljana) Lake Glumsoe Sven Joergensen Boris Kompare, Jure Žabkar, D. Vladušič

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RELEVANT PAPERS Clark and Matwin 93: also used qualitative constraints in numerical predictions Šuc, Vladušič and Bratko; IJCAI’03 Šuc, Vladušič and Bratko; Artificial Intelligence Journal, 2004 Šuc and Bratko; ECML’03 Šuc and Bratko; IJCAI’05

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