Capabilities and Prospects of I nductive Modeling Volodymyr STEPASHKO Prof., Dr. Sci., Head of Department INFORMATION TECHNOLOGIES FOR INDUCTIVE MODELING International Research and Training Centre of the Academy of Sciences of Ukraine 1
Layout 1. Historical aspects of IM 2. International events on IM 3. Attempt to define IM: what is it? 4. IM destination: what is this for? 5. IM explanation: basic algorithms and tools 6. Basic Theoretical Results 7. IM compared to ANN and CI 8. Real-world applications of IM 9. Main centers of IM research 10. IM development prospects 2
1. Historical aspects of I M 1968 First publication on GMDH: I вахненко O. Г . Метод групового урахування аргументів – конкурент методу стохастичної апроксимації // Автоматика . – 1968. – № 3. – С . 58-72. Terminology evolution : � heuristic self-organization of models (1970s) � inductive method of model building (1980s) � inductive learning algorithms for modeling (1992) � inductive modeling (1998) GMDH : Group Method of Data Handling MGUA : Method of Group Using of Arguments 3
4 A.G.I vakhnenko: GMDH originator
Main scientific results in inductive modelling theory: Foundations of cybernetic forecasting device construction Theory of models self-organization by experimental data Group method of data handling (GMDH) for automatic construction (self-organization) of model for complex systems Method of control with optimization of forecast Principles of noise-immunity modelling from noisy data Principles of polynomial networks construction Principle of neural networks construction with active neurons 5
Academician Ivakhnenko Academician Ivakhnenko • Originator of the scientific school of inductive modelling • Originator of the scientific school of inductive modelling • Author of 44 monographs and numerous articls • Author of 44 monographs and numerous articls • Prepared more than 200 Cand. Sci (Ph.D.) and 27 Doct. Sci • Prepared more than 200 Cand. Sci (Ph.D.) and 27 Doct. Sci 6
2. I nternational events on I M 2002 Lviv, Ukraine 1 st International Conference on Inductive Modelling ICIM’2002 2005 Kyiv, Ukraine 1 st International Workshop on Inductive Modelling IWIM’2002 2007 Prague, Czech Republic 2 nd International Workshop on Inductive Modelling IWIM’2007 2008 Kyiv, Ukraine 2 nd International Conference on Inductive Modelling ICIM’2008 2009 Krynica, Poland 3 rd International Workshop on Inductive Modelling IWIM’2009 2010 Yevpatoria, Crimea, Ukraine 3 rd International Conference on Inductive Modelling ICIM’2009 Zhukyn (near Kyiv, Ukraine) Annual International Summer School on Inductive Modelling 7
3. Attempt to define I M: what is it? IM is MGUA / GMDH IM is a technique for model self-organization IM is a technology for building models from noisy data IM is the technology of inductive transition from data to models under uncertainty conditions: � small volume of noisy data � unknown character and level of noise � inexact composition of relevant arguments (factors) � unknown structure of relationships in an object 8
4. I M destination: what is this for? IM is used for solving the following problems: � Modelling from experimental data � Forecasting of complex processes � Structure and parametric identification � Classification and pattern recognition � Data clasterization � Machine learning � Data Mining � Knowledge Discovery 9
5. I M explanation: algorithms and tools Basic Principles of GMDH as an Inductive Method Given : data sample of n observations after m input x 1 , x 2 ,…, x m and output y variables Find : model y = f(x 1 , x 2 ,…, x m , θ ) with minimum variance of prediction error − ∗ , = − ℑ f arg min C ( f ), C ( f ) model quality criterion set of models GMDH Task: ∈ ℑ f Basic principles of the GMDH as an inductive method : 1. generation of variants of the gradually complicated structures of models 2. successive selection of the best variants using the freedom of decisions choice 3. external addition (due to the sample division ) as the selection criterion ∈ ℑ f Part А Generation of models Sample f * Part В Calculation of criterion С ( f ) C → min 10
Main stages of the modeling process D D A A T T A A ( (s s a a m m p p l le e , , ) a a p p r r i io o r r y y i in n f fo o r rm m a a t ti io o n n ) s C h h o o i ic c e e o o f f a a m m o o d d e e l l c c l la a s s s C n S S t tr ru u c c t tu u r re e g g e e n n e e r r a a t ti io o n n P a P a r ra a m m e e t te e r r e e s s t ti im m a a t ti io o n C r r i it te e r r i io o n n m m i in n i im m i iz z a a t ti io o n n C s A d d e e q q u u a a c c y y a a n n a a l ly y s s i is A F F i in n i is s h h i in n g g t th h e e p p r r o o c c e e s s s s 11
GMDH features Model Classes : linear, polynomial, autoregressive, difference (dynamic), nonlinear of network type etc. Parameter estimation : Least Squares Method (LSM) Model structure generators : GMDH Generators Sorting-out Iterative Exhaustive Directed Multilayered Relaxative search search 12
Main generators of models structures 1. Combinatorial: ) m = θ = = y X , v 1 , ..., 2 ; d ( d , d ,..., d ) v v v 1 2 m 2. Combinatorial-selective: ) ) l i j = θ = = y ( X | x ) , s 1 , m , i , l 1 , F − − s s 1 s s s 1 3. Selective (multilayered iterative): + = ϑ + ϑ + ϑ + ϑ + ϑ r 1 r r r r r 2 r 2 y y y y y ( y ) ( y ) , l 1 i 2 j 3 i j 4 i 5 j l l l = = = 2 r 0 , 1 ,...; i , j 1 , F ; l 1 , C F 13
External Selection Criteria Given sample: W = ( X | y ), X [ n x m ], y [ n x1] Division into two subsamples: ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ W X y A A A = = = + = W ; X ; y ; n n n ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ A B W X y ⎣ ⎦ ⎣ ⎦ ⎣ ⎦ B B B Parameter estimation for a model y = X θ : ) − T 1 T θ = = ( X X ) X y , G A , B , W , G G G G G ) 2 = − θ AR y X Regularity criterion: B B B A ) ) 2 = θ − θ CB X X Unbiasedness criterion: W A W B 14
I M tools Information Technology ASTRID (Kyiv) KnowledgeMiner (Frank Lemke, Berlin) FAKE GAME (Pavel Kordik at al., Prague) GMDHshell (Oleksiy Koshulko, Kyiv) 15
6. Basic Theoretical Results * = f arg min C ( f ). f ∈ F F – set of model structures С – criterion of a model quality Structure of a model: ) ) = θ y f ( X , ) f f Estimation of parameters: ) θ = θ arg min Q ( ). f f m θ ∈ R f Q – criterion of the quality of model parameters estimation 16
Main concept : Self-organizing evolution of the model of optimal complexity under uncertainty conditions Main result: Complexity of the optimum forecasting model depends on the level of uncertainty in the data: the higher it is, the simpler (more robust) there must be the optimum model Main conclusion : GMDH is the method for construction of models with minimum variance of forecasting error 17
6 6 2 ) J ( s | σ s = 4 s = 3 2 = 2, 0 2 | s ) σ J ( σ s = 2 2 = 1,5 σ 5 5 s = 1 2 = 1, 0 σ 4 4 s = 0 3 3 b ( s )= 2 = 0,5 J σ = J ( s |0) 2 2 1 1 2 2 2 2 σ кр (2,3) σ кр (1,2) σ кр (0,1) σ 2 = 0 σ 0 0 0 0,5 1 1,5 2 2,5 0 1 2 3 4 s Illustration to the GMDH theory 18
7. I M compared to ANN and CI Selective (multilayered) GMDH algorithm: x f g 1 1 1 ∗ x f g f 2 2 2 x f g 3 3 3 x f g 4 4 4 2 2 C m ⇒ C F ⇒ F F m 19
Optimal structure of the multilayered net x f 1 1 ∗ x g f 2 2 x f 3 3 x f g 4 4 4 2 2 C m ⇒ C F ⇒ F F m 20
8. Real-world applications of I M 1. Prediction of tax revenues and inflation 2. Modelling of ecological processes activity of microorganisms in soil under influence of heavy metals irrigation of trees by processed wastewaters water ecology 3. System prediction of power indicators 4. Integral evaluation of the state of the complex multidimensional systems economic safety investment activity ecological state of water reservoirs power safety 5. Technology of informative-analytical support of operative management decisions 21
9. Main centers of I M research IRTC ITS NANU, Kyiv, Ukraine NTUU “KPI”, Kyiv, Ukraine KnowledgeMiner, Berlin, Germany CTU in Prague, Czech Sichuan University, Chengdu, China 22
10. I M development prospects The most promising directions : 1. Theoretical investigations 2. Integration of best developments of IM, NN and CI 3. Paralleling 4. Preprocessing 5. Ensembling 6. Intellectual interface 7. Case studes 23
THANK YOU! Volodymyr STEPASHKO Address: Prof. Volodymyr Stepashko, International Centre of ITS, Akademik Glushkov Prospekt 40, Kyiv, MSP, 03680, Ukraine. Phone: +38 (044) 526-30-28 Fax: +38 (044) 526-15-70 E-mail: stepashko@irtc.org.ua Web: www.mgua.irtc.org.ua 24
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