Ecien t relational learning from sparse data Lub o P op - PowerPoint PPT Presentation

E�cien t relational learning from sparse data Lub o� P op el�nsk� Kno wledge Disco v ery Group F acult y of Informatics, Masaryk Univ ersit y in Brno, Czec hia popel@fi.muni.cz http://www.fi.muni.cz/ kd Relational learning - learning in �rst-order logic Exact learning - learning from exact data Sparse data - not more than 5 training examples Generate&test top-do wn algoritms - from the most general h yp othesis

Assumption-based learning BK, E, bias, A=true � . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . � inductiv e engine fails program P assumption A . . . . . . . . . . . . . . . true . . . . . . . . . . . . . . . . . . . . . . A acceptable? . . . return(P) . fails . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . generate assumption assumption A 2

Generic algorithm of assumption-based learning Giv en: domain k now l edg e B K ; exampl e set E ; bias , assumption A = tr ue inductiv e engine I , o v ergeneral program P function f , that computes an assumption A acceptabilit y mo dule AM 1. Call I on B K [ P ; E [ A; bias . 0 � if I succeeds resulting in program P then call AM to v alidate the assumption A . 0 if A is accepted then return( P ) else go to (2). � else go to (2). 2. Call f to generate a new assumption A . If it fails, return(fail) and stop else go to (1). 3

WiM + inductiv e engine M ar k us depth-�rst searc h automatic setting of bias m ultiple predicate learning 2nd-order sc hema ma y b e emplo y ed generator of assumptions c ho ose the simplest p ositiv e example �nd its ne ar-miss acceptabilit y criterion mem b ersh ip oracle 4

WiM: results 2 � 4 examples for learning most of ILP b enc hmark predicates (list pro cessing, P eano v a aritmetik a) learning from p ositiv e examples only; negativ e examples, if an y , generated with W iM itself max. 1 query to the user less dep enden t on qualit y of examples easy to use 5

C R U S T AC E AN , S K I Lit a W iM : Randomly generated examples C R U S T AC E AN S K I Lit W iM 2 3 2 3 5 2 3 5 mem b er 0.65 0.76 0.70 0.89 0.95 0.80 0.97 0.97 last 0.74 0.89 0.71 0.72 0.94 0.76 0.89 0.94 app end 0.63 0.74 0.76 0.80 0.89 0.77 0.95 0.95 delete 0.62 0.71 0.75 0.88 1.00 0.85 0.88 0.97 rev erse 0.80 0.86 0.66 0.85 0.87 0.85 0.95 0.99 6

Randomly generated examples: Learning with assumptions # p os. 2 3 5 b ez s TP b ez s TP b ez s TP last 0.885 0.896 6 0.906 0.934 7 0.932 0.971 8 delete 0.882 0.962 8 0.857 0.937 7 0.874 0.943 7 leq 0.380 0.703 0 0.527 0.795 4 0.572 0.932 9 length 0.540 0.659 0 0.692 0.816 1 0.728 0.956 4 7

D WiM sc hema database sc hema and ob ject descriptions in F-logic ? GENERA TE � @ � @ R Domain kno wledge Learning set predicates @ � @ R � WiM ? the new class/attribute de�nition in F OL ? TRANSLA TE ? the new class/attribute de�nition in F-logic 8

Spatial database sc hema BRIDGE LINEAR PLANAR Object1 Geometry Geometry Object 2 FORESTRY BUILDING HIGHWAY_BRIDGE RIVER ROAD RAILWAY Named Named State FOREST_HOUSE FOREST WOOD Importance Forest 9

Inductiv e query language for mining in geographic data [PKDD'98] bridge(X,Y):- extract c haracteristic rule road(X),roadGeometry( X,Z) , for bridge river(Y),riverGeometr y(Y, U), from road, riv er. member(V,Z),member(W, U),W =V. extract discriminate rule forest(F) :- for forest geometry(F,GForest), area(GForest,Area), in con trast to w o o d 100 < Area. from p oin t of view area. 10

extract dep endency rule for di�eren tHouses differentHouses(FH,F,H) :- from forestHouse, forest, building distance(FH,F,D1), distance(H,F,D2), where building(B, GB), D1<D2. not forestHouse(B, F) from p oin t of view distance, less 11