Lifted Relational Team Embeddings for Predictive Sport Analytics - PowerPoint PPT Presentation

Introduction Model Results Lifted Relational Team Embeddings for Predictive Sport Analytics Gustav ˇ Filip ˇ Ondˇ rej Hub´ aˇ cek Sourek Zelezn´ y Czech Technical University in Prague

Introduction Model Results The Problem predicting future match outcome from historical data soccer matches results from EPL 2004–2016 no additional information Date Home Away Score H Score A 10/6/2004 Arsenal Chelsea 3 1 . . . . . . . . . . . . . . . 11/12/2016 Bolton Everton 2 2

Introduction Model Results Knowledge Representation Predicate Description home( Tid ) Team Tid is home team w.r.t. prediction match. away( Tid ) Team Tid is away team w.r.t. prediction match. team( Tid , name ) Team Tid has name name . win( Mid , Tid 1 , Tid 2 ) Win of home team Tid 1 over team Tid 2 in match Mid . draw( Mid , Tid 1 , Tid 2 ) Draw between home team Tid 1 and Tid 2 in match Mid . loss( Mid , Tid 1 , Tid 2 ) Loss of home team Tid 1 to team Tid 2 in match Mid . scored( Mid , Tid , n ) The team Tid scored more than n goals in match Mid . conceded( Mid , Tid , n ) The team Tid conceded more than n goals in match Mid . goal diff( Mid , n ) Difference in goals scored by the teams is greater than n . recency( Mid , n ) The match Mid was played more than n rounds ago.

Introduction Model Results Lifted Relational Neural Networks framework utilizing a fragment of relational fuzzy logic parameter training by gradient descend model = lifted template for neural network LRNN grounds the template w.r.t. the different examples different computational graph for each example

Introduction Model Results LRNN Toy Example Rules: (w m : foal ( A ) ← parent ( A , B ) ∧ horse ( B )) , (w n : foal ( A ) ← sibling ( A , B ) ∧ horse ( B )) , Facts: ( horse ( dakotta ), w 1 ) , ( horse ( cheyenne ) , w 2 ) , ( horse ( aida ),w 3 ) , ( parent ( star , aida ) , w 4 ) , ( parent ( star , cheyenne ) , w 5 ) , ( sibling ( star , dakotta ), w 6 ) Fact neurons Atoms neurons w 4 parent(star,aida) parent(star,aida) Rule neurons ∨ Aggregation neurons foal(star) w 3 horse(aida) horse(aida) ∧ horse(B) = ⇒ foal(A) foal(star) parent(A,B) ∧ ∨ Atom neuron ∗ w m w 5 parent(star,cheyenne) parent(star,cheyenne) foal(star) ∨ ∨ foal(star) w n ∧ w 2 horse(cheyenne) horse(cheyenne) horse(B) = sibling(A,B) ⇒ foal(A) foal(star) ∧ ∨ ∗ w 6 sibling(star,dakotta) sibling(star,dakotta) foal(star) ∨ ∧ w 1 horse(dakotta) horse(dakotta) ∨

Introduction Model Results Embedding Layer Embedding declaration: w (0) : type 1 ( T ) ← team ( T , arsenal ) 1 w (0) : type 2 ( T ) ← team ( T , arsenal ) 2 w (0) : type 3 ( T ) ← team ( T , arsenal ) 3 . . . w (0) : type 3 ( T ) ← team ( T , everton ) j Predictive rules: w (1) (1;1) : outcome ← home ( T 1) ∧ type 1 ( T 1) ∧ away ( T 2) ∧ type 1 ( T 2) . w (1) (1;2) : outcome ← home ( T 1) ∧ type 1 ( T 1) ∧ away ( T 2) ∧ type 2 ( T 2) . . . . w (1) (3;3) : outcome ← home ( T 1) ∧ type 3 ( T 1) ∧ away ( T 2) ∧ type 3 ( T 2) .

Introduction Model Results Relational Extension Extension: w (2) : outcome ( M , H , A ) ← win ( M , H , A ) 1 w (2) : outcome ( M , H , A ) ← draw ( M , H , A ) 2 w (2) : outcome ( M , H , A ) ← loss ( M , H , A ) 3 Predictive rules: w (1) h − h (1;1) : outcome ← home ( T 1) ∧ type 1 ( T 1) ∧ outcome ( M , T 1 , T 2) ∧ type 1 ( T 2) . w (1) h − a (1;1) : outcome ← home ( T 1) ∧ type 1 ( T 1) ∧ outcome ( M , T 2 , T 1) ∧ type 1 ( T 2) . w (1) h − h (1;2) : outcome ← home ( T 1) ∧ type 1 ( T 1) ∧ outcome ( M , T 1 , T 2) ∧ type 2 ( T 2) . . . . w (1) a − a (3;3) : outcome ← away ( T 1) ∧ type 3 ( T 1) ∧ outcome ( M , T 2 , T 1) ∧ type 3 ( T 2) .

Introduction Model Results Embeddings aston_villa 1.5 0.5 1.0 0.4 bolton blackburn_rovers manchester_city ipswich_town wolverhampton Home win rate 0.5 0.3 leicester_city charlton_athletic birmingham_city west_ham_united west_bromwich_albion reading arsenal norwich_city leeds_united watford portsmouth 0.2 0.0 manchester_united wigan_athletic crystal_palace sheffield_united middlesbrough stoke_city hull_city southampton bradford burnley fulham derby_county chelsea sunderland everton 0.1 0.5 blackpool coventry_city tottenham_hotspur liverpool newcastle_united 0.0 2 1 0 1 2 3

Introduction Model Results Comparison with SotA Baseline SotA RDN-Boost 0.23 Relational Embeddings Embeddings 0.22 0.21 0.20 0.19 2006 2008 2010 2012 2014 2016 Season Figure: Comparison of performance of the learners on English Premier League as measured by the RPS metric (lower is better).

Introduction Model Results Conclusion promising preliminary results easily applicable to different sports extensible with more information (goals scored, match recency, ...) natural incorporation of domain knowledge

Introduction Model Results Conclusion promising preliminary results easily applicable to different sports extensible with more information (goals scored, match recency, ...) natural incorporation of domain knowledge Thank you for your attention.