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Introduction Model Results
Introduction Model Results
Lifted Relational Team Embeddings for Predictive Sport Analytics - - PowerPoint PPT Presentation
Lifted Relational Team Embeddings for Predictive Sport Analytics - - PowerPoint PPT Presentation
Introduction Model Results Lifted Relational Team Embeddings for Predictive Sport Analytics Gustav Filip Ond rej Hub a cek Sourek Zelezn y Czech Technical University in Prague Introduction Model Results The Problem
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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, Tid1, Tid2) Win of home team Tid1 over team Tid2 in match Mid. draw(Mid, Tid1, Tid2) Draw between home team Tid1 and Tid2 in match Mid. loss(Mid, Tid1, Tid2) Loss of home team Tid1 to team Tid2 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.
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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
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Introduction Model Results
LRNN Toy Example
Rules: (wm : foal(A) ← parent(A, B) ∧ horse(B)), (wn : foal(A) ← sibling(A, B) ∧ horse(B)), Facts: (horse(dakotta), w1), (horse(cheyenne), w2), (horse(aida),w3), (parent(star, aida), w4), (parent(star, cheyenne), w5), (sibling(star,dakotta), w6)
parent(A,B)
∧
horse(B) =
⇒ foal(A)
sibling(A,B)
∧
horse(B) =
⇒ foal(A)
parent(star,aida) Fact neurons horse(aida) parent(star,cheyenne) horse(cheyenne) sibling(star,dakotta) horse(dakotta) parent(star,aida) Atoms neurons
∨
horse(aida)
∨
parent(star,cheyenne)
∨
horse(cheyenne)
∨
sibling(star,dakotta)
∨
horse(dakotta)
∨
foal(star) Rule neurons
∧
foal(star)
∧
foal(star)
∧
foal(star) Aggregation neurons ∗ foal(star) ∗ foal(star) Atom neuron
∨
w1 w4 w2 w5 w6 w3 wm wn
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Introduction Model Results
Embedding Layer
Embedding declaration: w (0)
1
: type1(T) ← team(T, arsenal) w (0)
2
: type2(T) ← team(T, arsenal) w (0)
3
: type3(T) ← team(T, arsenal) . . . w (0)
j
: type3(T) ← team(T, everton) Predictive rules:
w (1)
(1;1) : outcome ← home(T1) ∧ type1(T1) ∧ away(T2) ∧ type1(T2).
w (1)
(1;2) : outcome ← home(T1) ∧ type1(T1) ∧ away(T2) ∧ type2(T2).
. . .
w (1)
(3;3) : outcome ← home(T1) ∧ type3(T1) ∧ away(T2) ∧ type3(T2).
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Introduction Model Results
Relational Extension
Extension: w(2)
1
: outcome(M, H, A) ← win(M, H, A) w(2)
2
: outcome(M, H, A) ← draw(M, H, A) w(2)
3
: outcome(M, H, A) ← loss(M, H, A) Predictive rules:
w(1)
h−h(1;1) : outcome ← home(T1) ∧ type1(T1) ∧ outcome(M, T1, T2) ∧ type1(T2).
w(1)
h−a(1;1) : outcome ← home(T1) ∧ type1(T1) ∧ outcome(M, T2, T1) ∧ type1(T2).
w(1)
h−h(1;2) : outcome ← home(T1) ∧ type1(T1) ∧ outcome(M, T1, T2) ∧ type2(T2).
. . .
w(1)
a−a(3;3) : outcome ← away(T1) ∧ type3(T1) ∧ outcome(M, T2, T1) ∧ type3(T2).
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Introduction Model Results
Embeddings
2 1 1 2 3 0.5 0.0 0.5 1.0 1.5
arsenal aston_villa birmingham_city blackburn_rovers blackpool bolton bradford burnley charlton_athletic chelsea coventry_city crystal_palace derby_county everton fulham hull_city ipswich_town leeds_united leicester_city liverpool manchester_city manchester_united middlesbrough newcastle_united norwich_city portsmouth reading sheffield_united southampton stoke_city sunderland tottenham_hotspur watford west_bromwich_albion west_ham_united wigan_athletic wolverhampton
0.0 0.1 0.2 0.3 0.4 0.5 Home win rate
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Introduction Model Results
Comparison with SotA
2006 2008 2010 2012 2014 2016 Season 0.19 0.20 0.21 0.22 0.23 Baseline SotA RDN-Boost Relational Embeddings Embeddings
Figure: Comparison of performance of the learners on English Premier League as measured by the RPS metric (lower is better).
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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
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Introduction Model Results