Data Analytics for Digital Marketing Lecture for Advanced Digital & Social Me...
Boosting dl concept learners
1. Boosting DL Concept Learners
Nicola FANIZZI, Giuseppe RIZZO and Claudia d'AMATO
LACAM — Dipartimento di Informatica & CILA
Università degli studi di Bari Aldo Moro
ESWC 2019 — June 4th, 2019
4. Context & Motivations
Considering knowledge bases in the Web of Data
Goal: Inducing a classification function (predictive model) for a
target concept to assess the membership of (unseen) individuals
Supervised approach: each (training) example labeled as
positive/negative/uncertain
Possible Applications: approximate classification, semi-automatic KB
completion (assertional part)
6. Context & Motivations
Weak Model 1
Strong Model
Weak Model 2
⋮ ⋮
⋮ ⋮
Weak Model n
Strong model more predictive than weak models
Ensemble Classification (boosting, bagging,...)ⓘ
7. Context & Motivations
Contribution
A framework for confidence-rated boosting for DL concept
learners
pool of weak models as concepts with the related score
each model induced to cover hardest examples (leading to
misclassifications)
8. Example
Learn a classification function for the individuals w.r.t. the target
concept .
Training set :
(instances of with a known child),
(instances of )
Ensemble Model:
Father
K = {
{
Man ⊑ Person, Woman ⊑ Person, Artist ⊑ Person, Man ⊑ ¬Woman} ∪
Man(a), Man(b), Man(c), Woman(d), Woman(f), Artist(e), Robot(g),
hasChild(a, d), hasChild(b, e)}
T
Ps = {a, b} Man
Ns = {d, f} Woman
Us = {c, e, g}
{Person [0.4], ¬Woman [0.8], Person [0.5], ∃hasChild. ⊤ [0.9]}
10. Proposed Solution
Given and a set of training examples
Weight assigned to example (init. )
Ensemble of weak models (concepts) induced by a weak
learner ( DLF):
Confidence computed per weak model
Weights updated according to the coverage of the hypothesis
concept
decreased for examples covered by
increased for examples uncovered by
K T
wi ai = 1/|T|w
(0)
i
T Ct
ct
Ct
Ct
11. Coverage: Definition
An example covered by when
i.e., is correctly classified
x Ct
⎧
⎩
⎨
K ⊨ (x) if x ∈ PsCt
K ⊨ ¬ (x) if x ∈ NsCt
K ⊭ (x) ∧ K ⊭ ¬ (x) if x ∈ UsCt Ct
x
12. wDLF: Training
Given , weights associated to the examples, and a partial
description ( )
specialized via ref. operator ⟶ a set of concepts
score: difference between sum of the weights of the covered
ex.s and uncovered ex.s
heuristic: maximum difference between the scores of and
(gain)
T w
(t)
Ct = ⊤Ct
Ct ρ ⊑C
′
t
Ct
−∑
i| coveredai
wi
− −−−−−−−−
√
∑
i| uncoveredai
wi
− −−−−−−−−−−
√
C
′
t
Ct
13. Weight Updates
After is returned, weights of the examples updated:
for each example the new weight will be
where
with depending on the (ratio between the)sum of the weights of
covered and the uncovered (optimal value to minimize the training error)
update
Multiplied by for uncovered examples
Divided by for covered examples
Ct
ai w
(t)
i
= exp(− )w
(t)
i
w
(t)
i
ct
= − ⋅ (−1ct α^t )
I( , ( ))li ht ei
α^
exp ct
exp ct
14. Prediction
Given the model and a query individual
Prediction of single weak model :
if
if
otherwise
Final prediction: label according to weighted majority vote
sums of confidence values for the three labels
{ [ ]}Ct ct
T
t=1
a
Ct
+1 K ⊨ (a)Ct
−1 K ⊨ ¬ (a)Ct
0
=l
∗
argmax
l∈{+1,−1,0}
∑
t∈T
p( (x)=l)h
t
ct