=Paper=
{{Paper
|id=Vol-2003/NeSy17_paper8
|storemode=property
|title=Learning with Knowledge Graphs
|pdfUrl=https://ceur-ws.org/Vol-2003/NeSy17_paper8.pdf
|volume=Vol-2003
|authors=Volker Tresp,Yunpu Ma,Stephan Baier
|dblpUrl=https://dblp.org/rec/conf/nesy/TrespMB17
}}
==Learning with Knowledge Graphs==
https://ceur-ws.org/Vol-2003/NeSy17_paper8.pdf
Learning with Knowledge Graphs
Volker Tresp1,2 , Yunpu Ma1,2 , Stephan Baier2
1
Siemens AG, Corporate Technology, Munich, Germany
2
Ludwig-Maximilians-Universität München, Munich, Germany
Abstract. In recent years a number of large-scale triple-oriented knowl-
edge graphs have been generated. They are being used in research and in
applications to support search, text understanding and question answer-
ing. Knowledge graphs pose new challenges for machine learning, and
research groups have developed novel statistical models that can be used
to compress knowledge graphs, to derive implicit facts, and to detect
errors in the knowledge graph. In this paper we decribe the concept of
triple-oriented knowledge graphs and corresponding learning approaches.
We also discuss episodic knowledge graphs which are able to represent
temporal data; learning with episodic data can be the basis for decision
support systems, e.g. in a clinical context. Finally we discuss how knowl-
edge graphs can support perception, by mapping subsymbolic sensory
inputs, such as images, to semantic triples. A particular feature of our
approach would be that perception, episodic memory and semantic mem-
ory are highly interconnected and that, in a cognitive interpretation, all
rely on the same brain structures.
1 Semantic Knowledge Graphs
A technical realization of a semantic memory is a knowledge graph (KG) which
is a triple-oriented knowledge representation: A labelled link implies a (subject,
predicate, object) statement where subject and object are entities that are rep-
resented as the nodes in the graph and where the predicate labels the link from
subject to object. Large KGs have been developed that support search, text un-
derstanding and question answering [8]. A KG can be represented as a tensor
which maps indices to true or false
s, p, o 7→ Q
with Q ∈ {T, F}, and where s ∈ 1, . . . , N and o ∈ 1, . . . , N are indices for the N
entities used as subject and object, and where p ∈ 1, . . . , R is the index for the
predicate.
A statistical model for a KG can be obtained by a tensor model of the form
s, p, o 7→ ae(s) , ap , ae(o) 7→ P. (1)
Here e(s) and e(o) are the entities associated with subject and object, respec-
tively. The indices are first mapped to their latent representations ae(s) , ap , ae(o)
Copyright © 2017 for this paper by its authors. Copying permitted for private and academic purposes.
which are then mapped to a probability P ∈ [0, 1]. P ((s, p, o) = T|ae(s) , ap , ae(o) )
represents the Bernoulli probability that the triple (s, p, o) is true, and, when
normalized across all triples, P (s, p, o|ae(s) , ap , ae(o) ) stands for the categorical
probability that the triple (s, p, o) is selected as an answer in a query process. A
number of mathematical models have been developed for the mapping in Equa-
tion 1 (see [7]). A representative example is the RESCAL model [6], which is a
constraint Tucker2 tensor model.
2 Episodic Knowledge Graphs
Whereas a semantic KG model reflects the state of the world, e.g, of a clinic and
its patients, observations and actions describe factual knowledge about discrete
events. Generalizing the semantic KG, an episodic KG can be represented as a
4-way tensor with time index t as the map
s, p, o, t 7→ Q.
A statistical model for a KG can be obtained by a 4-way tensor model of the
form
s, p, o, t 7→ ae(s) , ap , ae(o) , at 7→ P (2)
where at is the latent representation for time index t.
The basis for the tight link between different memory functions is the “unique
representation hypothesis”, which states that an entity has a unique latent rep-
resentation in a technical application, but maybe also in the human brain [9].
As discussed in [11, 5] both the episodic KG and the semantic KG might rely
on the same representations, i.e., it was proposed that the semantic KG can be
derived from the episodic KG by a marginalization operation. Thus an episodic
fact might represent that “Jack, wasDiagnosed, Diabetes, on Jan 15”, the derived
semantic fact might be “Jack, hasDisease, Diabetes”. In [3, 4] medical decision
systems are described that combine semantic and episodic tensor representations
of data with recurrent neural network predictive models.
3 Perception
The tensor models permit generalization, i.e., the prediction of the probability of
triples which were not known to be true in the data. This is especially important
in perception, which we propose can be thought off as the mapping of subsym-
bolic sensory inputs to a semantic description in the form of a set of triples,
describing and explaining the sensory inputs. These triples then becomes part
of episodic memory.
Let ut,1 , . . . , ut,c , . . . , ut,C be the content of the sensory buffers at time t. We
propose that this sensory input can predict the latent representation for time in
the form of a map
ut,1 , . . . , ut,c , . . . , ut,C 7→ at .
2
This map at (ut , w) might be modelled by a deep neural network with weights
w. Perceptual decoding then produces likely triples from the probability distri-
bution (generalized nonlinear model) using
P (s, p, o; ae(s) , ap , ae(o) , at (ut , w)).
An episodic memory would simply store at , and memorizing simply means the
restoring of a past at , which then can be decoded as described [9, 10]. A semantic
memory uses the marginalizing approach describes in Section 2.
As another approach, there is the option to use P (s, p, o) or P (s, p, o, t) as a
semantic prior in sensory decoding. This was the basis for approaches to extract
triples from Web sources [2] and for the extraction of triples from images [1].
References
[1] Stephan Baier, Yunpu Ma, and Volker Tresp. Improving visual relationship de-
tection using semantic modeling of scene descriptions. In ISWC, 2017.
[2] Xin Dong, Evgeniy Gabrilovich, Geremy Heitz, Wilko Horn, Ni Lao, Kevin Mur-
phy, Thomas Strohmann, Shaohua Sun, and Wei Zhang. Knowledge Vault: A
Web-scale Approach to Probabilistic Knowledge Fusion. In KDD, 2014.
[3] Cristóbal Esteban, Danilo Schmidt, Denis Krompaß, and Volker Tresp. Predicting
sequences of clinical events by using a personalized temporal latent embedding
model. In Healthcare Informatics (ICHI), 2015 International Conference on, 2015.
[4] Yinchong Jang, Volker Tresp, and Peter Fasching. Predictive modeling of therapy
decisions in metastatic breast cancer with recurrent neural network encoder and
multinomial hierarchical regression decoder. In ICHI, 2017.
[5] Yunpu Ma, Volker Tresp, and Erik Daxberger. Embedding models for episodic
memory. In submitted, 2017.
[6] Maximilian Nickel, Volker Tresp, and Hans-Peter Kriegel. A Three-Way Model
for Collective Learning. In ICML, 2011.
[7] Maximilian Nickel, Kevin Murphy, Volker Tresp, and Evgeniy Gabrilovich. A
review of relational machine learning for knowledge graphs: From multi-relational
link prediction to automated knowledge graph construction. Proceedings of the
IEEE, 2015.
[8] Amit Singhal. Introducing the Knowledge Graph: things, not strings. Official
Google Blog, 2012.
[9] Volker Tresp, Cristóbal Esteban, Yinchong Yang, Stephan Baier, and Denis
Krompaß. Learning with memory embeddings. NIPS 2015 Workshop (extended
TR); arXiv:1511.07972, 2015.
[10] Volker Tresp, Yunpu Ma, and Stephan Baier. Tensor memories. In CCN, 2017.
[11] Volker Tresp, Yunpu Ma, Stephan Baier, and Yinchong Yang. Embedding learning
for declarative memories. In ESWC, 2017.
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