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Strategies for Processing and
Explaining Distributed Queries on
Linked Data
Rakebul Hasan
Wimmics
Inria Sophia Antipolis
Research Theme
 Distribute Query Processing
 Optimization techniques for querying Linked Data

 Distributed Query Explanation
 Query plan explanation
 How query solving works

 Query result explanation
 Why
 Where

1
DISTRIBUTE QUERY PROCESSING

2
Querying Linked Data
 Bottom-up strategies
 Discover sources during query processing by
following links between sources

 Top-down strategies
 Sources are known

3
Querying Linked Data
FedBench Query CD5: Find the director and the
genre of movies directed by Italians
SELECT ?film ?director ?genre WHERE {
?film dbpedia-owl:director ?director.
?director dbpedia-owl:nationalitydbpedia:Italy .
?xowl:sameAs ?film .
?xlinkedMDB:genre ?genre
}

4
Querying Linked Data
FedBench Query CD5: Find the director and the genre of movies
directed by Italians

SELECT ?film ?director ?genre WHERE {
SERVICE <http://dbpedia.org/sparql>{
?film dbpedia-owl:director ?director.
?director dbpedia-owl:nationalitydbpedia:Italy .
?xowl:sameAs ?film .
}
SERVICE <http://data.linkedmdb.org/sparql> {
?xlinkedMDB:genre ?genre
}
}

SPARQL 1.1 SERVICE clause

Need knowledge of which part of
the query should be solved by which endpoint

5
 Top-down approaches
 Data warehousing approach
 Virtual integration approach

6
Querying Linked Data
 Data warehousing approach
 Collect the data in a central triple store
 Process queries on that triple store

 Disadvantages
 Expensive preprocessing (data collection + integration)
and maintenance
 Data not up to date

7
Querying Linked Data
 Virtual integration approach
 A query federation middleware
 Parse and split into subqueries
 Source selection for subqueries
 Evaluate the subqueries against corresponding sources
directly
 Merge the results

 Advantages
 no preprocessing and maintenance
 up to date data
8
Running Example
Query LS6: Find KEGG drug names of all drugs in
Drugbank belonging to category Micronutrient

drugbank

http://www4.wiwiss.fu-berlin.de/drugbank/sparql

SELECT ?drug ?title WHERE {
?drug drugbank:drugCategorydrugbank-category:micronutrient .
?drug drugbank:casRegistryNumber ?id .
?keggDrugrdf:typekegg:Drug .
?keggDrug bio2rdf:xRef ?id .
?keggDrugpurl:title ?title .
}

KEGG

http://cu.bioportal.bio2rdf.org/sparql

DBpedia

http://data.linkedmdb.org/sparql

9
Parsing and Source Selecting
drugbank

Query LS6: Find KEGG drug names of all drugs in
Drugbank belonging to category Micronutrient
http://www4.wiwiss.fu-berlin.de/drugbank/sparql

?drug drugbank:drugCategorydrugbank-category:micronutrient
?drug drugbank:casRegistryNumber ?id

SELECT ?drug ?title WHERE {
?drug drugbank:drugCategorydrugbank-category:micronutrient .
?drug drugbank:casRegistryNumber ?id .
?keggDrugrdf:typekegg:Drug .
?keggDrug bio2rdf:xRef ?id .
?keggDrugpurl:title ?title .
}

KEGG

http://cu.bioportal.bio2rdf.org/sparql

?keggDrugrdf:typekegg:Drug
?keggDrug bio2rdf:xRef ?id
Send ask queries to all the sources
ASK {?drug drugbank:drugCategorydrugbank-category:micronutrient }
ASK {?drug drugbank:casRegistryNumber ?id }
ASK {?keggDrugrdf:typekegg:Drug }
ASK {?keggDrug bio2rdf:xRef ?id }
ASK {?keggDrugpurl:title ?title }

DBpedia

http://data.linkedmdb.org/sparql

?keggDrugpurl:title ?title

10
Evaluating subqueries
 Two options
 All triple patterns are individually evaluated
 Nested loop join (NLJ): evaluate iteratively pattern
by pattern

11
Evaluating subqueries
 Example of NLJ
SELECT ?drug ?title WHERE {
?drug drugbank:drugCategorydrugbank-category:micronutrient .
?drug drugbank:casRegistryNumber ?id .
?keggDrugrdf:typekegg:Drug .
?keggDrug bio2rdf:xRef ?id .
?keggDrugpurl:title ?title .
}

12
Optimization techniques
 Source Selection
 Indexing: characterization of RDF graphs
 Statistics based catalogue
 Caching

13
Optimization techniques
 Exclusive grouping
SELECT ?drug ?title WHERE {
?drug drugbank:drugCategorydrugbank-category:micronutrient .
?drug drugbank:casRegistryNumber ?id .
?keggDrugrdf:typekegg:Drug .
?keggDrug bio2rdf:xRef ?id .
?keggDrugpurl:title ?title .
}

14
Optimization techniques
 Bound join
 Effective for NLJ
 Mappings of variable values from the
intermediate result to the next subquery
 SPARQL 1.1 VALUES clause

15
Optimization techniques
 Hash join
 Hash table for intermediate mappings

16
Optimization techniques
 FILTER optimization
 Evaluating the subqueries with corresponding
FILTERS
 Reduces the number of intermediate results

17
Optimization techniques
 Parallelization
 Effective for individual subquery evaluation
approach

18
Optimization techniques
 Join order
 Selectivity estimation: join order heuristic based
on the number of bound and free variables [1]
 Statistics: based on cardinalities of the triple
patterns [2]

[1] M. Stocker, A. Seaborne, A. Bernstein, C. Kiefer, and D. Reynolds. SPARQL basic graph pattern optimization using selectivity estimation.
In Proceedings of the 17th international conference on World Wide Web (WWW '08)
[2] A. Harth, K. Hose, M. Karnstedt, A. Polleres, K. Sattler, and J. Umbrich. Data summaries for on-demand queries over linked data.
In Proceedings of the 19th international conference on World wide web (WWW '10)

19
Selectivity Estimation
 Ideal for the Linked Data scenario
 No need for statistics about the underlying data
 Estimations can be wrong however
BGP

Number of results

Selectivity
estimation

?v1 p1 ?v2
?v1 p2 ?v3

5

2

?v4 p3 c1
?v4 p4 ?v1

10

1

20
Query Performance Prediction
 Learn query performance from already
executed queries
 Statistics about the underlying data not
required
 Applications
 Query optimization: join order
 Workload management/scheduling

21
Regression
Learn a mapping function
f(X) = y
X = feature vector, vector representation of SPARQL query
y = performance metric (e.g. latency, number of results)

Support vector machine with nu-SVR
k-nearest neighbors regression

22
Feature Extraction
 How can we represent SPARQL queries as
vectors?

23
SPARQL
 SPARQL algebra features
 Graph pattern features

24
SPARQL Algebra

http://www.w3.org/TR/sparql11-query/#sparqlQuery

25
SPARQL Algebra Features

26
Graph Pattern Features

27
Graph Pattern Features
 Clustering Training Queries
 K-mediods clustering algorithm with
approximated edit distance as distance function
 Selects data points as cluster centers
 Arbitrary distance function

28
Graph Pattern Features
 Graph Edit Distance
 Minimum amount of distortion needed to
transform one graph to another

 Compute similarity by inversing distance

29
Graph Pattern Features
 Graph Edit Distance
 Usually computed using A* search
 Exponential running time

 Bipartite matching based approximated graph edit
distance with
 Previous research shows accurate results with
classification problems

30
Experiment Setup
 Triple store and hardware
 Jena TDB 1.0.0
 16 GB memory
 2.53 GHz CPU
 48 GB system RAM
 Linux 2.6.32 operating system

31
Experiment Setup
 Datasets
 Training, validation, test datasets generated from
25 DBPSB query templates
 1260 training queries
 420 validation queries
 420 test queries

 RDF data: DBpedia 3.5.1 with 100% scaling factor
from DBPSB framework

32
Prediction Models
 Support Vector Machine (SVM) with the nuSVR kernel for regression
 k-nearest neighbors (k-NN) regression
 Euclidean distance as the distance function
 k-dimensional tree (k-d tree) data structure to
compute the nearest neighbors

33
Evaluation Measures
 Coefficient of determination

 Root mean squared error (RMSE)

34
Predicting Query Execution Time
 SPARQL algebra features

35
Predicting Query Execution Time
 SPARQL algebra and graph pattern features

36
Whats Next
 Apply QPP in join order optimization

 Benchmarking
 FedBench: a benchmarking framework for
federated query processing

 Systematic generation of training queries
 Bootstrapping
 Refining training queries from query logs
37
Statistical Analysis of Query Logs
 Approach to Systematic generation of training queries

Mario Arias, Javier D. Fern叩ndez, Miguel A. Mart鱈nez-Prieto, Pablo de la Fuente: An Empirical Study of Real-World SPARQL Queries,
1st International Workshop on Usage Analysis and the Web of Data,
co-located with the 20th International World Wide Web Conference (WWW2011)

38
Summary
 Distributed query processing
 Optimization techniques
 Query performance prediction
 Join order optimization

39
DISTRIBUTED QUERY EXPLANATION

40
Query Explanation
 Query plan explanation
 Query result explanation
 Motivation
 Understanding
 Transparency
 Trust

41
Query Explanation in the Semantic
Web
Query plan explanation

Query result explanation

Jena
Sesame
Virtuoso

*

BigOWLIM

+

* Explanation of SPARQL to SQL translation
+ a debugging feature on the query engine side
42
Distributed Query Explanation in the
Semantic Web
Query plan explanation

Query result explanation

FedX
DARQ
SemWIQ
ADERIS
Anapsid

43
ADERIS Query Plan Explanation

44
Related Work
 Database: Why, how, where provenance
 Semantic Web:
 Inference explanation
 Provenance
 Generating justifications

45
Distributed Query Explanation
What We Provide
 Query plan explanation  Work in progress
 Prior to query execution
 Includes predicted performance metrics

 After query execution with performance metrics

 Query result explanation
 Why provenance
 Where provenance

46
Query Result Explanation

(RDF model, Query, Result)
Result Explainer
Plug-in

Can be any RDF model (RDF graph, SPARQL endpoint)

We generate result explanations by querying this model for why provenance

47
Why Provenance
 Triples in virtual model from which the result
is derived
<http://example.org/book/book8>
<http://purl.org/dc/elements/1.1/creator>
<http://www-sop.inria.fr/members/Alice> ;
<http://purl.org/dc/elements/1.1/title>
"Distributed Query Processing for Linked Data" .
<http://www-sop.inria.fr/members/Charlie>
<http://xmlns.com/foaf/0.1/name>
"Charlie" .
<http://www-sop.inria.fr/members/Alice>
<http://xmlns.com/foaf/0.1/knows>
<http://www-sop.inria.fr/members/Charlie> ;
<http://xmlns.com/foaf/0.1/name>
"Alice" .

48
Where Provenance
 Keep the provenance of sources in the virtual model
fedqld:source1 {
<http://example.org/book/book8>
<http://purl.org/dc/elements/1.1/creator>
<http://www-sop.inria.fr/members/Alice> ;
<http://purl.org/dc/elements/1.1/title>
"Distributed Query Processing for Linked Data" .
}
fedqld:source2 {
<http://www-sop.inria.fr/members/Charlie>
<http://xmlns.com/foaf/0.1/name>
"Charlie" .

Where the triples in this
graph come from

<http://www-sop.inria.fr/members/Alice>
<http://xmlns.com/foaf/0.1/knows>
<http://www-sop.inria.fr/members/Charlie> ;
<http://xmlns.com/foaf/0.1/name>
"Alice" .
}
fedqld:prov {
fedqld:source1 void:sparqlEndpoint<http://localhost:3030/books/query> .
fedqld:source2 void:sparqlEndpoint<http://localhost:3031/person/query> .
}

49
Whats next
 Explanation user interfaces
 Evaluating the impacts of our explanations

50
References




Andreas Schwarte, Peter Haase, KatjaHoose, Ralf Schenkel, and Michael Schmidt. Fedx: A federation layer for
distributed query processing on linked open data. In ESWC, 2011
Shinji Kikuchi, Shelly Sachdeva, SubhashBhalla, Steven Lynden, Isao Kojima, AkiyoshiMatono, and Yusuke Tanimura.
Adaptive integration of distributed semantic web data. Databases in Networked Information Systems
Michael Schmidt, Olaf G旦rlitz, Peter Haase, G端nter Ladwig, Andreas Schwarte, and Thanh Tran. 2011. FedBench: a
benchmark suite for federated semantic data query processing. In Proceedings of the 10th international
conference on The semantic web - Volume Part I (ISWC'11)

51

More Related Content

Strategies for Processing and Explaining Distributed Queries on Linked Data

  • 1. Strategies for Processing and Explaining Distributed Queries on Linked Data Rakebul Hasan Wimmics Inria Sophia Antipolis
  • 2. Research Theme Distribute Query Processing Optimization techniques for querying Linked Data Distributed Query Explanation Query plan explanation How query solving works Query result explanation Why Where 1
  • 4. Querying Linked Data Bottom-up strategies Discover sources during query processing by following links between sources Top-down strategies Sources are known 3
  • 5. Querying Linked Data FedBench Query CD5: Find the director and the genre of movies directed by Italians SELECT ?film ?director ?genre WHERE { ?film dbpedia-owl:director ?director. ?director dbpedia-owl:nationalitydbpedia:Italy . ?xowl:sameAs ?film . ?xlinkedMDB:genre ?genre } 4
  • 6. Querying Linked Data FedBench Query CD5: Find the director and the genre of movies directed by Italians SELECT ?film ?director ?genre WHERE { SERVICE <http://dbpedia.org/sparql>{ ?film dbpedia-owl:director ?director. ?director dbpedia-owl:nationalitydbpedia:Italy . ?xowl:sameAs ?film . } SERVICE <http://data.linkedmdb.org/sparql> { ?xlinkedMDB:genre ?genre } } SPARQL 1.1 SERVICE clause Need knowledge of which part of the query should be solved by which endpoint 5
  • 7. Top-down approaches Data warehousing approach Virtual integration approach 6
  • 8. Querying Linked Data Data warehousing approach Collect the data in a central triple store Process queries on that triple store Disadvantages Expensive preprocessing (data collection + integration) and maintenance Data not up to date 7
  • 9. Querying Linked Data Virtual integration approach A query federation middleware Parse and split into subqueries Source selection for subqueries Evaluate the subqueries against corresponding sources directly Merge the results Advantages no preprocessing and maintenance up to date data 8
  • 10. Running Example Query LS6: Find KEGG drug names of all drugs in Drugbank belonging to category Micronutrient drugbank http://www4.wiwiss.fu-berlin.de/drugbank/sparql SELECT ?drug ?title WHERE { ?drug drugbank:drugCategorydrugbank-category:micronutrient . ?drug drugbank:casRegistryNumber ?id . ?keggDrugrdf:typekegg:Drug . ?keggDrug bio2rdf:xRef ?id . ?keggDrugpurl:title ?title . } KEGG http://cu.bioportal.bio2rdf.org/sparql DBpedia http://data.linkedmdb.org/sparql 9
  • 11. Parsing and Source Selecting drugbank Query LS6: Find KEGG drug names of all drugs in Drugbank belonging to category Micronutrient http://www4.wiwiss.fu-berlin.de/drugbank/sparql ?drug drugbank:drugCategorydrugbank-category:micronutrient ?drug drugbank:casRegistryNumber ?id SELECT ?drug ?title WHERE { ?drug drugbank:drugCategorydrugbank-category:micronutrient . ?drug drugbank:casRegistryNumber ?id . ?keggDrugrdf:typekegg:Drug . ?keggDrug bio2rdf:xRef ?id . ?keggDrugpurl:title ?title . } KEGG http://cu.bioportal.bio2rdf.org/sparql ?keggDrugrdf:typekegg:Drug ?keggDrug bio2rdf:xRef ?id Send ask queries to all the sources ASK {?drug drugbank:drugCategorydrugbank-category:micronutrient } ASK {?drug drugbank:casRegistryNumber ?id } ASK {?keggDrugrdf:typekegg:Drug } ASK {?keggDrug bio2rdf:xRef ?id } ASK {?keggDrugpurl:title ?title } DBpedia http://data.linkedmdb.org/sparql ?keggDrugpurl:title ?title 10
  • 12. Evaluating subqueries Two options All triple patterns are individually evaluated Nested loop join (NLJ): evaluate iteratively pattern by pattern 11
  • 13. Evaluating subqueries Example of NLJ SELECT ?drug ?title WHERE { ?drug drugbank:drugCategorydrugbank-category:micronutrient . ?drug drugbank:casRegistryNumber ?id . ?keggDrugrdf:typekegg:Drug . ?keggDrug bio2rdf:xRef ?id . ?keggDrugpurl:title ?title . } 12
  • 14. Optimization techniques Source Selection Indexing: characterization of RDF graphs Statistics based catalogue Caching 13
  • 15. Optimization techniques Exclusive grouping SELECT ?drug ?title WHERE { ?drug drugbank:drugCategorydrugbank-category:micronutrient . ?drug drugbank:casRegistryNumber ?id . ?keggDrugrdf:typekegg:Drug . ?keggDrug bio2rdf:xRef ?id . ?keggDrugpurl:title ?title . } 14
  • 16. Optimization techniques Bound join Effective for NLJ Mappings of variable values from the intermediate result to the next subquery SPARQL 1.1 VALUES clause 15
  • 17. Optimization techniques Hash join Hash table for intermediate mappings 16
  • 18. Optimization techniques FILTER optimization Evaluating the subqueries with corresponding FILTERS Reduces the number of intermediate results 17
  • 19. Optimization techniques Parallelization Effective for individual subquery evaluation approach 18
  • 20. Optimization techniques Join order Selectivity estimation: join order heuristic based on the number of bound and free variables [1] Statistics: based on cardinalities of the triple patterns [2] [1] M. Stocker, A. Seaborne, A. Bernstein, C. Kiefer, and D. Reynolds. SPARQL basic graph pattern optimization using selectivity estimation. In Proceedings of the 17th international conference on World Wide Web (WWW '08) [2] A. Harth, K. Hose, M. Karnstedt, A. Polleres, K. Sattler, and J. Umbrich. Data summaries for on-demand queries over linked data. In Proceedings of the 19th international conference on World wide web (WWW '10) 19
  • 21. Selectivity Estimation Ideal for the Linked Data scenario No need for statistics about the underlying data Estimations can be wrong however BGP Number of results Selectivity estimation ?v1 p1 ?v2 ?v1 p2 ?v3 5 2 ?v4 p3 c1 ?v4 p4 ?v1 10 1 20
  • 22. Query Performance Prediction Learn query performance from already executed queries Statistics about the underlying data not required Applications Query optimization: join order Workload management/scheduling 21
  • 23. Regression Learn a mapping function f(X) = y X = feature vector, vector representation of SPARQL query y = performance metric (e.g. latency, number of results) Support vector machine with nu-SVR k-nearest neighbors regression 22
  • 24. Feature Extraction How can we represent SPARQL queries as vectors? 23
  • 25. SPARQL SPARQL algebra features Graph pattern features 24
  • 29. Graph Pattern Features Clustering Training Queries K-mediods clustering algorithm with approximated edit distance as distance function Selects data points as cluster centers Arbitrary distance function 28
  • 30. Graph Pattern Features Graph Edit Distance Minimum amount of distortion needed to transform one graph to another Compute similarity by inversing distance 29
  • 31. Graph Pattern Features Graph Edit Distance Usually computed using A* search Exponential running time Bipartite matching based approximated graph edit distance with Previous research shows accurate results with classification problems 30
  • 32. Experiment Setup Triple store and hardware Jena TDB 1.0.0 16 GB memory 2.53 GHz CPU 48 GB system RAM Linux 2.6.32 operating system 31
  • 33. Experiment Setup Datasets Training, validation, test datasets generated from 25 DBPSB query templates 1260 training queries 420 validation queries 420 test queries RDF data: DBpedia 3.5.1 with 100% scaling factor from DBPSB framework 32
  • 34. Prediction Models Support Vector Machine (SVM) with the nuSVR kernel for regression k-nearest neighbors (k-NN) regression Euclidean distance as the distance function k-dimensional tree (k-d tree) data structure to compute the nearest neighbors 33
  • 35. Evaluation Measures Coefficient of determination Root mean squared error (RMSE) 34
  • 36. Predicting Query Execution Time SPARQL algebra features 35
  • 37. Predicting Query Execution Time SPARQL algebra and graph pattern features 36
  • 38. Whats Next Apply QPP in join order optimization Benchmarking FedBench: a benchmarking framework for federated query processing Systematic generation of training queries Bootstrapping Refining training queries from query logs 37
  • 39. Statistical Analysis of Query Logs Approach to Systematic generation of training queries Mario Arias, Javier D. Fern叩ndez, Miguel A. Mart鱈nez-Prieto, Pablo de la Fuente: An Empirical Study of Real-World SPARQL Queries, 1st International Workshop on Usage Analysis and the Web of Data, co-located with the 20th International World Wide Web Conference (WWW2011) 38
  • 40. Summary Distributed query processing Optimization techniques Query performance prediction Join order optimization 39
  • 42. Query Explanation Query plan explanation Query result explanation Motivation Understanding Transparency Trust 41
  • 43. Query Explanation in the Semantic Web Query plan explanation Query result explanation Jena Sesame Virtuoso * BigOWLIM + * Explanation of SPARQL to SQL translation + a debugging feature on the query engine side 42
  • 44. Distributed Query Explanation in the Semantic Web Query plan explanation Query result explanation FedX DARQ SemWIQ ADERIS Anapsid 43
  • 45. ADERIS Query Plan Explanation 44
  • 46. Related Work Database: Why, how, where provenance Semantic Web: Inference explanation Provenance Generating justifications 45
  • 47. Distributed Query Explanation What We Provide Query plan explanation Work in progress Prior to query execution Includes predicted performance metrics After query execution with performance metrics Query result explanation Why provenance Where provenance 46
  • 48. Query Result Explanation (RDF model, Query, Result) Result Explainer Plug-in Can be any RDF model (RDF graph, SPARQL endpoint) We generate result explanations by querying this model for why provenance 47
  • 49. Why Provenance Triples in virtual model from which the result is derived <http://example.org/book/book8> <http://purl.org/dc/elements/1.1/creator> <http://www-sop.inria.fr/members/Alice> ; <http://purl.org/dc/elements/1.1/title> "Distributed Query Processing for Linked Data" . <http://www-sop.inria.fr/members/Charlie> <http://xmlns.com/foaf/0.1/name> "Charlie" . <http://www-sop.inria.fr/members/Alice> <http://xmlns.com/foaf/0.1/knows> <http://www-sop.inria.fr/members/Charlie> ; <http://xmlns.com/foaf/0.1/name> "Alice" . 48
  • 50. Where Provenance Keep the provenance of sources in the virtual model fedqld:source1 { <http://example.org/book/book8> <http://purl.org/dc/elements/1.1/creator> <http://www-sop.inria.fr/members/Alice> ; <http://purl.org/dc/elements/1.1/title> "Distributed Query Processing for Linked Data" . } fedqld:source2 { <http://www-sop.inria.fr/members/Charlie> <http://xmlns.com/foaf/0.1/name> "Charlie" . Where the triples in this graph come from <http://www-sop.inria.fr/members/Alice> <http://xmlns.com/foaf/0.1/knows> <http://www-sop.inria.fr/members/Charlie> ; <http://xmlns.com/foaf/0.1/name> "Alice" . } fedqld:prov { fedqld:source1 void:sparqlEndpoint<http://localhost:3030/books/query> . fedqld:source2 void:sparqlEndpoint<http://localhost:3031/person/query> . } 49
  • 51. Whats next Explanation user interfaces Evaluating the impacts of our explanations 50
  • 52. References Andreas Schwarte, Peter Haase, KatjaHoose, Ralf Schenkel, and Michael Schmidt. Fedx: A federation layer for distributed query processing on linked open data. In ESWC, 2011 Shinji Kikuchi, Shelly Sachdeva, SubhashBhalla, Steven Lynden, Isao Kojima, AkiyoshiMatono, and Yusuke Tanimura. Adaptive integration of distributed semantic web data. Databases in Networked Information Systems Michael Schmidt, Olaf G旦rlitz, Peter Haase, G端nter Ladwig, Andreas Schwarte, and Thanh Tran. 2011. FedBench: a benchmark suite for federated semantic data query processing. In Proceedings of the 10th international conference on The semantic web - Volume Part I (ISWC'11) 51

Editor's Notes

  • #2: Overview of distributed query processing, extracting interesting features from sparql queries for machine learning algorithms, explaining sparql queries
  • #30: The graph edit distance between two graphs is the minimum amount of distortion needed to transform one graph to another.The minimum amount of distortion is the sequence of edit operations with minimum cost. The edit operations are deletions, insertions, and substitutions of nodes and edges.
  • #35: RMSD represents the sample standard deviation of the differences between predicted values and observed valuesprediction errors when computed out-of-sample
  • #36: As the figures show, predictions for queries from templates 15, 22, 24, and 25 have large errors. Execution times of the queries from template 15 range from 1 ms to 21 ms, template 22 range from 1 ms to 22 ms, and template 25 range from 1 ms to 24 ms. For this reason, many data points in range of 1 ms to 24 ms are distant from the perfect prediction line in Figure~\ref{fig:all_predictions}(a). Execution times of the queries from template 24 range from 86 ms to 110 ms. Many data points at this interval are at even more distance from the perfect prediction line than the interval 1 ms to 24 ms. This explains the highest error for queries belonging to template 25.
  • #39: Refining training queries from query logs by considering the statistically significant characteristics Bootstrapping: Starting with a initial set of properties, resources and literals and than generate training queries by permutations and combinations of the statistically significant features Simplifying the pattern features: join features, triple pattern features, pattern graph features to represent query patterns
  • #46: our goal is not to find the minimal parts of axioms in a justification which are required to hold an entailment.
  • #49: triples in the virtual model for the query result are causes