limits of learning in incomplete networks · regression weights feature vector of node i. nol...
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Limits of Learning in Incomplete Networks
Timothy [email protected]
In collaboration with
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Timothy Sakharov Sahely Bhadra Tina Eliassi-Rad
Supported by NSF CNS-1314603 & NSF IIS-1741197
Background: Incomplete Networks
- Networkdataisoftenincomplete
- Acquiringmoredataisoftenexpensiveand/orhard
- Researchquestion:Givenanetworkeddatasetandlimitedresourcestocollectmoredata,howcanyougetthemostbangforyourbuck?
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Two general approaches to network completion
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CollectmoredataDon’tcollectmoredata
Two general approaches to network completion
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Collectmoredata
Assumeanetworkmodel
Combinenetworkmodelwithincompletedatatogetamodelofthenetworkstructure
Infermissingdatafromthismodel
- [Kimetal.2011]- [Chenetal.2018]
Don’tcollectmoredata
Collectmoredata
Two general approaches to network completion
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EstimateStatisticsfrompartiallyobservednetwork- [Soundarajanetal.2015]- [Soundarajanetal.2016]Utilizeanexplore-exploitapproach- [PfeifferIIIetal.2014]- [Soundarajanetal.2017]- [Muraietal.2018]- [Madhawaetal.2018]- Thiswork!
Assumeanetworkmodel
Combinenetworkmodelwithincompletedatatogetamodelofthenetworkstructure
Infermissingdatafromthismodel
- [Kimetal.2011]- [Chenetal.2018]
Don’tcollectmoredata
Our solution: Network Online Learning (NOL)
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- Learntogrowanincompletenetworkthroughsequential,optimalqueries(tosomeAPI)
- Agnostictobothdatadistributions andsamplingmethod
- Interpretablefeaturesthatarecomputableonline
- ResearchQuestion:Givenanetworkeddatasetandlimitedresourcestocollectmoredata,howcanyougetthemostbangforyourbuck?
Assumptions
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Amodeloftheunderlyinggraph.
Howtheinitialsamplewascollected.
WeknowtheAPIaccessmodel(completevsincompletequeries).
Theunderlyingnetworkisstatic(probingthesamenodetwicegivesnonewinformation).
Weassume... Wedonotassume...
Inputs:
- : Incomplete network
- b : probing budget
- r : reward function
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Probe b times to maximize cumulative reward
Output:
Network after b probes
Network Online Learning (NOL)
Example reward function: - number of new nodes observed
NOL algorithm
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NOL algorithm
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NOL algorithm
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Observe the current state
NOL algorithm
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Observe the current state
Feature vector of node iRegression weights
NOL algorithm
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Observe the current state
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Observe the current state
Choose the next action
NOL algorithm
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Observe the current state
Choose the next action
NOL algorithm
Take action, update network, collect reward
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Observe the current state
Choose the next action
Take action, update network, collect reward
Update parameters
NOL algorithm
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Observe the current state
Choose the next action
Take action, update network, collect reward
Update parameters
NOL algorithm
Online linear regression following Strehl et al., NIPS 2008.
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Observe the current state
Choose the next action
Take action, update network, collect reward
Repeat until budget depleted
Update parameters
NOL algorithm
NOL algorithm
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1. Observe the current state
2. Choose the next action
3. Take action, update network, collect reward
4. Update parameters
5. Repeat until budget depleted
Features
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Features
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i
Feature: In-sample degree
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i
Feature: In-sample clustering coefficient
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i
Feature: Normalized size of connected component
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i
Feature: Fraction of probed neighbors
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i
Feature: Lost Reward
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u v
wKey idea: The order in which we probe nodes can impact the reward they yield.
Feature: Lost Reward
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Unobserved node (potential reward for u or v)
Partially observed nodes
u v
wKey idea: The order in which we probe nodes can impact the reward they yield.
ResearchQuestion:Givenanetworkeddataset,andlimitedresourcestocollectmoredata,howcanyougetthemostbangforyourbuck?
- Potentialbangforyourbuckdependsonnetworkstructure!
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Heterogeneity in network properties creates a learning “spectrum”
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Heterogeneity in network properties creates a learning “spectrum”
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Learning not useful
Heuristics optimal
Heterogeneity in network properties creates a learning “spectrum”
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Potential for learning
Learning not useful
Heuristics optimal
Heterogeneity in network properties creates a learning “spectrum”
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Homogeneous degree dist.
Potential for learning
Learning not useful
Heuristics optimal
Heterogeneity in network properties creates a learning “spectrum”
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Learning not useful
Homogeneous degree dist.
Heterogenous degree dist.
1Avrachenkovetal.INFOCOMWKSHPS (2014)
Heuristics optimal1
Potential for learning
Heterogeneity in network properties creates a learning “spectrum”
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1Avrachenkovetal.INFOCOMWKSHPS (2014)
Homogeneous degree dist.
Heterogenous degree dist. with rich structure
Heterogenous degree dist.
Potential for learning
Learning not useful
Heuristics optimal1
Experiments
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Heuristic Baselines
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- Highdegree- Probetheunprobednodewithmaximumdegree
- Highdegreew/jump- Probetheunprobednodewithmaximumdegree,randomlyjump
withprobabilityp- Lowdegree
- Probetheunprobednodewithminimumdegree- Random
- Probeanodechosenuniformlyatrandomfromtheunprobednodes
iKNN-UCB [Madhawa+ArXivpreprint,2018]
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- K-NearestNeighborsUpperConfidenceBound- Nonparametricmulti-armedbanditapproach
- Choosenodetoprobebycombiningnearestneighborrewardinformation(basedonEuclideandistancebetweenfeaturevectors)+extentofpreviousexplorationofsimilaractions
Heterogeneity in network properties creates a learning “spectrum”
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Homogeneous degree dist.
Heterogenous degree dist. with rich structure
Heterogenous degree dist.
Potential for learning
Learning not useful
Heuristics optimal
Heterogeneity in network properties creates a learning “spectrum”
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Learning not useful
Heuristics optimal
Potential for learning
Homogenous degree dist.
Heterogenous degree dist.
Heterogenous degree dist. with rich structure
Heterogeneity in network properties creates a learning “spectrum”
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Learning not useful
Heuristics optimal
Potential for learning
Erdos-Renyi Model
Heterogenous degree dist. with rich structure
Heterogenous degree dist.
Heterogeneity in network properties creates a learning “spectrum”
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Learning not useful
Heuristics Optimal
Potential for learning
Erdos-Renyi Model
BTER Model1
1C.Seshadhrietal.PhysicalReviewE (2012)
Heterogenous degree dist.
Heterogeneity in network properties creates a learning “spectrum”
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Learning not useful
Heuristics Optimal
Potential for learning
Erdos-Renyi Model
Barabasi-Albert Model
BTER Model1
1C.Seshadhrietal.PhysicalReviewE (2012)
Results - Learning Spectrum
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Learning not useful
Heuristics Optimal
Potential for learning
Erdos-Renyi Model
Barabasi-Albert Model
BTER Model
Results - Learning Spectrum
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Learning not useful
Heuristics Optimal
Potential for learning
Erdos-Renyi Model
Barabasi-Albert Model
Allmethodsareindistinguishable,learningdoesn’thelporhurt!
BTER Model
Results - Learning Spectrum
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Heuristics Optimal
Potential for learning
Erdos-Renyi Model
Barabasi-Albert Model
Allmethodsareindistinguishable,learningdoesn’thelporhurt!
Learning not useful
BTER Model
Results - Learning Spectrum
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Heuristics Optimal
Potential for learning
Erdos-Renyi Model
Barabasi-Albert Model
HighdegreeheuristicisoptimalinBAmodel,butNOLlearnstoprobeliketheheuristic!
Allmethodsareindistinguishable,learningdoesn’thelporhurt!
Learning not useful
BTER Model
Results - Learning Spectrum
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Heuristics Optimal
Potential for learning
Erdos-Renyi Model
Barabasi-Albert Model
Allmethodsareindistinguishable,learningdoesn’thelporhurt!
HighdegreeheuristicisoptimalinBAmodel,butNOLlearnstoprobeliketheheuristic!
Learning not useful
BTER Model
Heterogeneity in network properties creates a learning “spectrum”
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Learning Not Useful
Heuristics Optimal
Potential for learning
Coauthorshipnetwork
Citationnetwork
EmailCommunicationNetwork
N=23kE=89k△s=78.7k
N=36.7kE=184k△s=727k
N=6.7kE=17k△s=21.6k
DBLP Cora Enron
Heterogeneity in network properties creates a learning “spectrum”
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Learning Not Useful
Heuristics Optimal
Potential for learning
✓✓✓DBLP Cora Enron
Summary
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- NetworkOnlineLearning canlearntoprobeonlinewithminimalassumptions
- Successistiedtopropertiesoftheunderlyingnetwork:
- Spectrumbasedonobjectivefunctionbeingmaximized(degreedistributionintheseexperiments)
- NOLcanlearntobehaveliketheoptimalheuristic
- Preliminaryexperimentssuggestsomerealworldcomplexnetworksfallinthe“learnable”category
References
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Kimetal.(2011).TheNetworkCompletionProblem:InferringMissingNodesandEdgesinNetworks.SIAMInternationalConferenceonDataMining.
Seshadhrietal.(2012).Communitystructureandscale-freecollectionsofErdos-Renyigraphs,PhysicalReviewE.
Avrachenkovetal.(2014).Payfew,influencemost:Onlinemyopicnetworkcovering.Proceedings- IEEEINFOCOM.
PfeifferIIIetal.(2014).ActiveExplorationinNetworks:UsingProbabilisticRelationshipsforLearningandInference.InProceedingsofthe23rdACMInternationalConferenceonConferenceonInformationandKnowledgeManagement.
Soundarajanetal.(2015).MaxOutProbe:AnAlgorithmforIncreasingtheSizeofPartiallyObservedNetworks.The2015NIPSWorkshoponNetworksintheSocialandInformationSciences.
Soundarajanetal.(2016).MaxReach:Reducingnetworkincompletenessthroughnodeprobes.2016IEEE/ACMInternationalConferenceonAdvancesinSocialNetworksAnalysisandMining(ASONAM).
Soundarajanetal.(2017).ε-WGX:AdaptiveEdgeProbingforEnhancingIncompleteNetworks.InProceedingsofthe2017ACMonWebScienceConference.
Muraietal.(2018).SelectiveHarvestingOverNetworks.DataMiningandKnowledgeDiscovery.
Madhawaetal.(2018).ExploringPartiallyObservedNetworkswithNonparametricBandits.arXiv:1804.07059.
Chenetal.(2018).FlexibleModelSelectionforMechanisticNetworkModelsviaSuperLearner.arXiv:1804.00237.
Thanks!
Slides at http://eliassi.org/larock_netsci18.pdf