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A simple method for multi-relational outlier detection

Sarah Riahi and Oliver SchulteSchool of Computing ScienceSimon Fraser UniversityVancouver, Canada

With tools that you probably have around the house lab.#/13If you use insert slide number under Footer, that text box only displays the slide number, not the total number of slides. So I use a new textbox for the slide number in the master.This is a version of Equity.Question: can you interpret the graphical models in a causal way?1A simple method for multi-relational outlier detectiona

#/13to explain the subtitle2System FlowFlach, P. A. (1999), Knowledge representation for inductive learning'Symbolic and Quantitative Approaches to Reasoning and Uncertainty', Springer, pp. 160--167.

CompleteDatabasePopulation ParameterValuesrestrict to target individual

vector normoutlier scoreIndividual ProfileIndividual ParameterValuesParameter Learning AlgorithmParameter Learning AlgorithmModel........Input: Model, database, target individual.Output: an outlier score#/13can use any parameter learning algorithm3ExampleA simple method for multi-relational outlier detection Model = Markov Logic Network learned for Premier League Season 2011-2012

FormulasEstimated Population ParametersEstimatedParameters for P=van PersieSavesMade(P,M)=med AND shotsOnTarget(P,M)=low AND ShotEff(P,M)=low0.020.56SavesMade(P,M)=med AND shotsOnTarget(P,M)=high AND ShotEff(P,M)=high3.550.36... (331 formulas)........

#/13Evaluation: Synthetic DataA simple method for multi-relational outlier detectionTwo Features.Designed so that outliers are easy to distinguish from normals (sanity check).Normals have a strong correlation, outliers none.Outliers have a strong correlation, normals none.Correlations are the same, but marginals are very different.#/13Bayesian Network RepresentationF1=ShotEfficiencyF2=Match_ResulltP(F1=1)= % 50P(F2=0|F1=0)= % 90P(F2=1|F1=1)= % 90Normal=StrikerP(F1=1)= % 50P(F2=1)= % 50Outlier=MidFielderP(F1=1)= % 50P(F1=1)= % 50(a)(b)P(F2=1)= % 50P(F2=0|F1=0)= % 90P(F2=1|F1=1)= % 90F1=ShotEfficiencyF2=Match_ResulltNormal=StrikerF1=TackleEfficiencyF2=Match_ResulltF1=TackleEfficiencyF2=Match_ResulltOutlier=MidFielder#/13Sarah: can you fix this?6ResultsAD = Breunig, M.; Kriegel, H.-P.; Ng, R. T. & Sander, J. (2000), LOF: Identifying Density-Based Local Outliers, in ACM SIGMOD'.LOG = Riahi, F.; Schulte, O. & Liang, Q. (2014), 'A Proposal for Statistical Outlier Detection in Relational Structures', AAAI-StarAI Workshop on Statistical-Relational AI.

Metric = Area Under Curve ELD = average L1-norm KLD = average difference AD = use single feature marginals only (unit clauses) LOG = outlier score = log-likelihood #/13Riahi, F.; Schulte, O. & Liang, Q. (2014), 'A Proposal for Statistical Outlier Detection in Relational Structures', AAAI-StarAI Workshop on Statistical-Relational AI.Breunig, M.; Kriegel, H.-P.; Ng, R. T. & Sander, J. (2000), LOF: Identifying Density-Based Local Outliers, in ACM SIGMOD'.

7A simple method for multi-relational outlier detection

Case Study: Single Features Which formulas/rules influence outlier score the most? interpretability Which unit clauses influence outlier score the most?

#/138MovieLens looked at 300 movies. Around 10,000 ratings.Novak, P. K.; Webb, G. I. & Wrobel, S. (2009), 'Supervised descriptive rule discovery: A unifying survey of contrast set, emerging pattern and subgroup mining', Journal of Machine Learning Research. Maervoet, J.; Vens, C.; Vanden Berghe, G.; Blockeel, H. & De Causmaecker, P. (2012), 'Outlier Detection in Relational Data: A Case Study', Expert Systems and Applications

Case Study: Correlations Which formulas/rules influence outlier score the most? interpretability Which associations influence outlier score the most? Related to exception mining (Novak et al. 2009)IndividualRuleConfidenceIndividualConfidenceClassEdin DzekoShotEff = high AND TackleEff = medium DribbleEff = low50%38%Van PersieShotEff = high AND TimePlayed = high ShotsOnTarget = high70%50%Confidence = conditional probability#/139Registration is a binary function. Also a partial function.Distribution Divergence PerspectiveHalpern, An analysis of first-order logics of probability, AI Journal 1990.de Raedt, L. (2008), Logical and Relational Learning, Springer. Ch.9

Joint Value AssignmentsFrequency for Random StrikerFrequency forP=van PersieSavesMade(P,M)=low AND shotsOnTarget(P,M)=low AND ShotEff(P,M)=low22%10%SavesMade(P,M)=low AND shotsOnTarget(P,M)=high AND ShotEff(P,M)=high30%62%........ Outlier Score = Dissimilarity measure between Random Individual and Target Individual. In our work, dissimilarity measure = distribution divergence. Could leverage other distance-type metrics as well.

#/13Like kernel10Propositionalization for Outlier DetectionLippi, M.; Jaeger, M.; Frasconi, P. & Passerini, A. (2011), 'Relational information gain', Machine Learning 83(2), 219239.

PlayersSavesMade(P,M)=med AND shotsOnTarget(P,M)=low AND ShotEff(P,M)=lowSavesMade(P,M)=med AND shotsOnTarget(P,M)=high AND ShotEff(P,M)=high(331 more)

Wayne Rooney13%10%...van Persie50%62%........... Construct 331-dimensional attribute vector for each individual. One frequency/count value for each formula pseudo-i.i.d data view. Like n-grams. Apply standard single-table analysis methods. Could also use learned weights instead of sufficient statistics.#/13Like kernel11Propositionalization ResultsA simple method for multi-relational outlier detection LowCor = Normals have low correlation.HighCor = Normals have high correlation.#/13Show demo in MySQL unielwin_copy.

12SummaryOutlier detection based on a statistical-relational model.Basic Idea: compare individual profile to entire population.Leverage parameter learning:Learn parameter values for individual.Learn parameter values for entire population.Outlier score = parameter vector difference.E.g. average L1-distance.Leverage relational distance between individuals.In our work, distance distribution divergence.Outlier score = divergence between individual distribution and population distribution.Another approach: Model-based propositionalization for outlier detection.Attribute-values = frequency counts for patterns in model structure.

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