Event Forecasting with Pattern Markov Chains Elias Alevizos, - PowerPoint PPT Presentation

Event Forecasting with Pattern Markov Chains Event Forecasting with Pattern Markov Chains Elias Alevizos, Alexander Artikis, George Paliouras Complex Event Recognition lab, Institute of Informatics & Telecommunications National Centre for Scientific Research “Demokritos” http://cer.iit.demokritos.gr/

Event Forecasting with Pattern Markov Chains Introduction Motivation 50 $ 100 $ 200 $ 500 $ · · · start 0 1 2 3

Event Forecasting with Pattern Markov Chains Introduction Motivation 50 $ 100 $ 200 $ 500 $ · · · start 0 1 2 3 ◮ Is this a fraud?

Event Forecasting with Pattern Markov Chains Introduction Motivation 50 $ 100 $ 200 $ 500 $ · · · start 0 1 2 3 ◮ Is this a fraud? ◮ How long will it last?

Event Forecasting with Pattern Markov Chains Introduction Motivation 50 $ 100 $ 200 $ 500 $ · · · start 0 1 2 3 ◮ Is this a fraud? ◮ How long will it last? ◮ With what probability?

Event Forecasting with Pattern Markov Chains Introduction Online Probabilistic Complex Event Forecasting ◮ Patterns defined as regular expressions. ◮ Consume streams of events and forecast when a pattern is expected to be fully matched. ◮ Revise forecasts to reflect changes in the state of the pattern. ◮ Remember “arbitrarily” long sequences.

Event Forecasting with Pattern Markov Chains Introduction Assumptions ◮ Selection strategy: (partition)-contiguity . ◮ Stream generated by a m -order Markov process. ◮ Stream stationary. ◮ A forecast reports for how many transitions we will have to wait until a full match.

Event Forecasting with Pattern Markov Chains Theory Regular Expression → Pattern Markov Chain R = a · c · c . Σ = { a , b , c } . No memory. b, c b a a c c start 0 1 2 3 a b a b, c

Event Forecasting with Pattern Markov Chains Theory Regular Expression → Pattern Markov Chain R = a · c · c . Σ = { a , b , c } . No memory. b, c b a a c c start 0 1 2 3 a b a b, c P ( b ) P ( b ) + P ( c ) 1 . 0 P ( a ) P ( c ) P ( c ) 0 1 2 3 P ( b ) P ( a ) P ( a )

Event Forecasting with Pattern Markov Chains Theory Regular Expression → Pattern Markov Chain P ( b | c ) P ( b | b ) P ( a | a ) 1 . 0 P ( a | b ) P ( c | a ) P ( c | c ) 0 b 1 a 2 c 3 c P ( b | a ) P ( a | c ) P ( c | b ) P ( b | c ) P ( a | c ) 0 c P ( c | c )

Event Forecasting with Pattern Markov Chains Implementation Waiting-Time and Forecasts ◮ Warm-up period to learn distributions. ◮ Set a threshold, e.g., P fcast = 50%. 1 state:0 Completion Probability interval:5,12 0.8 state:1 state:2 0.6 a state:3 a 0.4 a a b b b 0.2 start 0 1 2 3 4 0 a b 1 2 3 4 5 6 7 8 9 10 11 12 b Number of future events

Event Forecasting with Pattern Markov Chains Implementation Example: R = a · b · b · b . a a a a b b b start 0 1 2 3 4 a b b 1 state:1 Completion Probability interval:3,8 0.8 0.6 0.4 0.2 0 1 2 3 4 5 6 7 8 9 10 11 12 Number of future events

Event Forecasting with Pattern Markov Chains Implementation Example: R = a · b · b · b . a a a a b b b start 0 1 2 3 4 a b b 1 state:2 Completion Probability interval:2,4 0.8 0.6 0.4 0.2 0 1 2 3 4 5 6 7 8 9 10 11 12 Number of future events

Event Forecasting with Pattern Markov Chains Implementation Example: R = a · b · b · b . a a a a b b b start 0 1 2 3 4 a b b 1 state:3 Completion Probability interval:1,1 0.8 0.6 0.4 0.2 0 1 2 3 4 5 6 7 8 9 10 11 12 Number of future events

Event Forecasting with Pattern Markov Chains Empirical Analysis Credit Card Fraud Management: Real Dataset ( m = 1). 100 0.8 80 Prediction Threshold 0.6 60 40 0.4 20 0.2 0 0 1 2 3 4 5 6 7 State 10 15 0.8 0.8 8 Prediction Threshold Prediction Threshold 10 0.6 0.6 6 4 0.4 0.4 5 2 0.2 0.2 0 0 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7 State State

Event Forecasting with Pattern Markov Chains Empirical Analysis Credit Card Fraud Management: Real Dataset ( m = 3). 100 0.8 Prediction Threshold 80 0.6 60 40 0.4 20 0.2 0 1 1 1 2 1 3 2 1 0 1 2 3 4 5 6 7 State 10 15 0.8 0.8 8 Prediction Threshold Prediction Threshold 10 0.6 6 0.6 4 0.4 0.4 5 2 0.2 0.2 0 0 1 1 1 2 1 3 1 1 1 2 1 3 0 1 2 2 1 3 4 5 6 7 0 1 2 2 1 3 4 5 6 7 State State

Event Forecasting with Pattern Markov Chains Empirical Analysis Maritime Monitoring: Real Dataset. R = Turn · GapStart · GapEnd · Turn , where Turn = ( TurnNorth + TurnEast + TurnSouth + TurnWest ) 100 0.8 80 Prediction Threshold 0.6 60 40 0.4 20 0.2 0 3 te 7 tw 9 tn 11 ts 13 gse 14 gsn 15 gsw 16 gss 17 gen 18 gew 19 ges 20 gee State 10 350 0.8 300 0.8 8 Prediction Threshold Prediction Threshold 250 0.6 0.6 6 200 150 4 0.4 0.4 100 2 0.2 0.2 50 0 0 3 te 7 tw 9 tn 11 ts 13 gse 14 gsn 15 gsw 16 gss 17 gen 18 gew 19 ges 20 gee 3 te 7 tw 9 tn 11 ts 13 gse 14 gsn 15 gsw 16 gss 17 gen 18 gew 19 ges 20 gee State State

Event Forecasting with Pattern Markov Chains Empirical Analysis Summary & Future Work ◮ Contributions: ◮ Regular expressions as opposed to sequential patterns. ◮ Forecasts with guaranteed precision, if Markov process. ◮ Useful forecasts even in applications where we do not know beforehand the stream properties.

Event Forecasting with Pattern Markov Chains Empirical Analysis Summary & Future Work ◮ Contributions: ◮ Regular expressions as opposed to sequential patterns. ◮ Forecasts with guaranteed precision, if Markov process. ◮ Useful forecasts even in applications where we do not know beforehand the stream properties. ◮ Future work: ◮ Constraints on event properties. ◮ More selection strategies. ◮ Support drift. ◮ Forecasts that correspong to real time (not transitions).

Event Forecasting with Pattern Markov Chains Appendix Appendix

Event Forecasting with Pattern Markov Chains Appendix Validation tests 1 order=0 order=1 0.8 Precision score order=2 f(x)=x 0.6 0.4 0.2 0 0 0.2 0.4 0.6 0.8 1 Prediction threshold Figure: R = a · ( a + b ) ∗ · c 1 order=0 order=1 0.8 Precision score order=2 f(x)=x 0.6 0.4 0.2 0 0 0.2 0.4 0.6 0.8 1 Prediction threshold

Event Forecasting with Pattern Markov Chains Appendix Credit cards (precision for m = 1, 2, 3) 1 1 Precision (on recognized) Precision (on recognized) Precision (on ground truth) Precision (on ground truth) f(x)=x f(x)=x 0.8 0.8 Precision score Precision score 0.6 0.6 0.4 0.4 0.2 0.2 0 0 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 Prediction threshold Prediction threshold 1 Precision (on recognized) Precision (on ground truth) f(x)=x 0.8 Precision score 0.6 0.4 0.2 0 0 0.2 0.4 0.6 0.8 1 Prediction threshold

Event Forecasting with Pattern Markov Chains Appendix Maritime (precision) R = Turn · GapStart · GapEnd · Turn 1 Precision f(x)=x 0.8 Precision score 0.6 0.4 0.2 0 0 0.2 0.4 0.6 0.8 1 Prediction threshold

Event Forecasting with Pattern Markov Chains Appendix Maritime (precision) R = TurnNorth · ( TurnNorth + TurnEast ) ∗ · TurnSouth 1 order=1 order=2 0.8 f(x)=x Precision score 0.6 0.4 0.2 0 0 0.2 0.4 0.6 0.8 1 Prediction threshold