Veracity Managing Uncertain Data. Skript zur Vorlesung Datenbanksystem II Dr. Andreas Züfle
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1 Veracity Managing Uncertain Data Skript zur Vorlesung Datenbanksystem II Dr. Andreas Züfle
![potential annual consumer surplus from using personal location data [1] [1] McKinsey Global](/docs-images/95/126088098/images/2-3.jpg "Institute. Big data: The next frontier for innovation, competition, and productivity.")
2 Geo-Spatial Data Huge flood of geo-spatial data Modern technology New user mentality Great research potential New applications Innovative research Economic Boost $600 billion potential annual consumer surplus from using personal location data [1] [1] McKinsey Global Institute. Big data: The next frontier for innovation, competition, and productivity. June
3 Spatio-Temporal Data (object, location, time) triples Queries: Find friends that attended the same concert last saturday Best case: Continuous function GPS log taken from a thirty minute drive through Seattle Dataset provided by: P. Newson and J. Krumm. Hidden Markov Map Matching Through Noise and Sparseness. ACMGIS
4 Sources of Uncertainty Missing Observations Missing GPS signal RFID sensors available in discrete locations only Wireless sensor nodes sending infrequently to preserve energy Infrequent check-ins of users of geo-social networks Dataset provided by: E. Cho, S. A. Myers and J. Leskovek. Friendship and Mobility: User Movement in Location-Based Social Networks. SIGKDD
5 Sources of Uncertainty Uncertain Observations Imprecise sensor measurements (e.g. radio triangulation, Wi-Fi positioning) Inconsistent information (e.g. contradictive sensor data) Human errors (e.g. in crowd-sourcing applications) From database perspective, the position of a mobile object is uncertain Dataset provided by: E. Cho, S. A. Myers and J. Leskovek. Friendship and Mobility: User Movement in Location-Based Social Networks. SIGKDD
6 Uncertainty in Spatial Data At time 10:07: Where is an object having past observations at times 10:05am and 10:06am? 10:05 10:06 6
7 Previous Solution: Extrapolation Unknown positions are estimated using past observations No semantic information (road network, driver behaviour etc.) 10:05 10:06 10:07 7
8 Previous Solution: Aggregation Exploit semantic knowledge to obtain possible positions of an object Aggregate possible positions (expected position, most-likely position) 10:05 10:07 10:06 8
9 Geo-Spatial Data 9
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11 Research Challenge Include the uncertainty directly in the querying and mining process. 11
12 Research Challenge Include the uncertainty directly in the querying and mining process. Assess the reliability of similarity search and data mining results 12
13 Research Challenge Include the uncertainty directly in the querying and mining process. Assess the reliability of similarity search and data mining results Enhance the underlying decision-making process. 13
14 Overview 1. Introduction to Probability Theory 2. Case Study: Probabilistic Count Queries 14
15 Overview 1. Introduction to Probability Theory 2. Case Study: Probabilistic Count Queries 15
16 Probability Theory: Random Variables A random variable is a variable whose value is subject to variations due to chance. The set of possible outcomes of is denoted as Ω. 16
17 Probability Theory: Random Variables A random variable is a variable whose value is subject to variations due to chance. The set of possible outcomes of is denoted as Ω. Example 1: Coin toss Ω, 17
18 Probability Theory: Random Variables A random variable is a variable whose value is subject to variations due to chance. The set of possible outcomes of is denoted as Ω. Example 1: Coin toss Ω, Example 2: Dice throw Ω 1,2,3,4,5,6 18
19 Probability Theory: Random Events Any Ω is called a random event. 19
20 Probability Theory: Random Events Any Ω is called a random event. Example 3: Dice throw Ω 1,2,3,4,5,6 Event A := An even number is thrown = 2,4,6 Ω 20
21 Probability Theory: Random Events Any Ω is called a random event. Example 3: Dice throw Ω 1,2,3,4,5,6 Event A := An even number is thrown = 2,4,6 Ω Example 4: Throw of two dice. Ω 1,2,3,4,5,6 1,1, 1,2,, 6,6 Event B := The sum of points thrown equals 4 = 1,3, 2,2, 3,1 Ω 21
22 Probability Theory: Random Events Any Ω is called a random event. Example 3: Dice throw Ω 1,2,3,4,5,6 Event A := An even number is thrown = 2,4,6 Ω Example 4: Throw of two dice. Ω 1,2,3,4,5,6 1,1, 1,2,, 6,6 Event B := The sum of points thrown equals 4 = 1,3, 2,2, 3,1 Ω Let be a random variable and let be a random event. Then denotes the probability that random variable takes a value in. 22
23 Probability Theory: Probability Mass Function Let Ω be finite or countably infinite. A function such that : Ω 0,1 1 is called probability mass function (pmf). 23
24 Probability Theory: Probability Mass Function Let Ω be finite or countably infinite. A function such that : Ω 0,1 1 is called probability mass function (pmf). A pmf is called pmf of a random variable X if for any Ω: 24
25 Probability Theory: Probability Mass Function Let Ω be finite or countably infinite. A function such that : Ω 0,1 1 is called probability mass function (pmf). A pmf is called pmf of a random variable X if for any Ω: Example 5: Dice throw Ω 1,2,3,4,5,
26 Possible World Semantics Uncertain Data In an uncertain database,,, each object is a random variable. 26
27 Possible World Semantics Uncertain Data In an uncertain database,,, each object is a random variable
28 Possible World Semantics Possible World Semantics The sample space Ω is defined by Ω Ω 0.4 Samples are called Possible Worlds. 28
29 Possible World Semantics Possible World Semantics The sample space Ω is defined by Ω Ω 0.4 Samples are called Possible Worlds. 29
30 Possible World Semantics Possible World Semantics The sample space Ω is defined by Ω Ω 0.4 Samples are called Possible Worlds. 30
31 Possible World Semantics Possible World Semantics The sample space Ω is defined by Ω Ω 0.4 Samples are called Possible Worlds. 31
32 Possible World Semantics Possible World Semantics The sample space Ω is defined by Ω Ω 0.4 Samples are called Possible Worlds. = 32
33 Possible World Semantics Possible World Semantics The sample space Ω is defined by Ω Ω 0.4 Samples are called Possible Worlds. = Assumption: : Ω 0,1 can be computed efficiently. 33
34 Possible World Semantics Answering Queries using PWS Let be a query predicate and let, Ω be an indicator function returning one if predicate holds in world and zero otherwise. The probability, of the event that a query predicate holds on an uncertain database is defined as,, 34
35 Possible Worlds: Example II A B C D E F G M N H O I P J Q R K L S T U V W X Y Z 35
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42 Too many possible worlds 42
43 Too many possible worlds Main challenge: - Answer queries efficiently. - Despite an exponential number of possible worlds 43
44 Overview 1. Introduction to Probability Theory 2. Case Study: Probabilistic Count Queries 44
45 Count Queries on Uncertain Data Querying Uncertain Spatial Data How many objects are located in the depicted circular region centered at query point q? q 15
46 Count Queries on Uncertain Data Querying Uncertain Spatial Data 2 possible worlds C A Main idea: Use polyomial multiplication to enumerate possible results H H q B 17
47 Count Queries on Uncertain Data Example: Querying Uncertain Spatial Data C 0.2 A H H 3 q 0.4 B 17
48 Count Queries on Uncertain Data Example: Querying Uncertain Spatial Data x x x C 0.2 A H H 3 q 0.4 B 18
49 Count Queries on Uncertain Data Example: Querying Uncertain Spatial Data x x x C 0.2 A H H 3 q B 19
50 Count Queries on Uncertain Data Example: Querying Uncertain Spatial Data x x x C 0.2 A H H 3 q B 20
51 Count Queries on Uncertain Data Example: Querying Uncertain Spatial Data x x x C 0.2 A H H 3 q B Probability that exactly two objects are inside the query region 21
52 Count Queries on Uncertain Data Example: Querying Uncertain Spatial Data x x x C 0.2 A H H 3 q B Polynomial time solution: Unify worlds that are equvalent with respect to the query predicate! 21
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