Learning Analytics. Dr. Bowen Hui Computer Science University of British Columbia Okanagan

Transcription

1 Learning Analytics Dr. Bowen Hui Computer Science University of British Columbia Okanagan

2 Last Time: Exercise Given the following code, build its PDG (follow table of vertex types) int sum( int array[] ) { // var declarations int index = 0; int len = array.length; // tally up each array element int sum = 0; while( index<len ) { sum = add( sum, array[index] ); index++; System.out.println( sum = + sum ); } // return total return sum; } 2

3 Recall: PDG Vertices Represent statements Each vertex has one and only one type See GPLAG paper for details 3

4 Recall: PDG Edges Model dependencies between vertices Control dependencies: connects a control vertex to another vertex whose statement will be executed if the condition is evaluated to true Data dependencies: connects vertices v 1 and v 2 if there is some variable var such that: v 1 may be assigned to var v 2 may use value in var There is an execution path from v 1 to v 2 in the code where there is no assignment to var 4

5 Exercise Solution For comparison, see next slide 5

6 PDG of Original Code Example taken from GPLAG paper Control dependencies Data dependencies 6

7 Problem Formulation Original Program Source P P Number of Procedures n m Converted PDG G G Suspect Size G = n G =m Subtasks: Given g G and g G, decide if g is plagiarized from g How to efficiently locate code pairs without n m comparisons? 7

8 Main Claims Restricted to 5 disguises (see above) 1. If g is subgraph isomorphic to g, then the corresponding procedure of g is considered as plagiarized from g 2. If g is γ- isomorphic to g, then the corresponding procedure of g is considered as plagiarized from g Note: 0 < γ 1 and γ is the mature rate of the detection 8

9 Recall Disguises PDGs generally immune to the following: Format alteration Identifier Renaming Statement Reordering Control Replacement Assuming correctness is preserved, PDG of plagiarized code is bigger Code Insertion 9

10 An inserted extra loop (within loop) that essentially does nothing Example taken from GPLAG paper loop loop Left graph (g) is subgraph isomorphic to right graph (g ) 10

11 Beyond 5 Disguises Detect cheats resulting in similar enough PDGs Example of having two variables merged into one: Simple code change that modifies vertices in PDG Set threshold γ which indicates proportion of overlap Suggested use of 0.9 More than 10% differences in PDGs is like rewriting code 11

12 Main Claims Restricted to 5 disguises (see above) 1. If g is subgraph isomorphic to g, then the corresponding procedure of g is considered as plagiarized from g Beyond 5 disguises 2. If g is γ- isomorphic to g, then the corresponding procedure of g is considered as plagiarized from g Note: 0 < γ 1 12

13 Graph Terminology Given two graphs, check isomorphism Define graph isomorphism A bijective function f: V V 2 is a graph morphism from a graph G = (V, E, μ, δ)to a graph G = (V, E, μ, δ ) if: μ v = μ f(v) e = v 1, v 2 E, e 2 = f v 1, f v 2 E 2 such that δ e = δ(e 2 ) e 2 = v 2 1, v 2 2 E 2, e = f _ 1 v 2 1, f _ 1 v 2 2 E such that δ e 2 = δ(e) One- to- one correspondence 13

14 Graph Terminology Given two graphs, check isomorphism Define graph isomorphism Define subgraph isomorphism An injective function f: V V 2 is a subgraph S G such that f is a graph isomorphism from G to S One- to- one mapping that preserves distinctness of elements in domain 14

15 Injective vs. Bijective 15

16 Graph Terminology Given two graphs, check isomorphism Define graph isomorphism Define subgraph isomorphism Define γ- Isomorphic A graph G is γ- isomorphic to G if there exists a subgraph S G such that S is subgraph isomorphic to G and S γ G where γ (0,1] Similar to computing distance between two graphs 16

17 Overall GPLAG Algorithm Inputs: P, P (and some parameters) Output: F, the set of PDG pairs considered to be involved in plagiarism (for human consideration) Steps: Construct G and G Efficiently identify g and g pairs to compare If g is γ- isomorphic to g Add to suspect set for output: F = F g, g 2 Return F 17

18 Overall GPLAG Algorithm Inputs: P, P (and some parameters) Output: F, the set of PDG pairs considered to be involved in plagiarism (for human consideration) Steps: Construct G and G Efficiently identify g and g pairs to compare If g is γ- isomorphic to g Add to suspect set for output: F = F g, g 2 Return F We skipped this 18

19 Key Ideas Detecting source code plagiarism is much harder than detecting plagiarism in natural language Lack idiosyncrasies Trivial changes can modify code logic and flow Representation: Models source code as program dependency graph (ignores superficial code variants) Algorithm: GPLAG: Uses graph isomorphism to detect plagiarism 19

20 Quiz #2 Format One single- sided 8.5 x11 cheatsheet allowed Questions: Decision scenarios: Given problem description, build a decision tree model and compute expected utility to obtain the best action Bound query: Given problem description, create a bound query, then given an answer to it, create a second bound query DBN: Given model, simulation environment, and graphs, interpret the results and explain how well the model works Cusum method: Given paragraph of text, create a cusum plot and draw conclusions from it 20

21 Project Presentation Time: 6-7 minutes per person Purpose: Early/midpoint feedback Let everyone know what everyone else is doing Content: Overview to indicate where you are in the project (slides or notes on board or handouts) If you are doing an individualized project option, you will need to give an overview of your project Demo one aspect of your project that you have implemented Dates: Tentative schedule on website 21

22 Project Submission Due date: 9:00am Dec. 15th What to submit: A report Documenting the steps in your project Referencing how your project steps relate to the code files Including an explanation of missing/buggy code Documenting test cases that work and test cases that don t Including a link to a video demo showing your program execution, trying out different test cases, and associated output of each case All code files and test scripts PowerPoint slides used from presentation (if any) 22