1 / 17

Efficient Evaluation and Generalization of Course Recommendations with Prerequisites

This research focuses on evaluating course recommendations based on sets of prerequisites, combining them efficiently to provide general recommendations satisfying various constraints. It explores algorithms like Breadth First, Greedy, and Top-Down to minimize costs and meet requirements, with adaptations for different types of recommendation structures. The study includes experiments on different graph types and strategies to optimize course package recommendations for users.

olinda
Télécharger la présentation

Efficient Evaluation and Generalization of Course Recommendations with Prerequisites

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Evaluating, Combining and Generalizing Recommendations with Prerequisites AdityaParameswaran Stanford University (with Profs. Hector Garcia-Molina and Jeffrey D. Ullman)

  2. Statistics (at Stanford): >10,000 registered users 37,000 listed courses 160,000 evaluations Overall 172 universities 100,000 users

  3. Course Recommendations • Instead of a traditional ranked list … • Recommend a good package satisfying • Prerequisites (e.g., algebra  calculus) • Requirements (e.g., > 3 math courses) • Planning constraints (e.g., no two in same slot) • Recent work on recommending packages • Yahoo! Travel Plans [De Choudhury et. al. WWW 10] Yahoo! Composite items [Roy et. al. SIGMOD 10] • Minimizing Cost [Xie et. al. RecSys 10] Prior Work

  4. Intuitive Example • Nodes represent all items not taken yet • Edges imply prerequisites Prerequisites: YES score: 29 A(5) B(6) E(2) C(3) D(7) J(8) G(7) H(8) K(9) I(2) Prerequisites: NO score: 32

  5. Example: General Prerequisites Set Theory Arithmetic Algebra Probability Adv. Math Geometry Optimization Algorithms Information Theory Statistics

  6. Formal Problem • Directed acyclic graph G(V, E) • with some nodes Labeled AND or OR • Every node x has a score(x) • Recommend k = |A| courses such that • score(a) is maximized {a ϵ A} • Prerequisites of all nodes are met Chain Graphs AND Graphs OR Graphs AND-OR Graphs 6

  7. Outline of Work Chain Graphs • Complexity • Chain Graphs: PTIME DP • AND / OR / AND-OR: NP-Hard • Adaptable Approx Algorithms • Breadth First • Greedy • Top Down • Worst case per structure • Complexity: DP > Greedy > Top Down > BF • Merge Algorithm • Experiments • Extensions to Fuzzy Prerequisites AND Graphs OR Graphs AND-OR Graphs For Chain Graphs Sample

  8. Chain Graph Algorithm 0 Score of best feasible set of j items from first i chains j k B [j, i] = max over all x {B [x, i–1] + 1 … (j—x)of ith chain} Complexity: O(nk2) • To pick j items from i chains: • Pick • x items from i-1 chains • First j – x items from the ith chain

  9. Breadth First Algorithm Illustration • K = 4 • Add items until k = 4 • Swap items A(5) B(6) C(3) D(7) E(2) J(8) G(7) H(8) K(9) I(2)

  10. Top Down & Greedy Algorithms • Algorithms between extremes • Efficient: Breadth First • Inefficient but Exact: Dynamic Programming • Top Down is the reverse of Breadth First • Add best items first, then try to add prerequisites • Greedy reasons about entire chains at once • Tries to add prefixes of chains with high avg score

  11. Outline of Work Chain Graphs • Complexity • Chain Graphs: PTIME DP • AND / OR / AND-OR: NP-Hard • Adaptable Approx Algorithms • Breadth First • Greedy • Top Down • Worst case per structure • Complexity: DP > Greedy > Top Down > BF • Merge Algorithm • Experiments • Extensions to Fuzzy Prerequisites AND Graphs OR Graphs AND-OR Graphs For Chain Graphs Sample

  12. Breadth First: Worst Case • Worst case in terms of: • d: maximum length of chain • m: max difference in score in a given chain lots of chains of depth d lots of singleton elements a - Є a - Є a - Є a a a a+m-Є a+m-Є a+m-Є difference = k/d x (da + (d-1)m) - ka = k/d x (d-1)m a+m-Є a+m-Є a+m-Є

  13. Experimental Setup • Measure How we perform • As fraction of DP (for chains) & no-prereqs (for AND graphs) • Vary: • n: number of components • d: max depth of chain / component • p: probability of a long chain / large component • k: size of package • Score: exponentially distributed

  14. Chain Graphs on Varying k Ratio of Dynamic Programming Solution Size of the desired package

  15. AND Graphs on Varying Ratio of No-prerequisite Solution Probability of Long Component

  16. Conclusions • Dynamic Programming Algorithm • Only for Chain Graphs • Guaranteed best recommendations • Greedy Value Algorithm • Adaptable to any structure • Almost as good recommendations as DP • With less complexity • Top Down and Breadth First • Even better complexity • Not as good recommendations as Greedy • Can be improved using Merge algorithm

  17. Chain Graphs on Varying p Ratio of Dynamic Programming Solution Probability of a long chain (k small)

More Related