# Learning Rankings via Convex Hull Separation

^{1}

TL;DR: Experiments indicate that the proposed algorithm for learning ranking functions from order constraints between sets—i.e. classes—of training samples is at least as accurate as the current state-of-the-art and several orders of magnitude faster than current methods.

Abstract: We propose efficient algorithms for learning ranking functions from order constraints between sets—i.e. classes—of training samples. Our algorithms may be used for maximizing the generalized Wilcoxon Mann Whitney statistic that accounts for the partial ordering of the classes: special cases include maximizing the area under the ROC curve for binary classification and its generalization for ordinal regression. Experiments on public benchmarks indicate that: (a) the proposed algorithm is at least as accurate as the current state-of-the-art; (b) computationally, it is several orders of magnitude faster and—unlike current methods—it is easily able to handle even large datasets with over 20,000 samples.

...read more

##### Citations

^{1}

2,244 citations

### Cites background from "Learning Rankings via Convex Hull S..."

...• Other learning-to-rank algorithms [15, 19, 32, 93, 109, 127, 142, 143, 144] that are based on association rules, decision systems, and other technologies; other theoretical analysis on ranking [50]; and applications of learning-to-rank methods [87, 128]....

[...]

1,752 citations

^{1}

828 citations

### Cites background from "Learning Rankings via Convex Hull S..."

...For other approaches to learning to rank, refer to [2, 11, 31]....

[...]

^{1}

496 citations

##### References

^{1}

38,164 citations

### "Learning Rankings via Convex Hull S..." refers background in this paper

...Note that enforcing the constraints defined above indeed implies the desired ordering, since we have: Aw + y ≥ −γ ≥ γ̂ + 1 ≥ γ̂ ≥ Aw − y It is also important to note the connection with Support Vector Machines (SVM) formulation [10, 14] for the binary case....

[...]

23,204 citations

### "Learning Rankings via Convex Hull S..." refers methods in this paper

...Ordinal regression and methods for handling structured output classes: For a classic description of generalized linear models for ordinal regre ssion, see [11]....

[...]

5,933 citations

### "Learning Rankings via Convex Hull S..." refers background in this paper

...B′u− w′[A− ′ − A+ ′ ] = 0, b′u ≤ −1, u ≥ 0, (7) Where the second equivalent form of the constraints was obtained by negation (as before), and the third equivalent form results from ourthird key insight: the application of Farka’s theorem of alternatives[9]....

[...]

4,297 citations

2,142 citations

### "Learning Rankings via Convex Hull S..." refers background in this paper

...Bu− w[A ′ − A ′ ] = 0, bu ≤ −1, u ≥ 0, (7) Where the second equivalent form of the constraints was obtai ned by negation (as before), and the third equivalent form results from our third key insight: the application of Farka’s theorem of alternatives[9]....

[...]