Surrogate Regret Bounds for Bipartite Ranking via Strongly Proper Losses
Authors: Shivani Agarwal
JMLR 2014 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | In this paper, we show that such (non-pairwise) surrogate regret bounds for bipartite ranking can be obtained in terms of a broad class of proper (composite) losses that we term as strongly proper. Our proof technique is much simpler than that of Kotlowski et al. (2011), and relies on properties of proper (composite) losses as elucidated recently by Reid and Williamson (2010, 2011) and others. Our result yields explicit surrogate bounds (with no hidden balancing terms) in terms of a variety of strongly proper losses, including for example logistic, exponential, squared and squared hinge losses as special cases. An immediate consequence is that standard algorithms minimizing such losses, such as standard logistic regression and boosting algorithms (assuming a universal function class and appropriate regularization), are in fact consistent for bipartite ranking; moreover, our results allow us to quantify the bipartite ranking regret in terms of the corresponding surrogate regret. Section 4 we define and characterize strongly proper losses. Section 5 contains our main result, namely a bound on the bipartite ranking regret in terms of the regret associated with any strongly proper loss, together with several examples. Section 6 gives a tighter bound under certain low-noise conditions via a recent result of Cl emen con and Robbiano (2011). The paper includes multiple theorems and their proofs, e.g., Theorem 4 A proper loss c : { 1} [0, 1] R+ is strictly proper if and only if Hc is strictly concave. Proof [of Theorem 4] Let c : { 1} [0, 1] R+ be a proper loss. |
| Researcher Affiliation | Academia | Shivani Agarwal EMAIL Department of Computer Science and Automation Indian Institute of Science Bangalore 560012, India |
| Pseudocode | No | The paper does not contain structured pseudocode or algorithm blocks. It focuses on theoretical proofs and mathematical derivations. |
| Open Source Code | No | The paper does not provide any explicit statements about releasing source code, nor does it include links to a code repository or mention code in supplementary materials. |
| Open Datasets | No | The paper is theoretical and focuses on mathematical properties of loss functions and regret bounds based on an 'unknown distribution D'. It does not describe or use any specific empirical datasets, thus no access information for datasets is provided. |
| Dataset Splits | No | The paper does not utilize empirical datasets, and therefore no information about dataset splits for training, validation, or testing is provided. |
| Hardware Specification | No | The paper is theoretical and does not describe any experimental procedures or the hardware used to conduct them. |
| Software Dependencies | No | The paper is theoretical and does not describe any specific software dependencies or versions used for implementation or experiments. |
| Experiment Setup | No | The paper is theoretical and does not describe any experimental setup, including hyperparameters or system-level training settings. |