Exact Passive-Aggressive Algorithms for Learning to Rank Using Interval Labels

In this paper, we propose exact passive-aggressive (PA) online algorithms for learning to rank. The proposed algorithms can be used even when we have interval labels instead of actual labels for examples. The proposed algorithms solve a convex optimization problem at every trial. We find exact solut...

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Bibliographic Details
Published in:arXiv.org 2018-08
Main Authors: Manwani, Naresh, Chandra, Mohit
Format: Article
Language:English
Subjects:
Algorithms
Computational geometry
Convexity
Distance learning
Labels
Machine learning
Optimization
Thresholds
Online Access:Get full text
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Summary:In this paper, we propose exact passive-aggressive (PA) online algorithms for learning to rank. The proposed algorithms can be used even when we have interval labels instead of actual labels for examples. The proposed algorithms solve a convex optimization problem at every trial. We find exact solution to those optimization problems to determine the updated parameters. We propose support class algorithm (SCA) which finds the active constraints using the KKT conditions of the optimization problems. These active constrains form support set which determines the set of thresholds that need to be updated. We derive update rules for PA, PA-I and PA-II. We show that the proposed algorithms maintain the ordering of the thresholds after every trial. We provide the mistake bounds of the proposed algorithms in both ideal and general settings. We also show experimentally that the proposed algorithms successfully learn accurate classifiers using interval labels as well as exact labels. Proposed algorithms also do well compared to other approaches.
ISSN:2331-8422
DOI:10.48550/arxiv.1808.06107