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Area under the ROC curve (AUC) is a standard metric that is used to measure classification performance for imbalanced class data. Developing stochastic learning algorithms that maximize AUC over accuracy is of practical interest. However, AUC maximization presents a challenge since the learning objective function is defined over a pair of instances of opposite classes. Existing methods circumvent this issue but with high space and time complexity. From our previous work of redefining AUC optimization as a convex-concave saddle point problem, we propose a new stochastic batch learning algorithm for AUC maximization. The key difference from our previous work is that we assume that the underlying distribution of the data is uniform, and we develop a batch learning algorithm that is a stochastic primal-dual algorithm (SPDAM) that achieves a linear convergence rate. We establish the theoretical convergence of SPDAM with high probability and demonstrate its effectiveness on standard benchmark datasets.
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Stability and optimization error of stochastic gradient descent for pairwise learning
In this paper, we study the stability and its trade-off with optimization error for stochastic gradient descent (SGD) algorithms in the pairwise learning setting. Pairwise learning refers to a learning task which involves a loss function depending on pairs of instances among which notable examples are bipartite ranking, metric learning, area under ROC curve (AUC) maximization and minimum error entropy (MEE) principle. Our contribution is twofolded. Firstly, we establish the stability results for SGD for pairwise learning in the convex, strongly convex and non-convex settings, from which generalization errors can be naturally derived. Secondly, we establish the trade-off between stability and optimization error of SGD algorithms for pairwise learning. This is achieved by lower-bounding the sum of stability and optimization error by the minimax statistical error over a prescribed class of pairwise loss functions. From this fundamental trade-off, we obtain lower bounds for the optimization error of SGD algorithms and the excess expected risk over a class of pairwise losses. In addition, we illustrate our stability results by giving some specific examples of AUC maximization, metric learning and MEE.
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- Award ID(s):
- 1816227
- PAR ID:
- 10169504
- Date Published:
- Journal Name:
- Analysis and Applications
- ISSN:
- 0219-5305
- Page Range / eLocation ID:
- 1 to 41
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1142/S0219530519400062
