Abstract
Due to its wide applications and learning efficiency, online ordinal regression using perceptron algorithms with interval labels (PRIL) has been increasingly applied to solve ordinal ranking problems. However, it is still a challenge for the PRIL method to handle noise labels, in which case the ranking results may change dramatically. To tackle this problem, in this paper, we propose noise-resilient online learning algorithms using ramp loss function, called PRIL-RAMP, and its nonlinear variant K-PRIL-RAMP, to improve the performance of PRIL method for noisy data streams. The proposed algorithms iteratively optimize the decision function under the framework of online gradient descent (OGD), and we justify the algorithms by showing the order preservation of thresholds. It is validated in the experiments that both approaches are more robust and efficient to noise labels than state-of-the-art online ordinal regression algorithms on real-world datasets.
Highlights
Ordinal regression, called ranking learning, plays a central role in the learning task where the labels of data samples need to be ordered
We introduce the proposed perceptron algorithms with interval labels (PRIL)-RAMP and K-PRIL-RAMP algorithms and discuss the order preservation of thresholds of the proposed algorithms
We present the PRIL-RAMP procedure to minimize the estimated risk using the online gradient descent (OGD) structure [14] of ramp loss in online ordinary regression
Summary
Called ranking learning, plays a central role in the learning task where the labels of data samples need to be ordered. It has been routinely used in social ranking tasks, e.g., collaborative filtering [1], ecology [2], and detecting the severity of Alzheimer disease [3], to name a few. In contrast to other types of regression analysis, ordinal regression describes the relationship between variables where the order matters. Ordinal regression requires a linear (nonlinear) function and a set of K − 1 thresholds, where each threshold corresponds to a class. Ordinal regression distinguishes multiclassification in the sense that the output labels have a natural order
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