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Label Distribution Learning (LDL) assigns soft labels, a.k.a. degrees, to asample. In reality, it is always laborious to obtain complete degrees, givingbirth to the Incomplete LDL (InLDL). However, InLDL often suffers fromperformance degeneration. To remedy it, existing methods need one or moreexplicit regularizations, leading to burdensome parameter tuning and extracomputation. We argue that label distribution itself may provide useful prior,when used appropriately, the InLDL problem can be solved without any explicitregularization. In this paper, we offer a rational alternative to use such aprior. Our intuition is that large degrees are likely to get more concern, thesmall ones are easily overlooked, whereas the missing degrees are completelyneglected in InLDL. To learn an accurate label distribution, it is crucial notto ignore the small observed degrees but to give them properly large weights,while gradually increasing the weights of the missing degrees. To this end, wefirst define a weighted empirical risk and derive upper bounds between theexpected risk and the weighted empirical risk, which reveals in principle thatweighting plays an implicit regularization role. Then, by using the prior ofdegrees, we design a weighted scheme and verify its effectiveness. To sum up,our model has four advantages, it is 1) model selection free, as no explicitregularization is imposed; 2) with closed form solution (sub-problem) andeasy-to-implement (a few lines of codes); 3) with linear computationalcomplexity in the number of samples, thus scalable to large datasets; 4)competitive with state-of-the-arts even without any explicit regularization.

No Regularization is Needed: An Efficient and Effective Model for Incomplete Label Distribution Learning