  Label Distribution Learning (LDL) assigns soft labels, a.k.a. degrees, to a
sample. In reality, it is always laborious to obtain complete degrees, giving
birth to the Incomplete LDL (InLDL). However, InLDL often suffers from
performance degeneration. To remedy it, existing methods need one or more
explicit regularizations, leading to burdensome parameter tuning and extra
computation. We argue that label distribution itself may provide useful prior,
when used appropriately, the InLDL problem can be solved without any explicit
regularization. In this paper, we offer a rational alternative to use such a
prior. Our intuition is that large degrees are likely to get more concern, the
small ones are easily overlooked, whereas the missing degrees are completely
neglected in InLDL. To learn an accurate label distribution, it is crucial not
to ignore the small observed degrees but to give them properly large weights,
while gradually increasing the weights of the missing degrees. To this end, we
first define a weighted empirical risk and derive upper bounds between the
expected risk and the weighted empirical risk, which reveals in principle that
weighting plays an implicit regularization role. Then, by using the prior of
degrees, 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 explicit
regularization is imposed; 2) with closed form solution (sub-problem) and
easy-to-implement (a few lines of codes); 3) with linear computational
complexity in the number of samples, thus scalable to large datasets; 4)
competitive with state-of-the-arts even without any explicit regularization.

Machine Learning;Machine Learning