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

arXiv: https://arxiv.org/abs/2308.07047 · HTML: https://mlsanity.com/paper/2308.07047/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 40 references that are in the map.
- First posted on arXiv 14 Aug 2023.

## Builds on (most cited first, 7 of 7)

- [A vector-contraction inequality for Rademacher complexities](https://mlsanity.com/paper/1605.00251/) (2016)
- [Label Distribution Learning](https://mlsanity.com/paper/1408.6027/) (2014)
- [Learning in an Uncertain World: Representing Ambiguity Through Multiple Hypotheses](https://mlsanity.com/paper/1612.00197/) (2016)
- [Projection onto the probability simplex: An efficient algorithm with a simple proof, and an application](https://mlsanity.com/paper/1309.1541/) (2013)
- [SCUT-FBP5500: A Diverse Benchmark Dataset for Multi-Paradigm Facial Beauty Prediction](https://mlsanity.com/paper/1801.06345/) (2018)
- [Label Distribution Learning Forests](https://mlsanity.com/paper/1702.06086/) (2017)
- [SCUT-FBP: A Benchmark Dataset for Facial Beauty Perception](https://mlsanity.com/paper/1511.02459/) (2015)

## Built on by (most cited first, 1 of 1)

- [A Survey on Incomplete Multi-label Learning: Recent Advances and Future Trends](https://mlsanity.com/paper/2406.06119/) (2024)

## Abstract (arXiv)

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.