Label Encoding for Regression Networks

Regression is reformulated to predicting a binary code of length M with M binary classifiers. With carefully chosen encoding and decoding schemes, the resulting neural networks outperform those trained with standard regression by a large margin - should be very useful for practitioners!

In the ICLR paper [Sha22L] the authors propose a highly creative reformulation of regression that significantly outperforms standard regression with neural networks (e.g. optimizing MSE) in their experiments. Their approach can be summarized as:

  1. Quantizing the target $y$ into $N$ values (in a simple, uniform fashion)
  2. Encoding the quantized targets as binary strings of size $M$. There are $2^{M \choose N}$ possible encodings
  3. Instead of learning to predict the target directly, $M$ binary classifiers are trained to predict the entries of the binary code from step 2.
  4. At inference time, the predicted codes are decoded back to the target. For that, either the binary predictions or the predicted confidences of the $M$ classifiers can be used.

The idea is inspired by earlier work on using classifiers for ordinal regression and on using binary encodings for phrasing multiclass classification as multi-binary-classification. The procedure described above was dubbed BEL regression. It has a lot of moving parts - there are many possible encoding and decoding schemes, also the hyperparameter $N$ is important. The authors perform a theoretical and experimental analysis of various schemes and give arguments for selecting some over the other. In the end, the best performing encoding / decoding choice depends on the dataset and the networks used. These best performing combinations outperformed standard regression by a large margin! See the figure below for their comparison on several data sets.

Thus, if you care a lot about having low-error neural network regression algorithms and don’t mind performing some hyperparameter search, this approach might be useful for you! The authors provide a reference implementation but for your own project you would likely need to do some implementing on your own.

This work does not compare the performance of BEL regression with non-network regressors like tree-based approaches which often outperform neural networks. Before implementing the proposed label encoding, I personally would first try something like LightGBM.