# Reformulating van Rijsbergen's Fβ metric for weighted binary cross-entropy

arXiv: https://arxiv.org/abs/2210.16458 · HTML: https://mlsanity.com/paper/2210.16458/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 62 references that are in the map.
- First posted on arXiv 29 Oct 2022.

## Builds on (most cited first, 17 of 17)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [MobileNetV2: Inverted Residuals and Linear Bottlenecks](https://mlsanity.com/paper/1801.04381/) (2018)
- [Deep Learning in Neural Networks: An Overview](https://mlsanity.com/paper/1404.7828/) (2014)
- [Learning from Noisy Labels with Deep Neural Networks: A Survey](https://mlsanity.com/paper/2007.08199/) (2020)
- [Deep Neural Networks and Tabular Data: A Survey](https://mlsanity.com/paper/2110.01889/) (2021)
- [Pervasive Label Errors in Test Sets Destabilize Machine Learning Benchmarks](https://mlsanity.com/paper/2103.14749/) (2021)
- [Dice Loss for Data-imbalanced NLP Tasks](https://mlsanity.com/paper/1911.02855/) (2019)
- [The Real-World-Weight Cross-Entropy Loss Function: Modeling the Costs of Mislabeling](https://mlsanity.com/paper/2001.00570/) (2020)
- [Annotation Error Detection: Analyzing the Past and Present for a More Coherent Future](https://mlsanity.com/paper/2206.02280/) (2022)
- [Localization Recall Precision (LRP): A New Performance Metric for Object Detection](https://mlsanity.com/paper/1807.01696/) (2018)
- [A Ranking-based, Balanced Loss Function Unifying Classification and Localisation in Object Detection](https://mlsanity.com/paper/2009.13592/) (2020)
- [sigmoidF1: A Smooth F1 Score Surrogate Loss for Multilabel Classification](https://mlsanity.com/paper/2108.10566/) (2021)
- [Striking the Right Balance: Recall Loss for Semantic Segmentation](https://mlsanity.com/paper/2106.14917/) (2021)
- [Testing DNN Image Classifiers for Confusion & Bias Errors](https://mlsanity.com/paper/1905.07831/) (2019)
- [A surrogate loss function for optimization of Fβ score in binary classification with imbalanced data](https://mlsanity.com/paper/2104.01459/) (2021)
- [Maximum F1-score training for end-to-end mispronunciation detection and diagnosis of L2 English speech](https://mlsanity.com/paper/2108.13816/) (2021)

## Abstract (arXiv)

The separation of performance metrics from gradient based loss functions may not always give optimal results and may miss vital aggregate information. This paper investigates incorporating a performance metric alongside differentiable loss functions to inform training outcomes. The goal is to guide model performance and interpretation by assuming statistical distributions on this performance metric for dynamic weighting. The focus is on van Rijsbergens Fβ metric -- a popular choice for gauging classification performance. Through distributional assumptions on the Fβ, an intermediary link can be established to the standard binary cross-entropy via dynamic penalty weights. First, the Fβ metric is reformulated to facilitate assuming statistical distributions with accompanying proofs for the cumulative density function. These probabilities are used within a knee curve algorithm to find an optimal β or βopt. This βopt is used as a weight or penalty in the proposed weighted binary cross-entropy. Experimentation on publicly available data along with benchmark analysis mostly yields better and interpretable results as compared to the baseline for both imbalanced and balanced classes. For example, for the IMDB text data with known labeling errors, a 14% boost in F1 score is shown. The results also reveal commonalities between the penalty model families derived in this paper and the suitability of recall-centric or precision-centric parameters used in the optimization. The flexibility of this methodology can enhance interpretation.