# On the Importance of Firth Bias Reduction in Few-Shot Classification

arXiv: https://arxiv.org/abs/2110.02529 · HTML: https://mlsanity.com/paper/2110.02529/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 46 of its 102 references that are in the map.
- First posted on arXiv 6 Oct 2021.

## Builds on (most cited first, 30 of 46)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [Prototypical Networks for Few-shot Learning](https://mlsanity.com/paper/1703.05175/) (2017)
- [Matching Networks for One Shot Learning](https://mlsanity.com/paper/1606.04080/) (2016)
- [Learning to Compare: Relation Network for Few-Shot Learning](https://mlsanity.com/paper/1711.06025/) (2017)
- [A Closer Look at Few-shot Classification](https://mlsanity.com/paper/1904.04232/) (2019)
- [Learning to learn by gradient descent by gradient descent](https://mlsanity.com/paper/1606.04474/) (2016)
- [Meta-Learning with Latent Embedding Optimization](https://mlsanity.com/paper/1807.05960/) (2018)
- [Regularizing Neural Networks by Penalizing Confident Output Distributions](https://mlsanity.com/paper/1701.06548/) (2017)
- [Meta-Learning for Semi-Supervised Few-Shot Classification](https://mlsanity.com/paper/1803.00676/) (2018)
- [Rethinking Few-Shot Image Classification: a Good Embedding Is All You Need?](https://mlsanity.com/paper/2003.11539/) (2020)
- [TADAM: Task dependent adaptive metric for improved few-shot learning](https://mlsanity.com/paper/1805.10123/) (2018)
- [Meta-learning with differentiable closed-form solvers](https://mlsanity.com/paper/1805.08136/) (2018)
- [Dynamic Few-Shot Visual Learning without Forgetting](https://mlsanity.com/paper/1804.09458/) (2018)
- [Meta-SGD: Learning to Learn Quickly for Few-Shot Learning](https://mlsanity.com/paper/1707.09835/) (2017)
- [Meta-Dataset: A Dataset of Datasets for Learning to Learn from Few Examples](https://mlsanity.com/paper/1903.03096/) (2019)
- [A Baseline for Few-Shot Image Classification](https://mlsanity.com/paper/1909.02729/) (2019)
- [Few-Shot Learning via Embedding Adaptation with Set-to-Set Functions](https://mlsanity.com/paper/1812.03664/) (2018)
- [Meta Networks](https://mlsanity.com/paper/1703.00837/) (2017)
- [Probabilistic Model-Agnostic Meta-Learning](https://mlsanity.com/paper/1806.02817/) (2018)
- [SimpleShot: Revisiting Nearest-Neighbor Classification for Few-Shot Learning](https://mlsanity.com/paper/1911.04623/) (2019)
- [Low-Shot Learning from Imaginary Data](https://mlsanity.com/paper/1801.05401/) (2018)
- [Free Lunch for Few-shot Learning: Distribution Calibration](https://mlsanity.com/paper/2101.06395/) (2021)
- [Revisiting Natural Gradient for Deep Networks](https://mlsanity.com/paper/1301.3584/) (2013)
- [Boosting Few-Shot Visual Learning with Self-Supervision](https://mlsanity.com/paper/1906.05186/) (2019)
- [Charting the Right Manifold: Manifold Mixup for Few-shot Learning](https://mlsanity.com/paper/1907.12087/) (2019)
- [Negative Margin Matters: Understanding Margin in Few-shot Classification](https://mlsanity.com/paper/2003.12060/) (2020)

## Built on by (most cited first, 7 of 7)

- [Uncertainty Estimation by Fisher Information-based Evidential Deep Learning](https://mlsanity.com/paper/2303.02045/) (2023)
- [Inductive and Transductive Few-Shot Video Classification via Appearance and Temporal Alignments](https://mlsanity.com/paper/2207.10785/) (2022)
- [BECLR: Batch Enhanced Contrastive Few-Shot Learning](https://mlsanity.com/paper/2402.02444/) (2024)
- [Learning from Integral Losses in Physics Informed Neural Networks](https://mlsanity.com/paper/2305.17387/) (2023)
- [A Statistical Model for Predicting Generalization in Few-Shot Classification](https://mlsanity.com/paper/2212.06461/) (2022)
- [Robust Model-Based Optimization for Challenging Fitness Landscapes](https://mlsanity.com/paper/2305.13650/) (2023)
- [Taming Small-sample Bias in Low-budget Active Learning](https://mlsanity.com/paper/2306.11056/) (2023)

## Abstract (arXiv)

Learning accurate classifiers for novel categories from very few examples, known as few-shot image classification, is a challenging task in statistical machine learning and computer vision. The performance in few-shot classification suffers from the bias in the estimation of classifier parameters; however, an effective underlying bias reduction technique that could alleviate this issue in training few-shot classifiers has been overlooked. In this work, we demonstrate the effectiveness of Firth bias reduction in few-shot classification. Theoretically, Firth bias reduction removes the O(N-1) first order term from the small-sample bias of the Maximum Likelihood Estimator. Here we show that the general Firth bias reduction technique simplifies to encouraging uniform class assignment probabilities for multinomial logistic classification, and almost has the same effect in cosine classifiers. We derive an easy-to-implement optimization objective for Firth penalized multinomial logistic and cosine classifiers, which is equivalent to penalizing the cross-entropy loss with a KL-divergence between the uniform label distribution and the predictions. Then, we empirically evaluate that it is consistently effective across the board for few-shot image classification, regardless of (1) the feature representations from different backbones, (2) the number of samples per class, and (3) the number of classes. Finally, we show the robustness of Firth bias reduction, in the case of imbalanced data distribution. Our implementation is available at https://github.com/ehsansaleh/firthbiasreduction