# FIRAL: An Active Learning Algorithm for Multinomial Logistic Regression

arXiv: https://arxiv.org/abs/2409.07379 · HTML: https://mlsanity.com/paper/2409.07379/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 28 references that are in the map.
- First posted on arXiv 11 Sep 2024.

## Builds on (most cited first, 10 of 10)

- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Deep Bayesian Active Learning with Image Data](https://mlsanity.com/paper/1703.02910/) (2017)
- [A Survey of Deep Active Learning](https://mlsanity.com/paper/2009.00236/) (2020)
- [Discriminative Active Learning](https://mlsanity.com/paper/1907.06347/) (2019)
- [Bayesian Batch Active Learning as Sparse Subset Approximation](https://mlsanity.com/paper/1908.02144/) (2019)
- [Sub-sampled Cubic Regularization for Non-convex Optimization](https://mlsanity.com/paper/1705.05933/) (2017)
- [Finite-sample analysis of M-estimators using self-concordance](https://mlsanity.com/paper/1810.06838/) (2018)
- [Convergence Rates of Active Learning for Maximum Likelihood Estimation](https://mlsanity.com/paper/1506.02348/) (2015)
- [Competing with the Empirical Risk Minimizer in a Single Pass](https://mlsanity.com/paper/1412.6606/) (2014)
- [Asymptotic Analysis of Objectives based on Fisher Information in Active Learning](https://mlsanity.com/paper/1605.08798/) (2016)

## Abstract (arXiv)

We investigate theory and algorithms for pool-based active learning for multiclass classification using multinomial logistic regression. Using finite sample analysis, we prove that the Fisher Information Ratio (FIR) lower and upper bounds the excess risk. Based on our theoretical analysis, we propose an active learning algorithm that employs regret minimization to minimize the FIR. To verify our derived excess risk bounds, we conduct experiments on synthetic datasets. Furthermore, we compare FIRAL with five other methods and found that our scheme outperforms them: it consistently produces the smallest classification error in the multiclass logistic regression setting, as demonstrated through experiments on MNIST, CIFAR-10, and 50-class ImageNet.