# Multinomial Logistic Regression Algorithms via Quadratic Gradient

arXiv: https://arxiv.org/abs/2208.06828 · HTML: https://mlsanity.com/paper/2208.06828/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 7 references that are in the map.
- First posted on arXiv 14 Aug 2022.

## Builds on (most cited first, 3 of 3)

- [Privacy-Preserving Logistic Regression Training with A Faster Gradient Variant](https://mlsanity.com/paper/2201.10838/) (2022)
- [Volley Revolver: A Novel Matrix-Encoding Method for Privacy-Preserving Neural Networks (Inference)](https://mlsanity.com/paper/2201.12577/) (2022)
- [Multiclass classification by sparse multinomial logistic regression](https://mlsanity.com/paper/2003.01951/) (2020)

## Built on by (most cited first, 4 of 4)

- [Simplified Quadratic Gradient: A Unified Framework Bridging Gradient Descent and Newton-Type Methods by Synthesizing Hessians and Gradients](https://mlsanity.com/paper/2209.03282/) (2022)
- [Privacy-Preserving CNN Training with Transfer Learning: Multiclass Logistic Regression](https://mlsanity.com/paper/2304.03807/) (2023)
- [Privacy-Preserving 3-Layer Neural Network Training](https://mlsanity.com/paper/2308.09531/) (2023)
- [LFFR: Logistic Function For (single-output) Regression](https://mlsanity.com/paper/2407.09955/) (2024)

## Abstract (arXiv)

Multinomial logistic regression, also known by other names such as multiclass logistic regression and softmax regression, is a fundamental classification method that generalizes binary logistic regression to multiclass problems. A recently work proposed a faster gradient called textttquadratic gradient that can accelerate the binary logistic regression training, and presented an enhanced Nesterov's accelerated gradient (NAG) method for binary logistic regression. In this paper, we extend this work to multiclass logistic regression and propose an enhanced Adaptive Gradient Algorithm (Adagrad) that can accelerate the original Adagrad method. We test the enhanced NAG method and the enhanced Adagrad method on some multiclass-problem datasets. Experimental results show that both enhanced methods converge faster than their original ones respectively.