# Asymptotic Bayes risk of semi-supervised multitask learning on Gaussian mixture

arXiv: https://arxiv.org/abs/2303.02048 · HTML: https://mlsanity.com/paper/2303.02048/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 26 references that are in the map.
- First posted on arXiv 3 Mar 2023.

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

- [An Overview of Multi-Task Learning in Deep Neural Networks](https://mlsanity.com/paper/1706.05098/) (2017)
- [Optimal Errors and Phase Transitions in High-Dimensional Generalized Linear Models](https://mlsanity.com/paper/1708.03395/) (2017)
- [The role of regularization in classification of high-dimensional noisy Gaussian mixture](https://mlsanity.com/paper/2002.11544/) (2020)
- [Learning Gaussian Mixtures with Generalised Linear Models: Precise Asymptotics in High-dimensions](https://mlsanity.com/paper/2106.03791/) (2021)
- [Generalization error in high-dimensional perceptrons: Approaching Bayes error with convex optimization](https://mlsanity.com/paper/2006.06560/) (2020)
- [Theoretical Insights Into Multiclass Classification: A High-dimensional Asymptotic View](https://mlsanity.com/paper/2011.07729/) (2020)
- [Asymptotic Bayes risk for Gaussian mixture in a semi-supervised setting](https://mlsanity.com/paper/1907.03792/) (2019)
- [Phase transitions and optimal algorithms in high-dimensional Gaussian mixture clustering](https://mlsanity.com/paper/1610.02918/) (2016)
- [Consistent Semi-Supervised Graph Regularization for High Dimensional Data](https://mlsanity.com/paper/2006.07575/) (2020)
- [PCA-based Multi Task Learning: a Random Matrix Approach](https://mlsanity.com/paper/2111.00924/) (2021)

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

- [Analysing Multi-Task Regression via Random Matrix Theory with Application to Time Series Forecasting](https://mlsanity.com/paper/2406.10327/) (2024)
- [A Large Dimensional Analysis of Multi-task Semi-Supervised Learning](https://mlsanity.com/paper/2402.13646/) (2024)
- [Asymptotic Bayes risk of semi-supervised learning with uncertain labeling](https://mlsanity.com/paper/2403.17767/) (2024)
- [Optimal Exact Recovery in Semi-Supervised Learning: A Study of Spectral Methods and Graph Convolutional Networks](https://mlsanity.com/paper/2412.13754/) (2024)

## Abstract (arXiv)

The article considers semi-supervised multitask learning on a Gaussian mixture model (GMM). Using methods from statistical physics, we compute the asymptotic Bayes risk of each task in the regime of large datasets in high dimension, from which we analyze the role of task similarity in learning and evaluate the performance gain when tasks are learned together rather than separately. In the supervised case, we derive a simple algorithm that attains the Bayes optimal performance.