# A Bayesian approach to multi-task learning with network lasso

@article{Shimamura2021ABA, title={A Bayesian approach to multi-task learning with network lasso}, author={Kaito Shimamura and Shuichi Kawano}, journal={ArXiv}, year={2021}, volume={abs/2110.09040} }

Network lasso is a method for solving a multi-task learning problem through the regularized maximum likelihood method. A characteristic of network lasso is setting a different model for each sample. The relationships among the models are represented by relational coefficients. A crucial issue in network lasso is to provide appropriate values for these relational coefficients. In this paper, we propose a Bayesian approach to solve multi-task learning problems by network lasso. This approach…

## References

SHOWING 1-10 OF 18 REFERENCES

The Bayesian Lasso

- Mathematics
- 2008

The Lasso estimate for linear regression parameters can be interpreted as a Bayesian posterior mode estimate when the regression parameters have independent Laplace (i.e., double-exponential) priors.…

Classifying Partially Labeled Networked Data VIA Logistic Network Lasso

- Computer Science, MathematicsICASSP 2020 - 2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
- 2020

This work applies the network Lasso to classify partially labeled data points which are characterized by high-dimensional feature vectors to solve a regularized empirical risk minimization problem using the total variation of a classifier as a regularizer.

Localized Lasso for High-Dimensional Regression

- Mathematics, Computer ScienceAISTATS
- 2017

The localized Lasso is introduced, which is suited for learning models that are both interpretable and have a high predictive power in problems with high dimensionality and small sample size, and a simple yet efficient iterative least-squares based optimization procedure is proposed.

Multi-Task Feature Learning

- Mathematics, Computer ScienceNIPS
- 2006

The method builds upon the well-known 1-norm regularization problem using a new regularizer which controls the number of learned features common for all the tasks, and develops an iterative algorithm for solving it.

Inference with normal-gamma prior distributions in regression problems

- Mathematics
- 2010

This paper considers the efiects of placing an absolutely continuous prior distribution on the regression coe-cients of a linear model. We show that the posterior expectation is a matrix-shrunken…

Convex multi-task feature learning

- Mathematics, Computer ScienceMachine Learning
- 2007

It is proved that the method for learning sparse representations shared across multiple tasks is equivalent to solving a convex optimization problem for which there is an iterative algorithm which converges to an optimal solution.

Network Lasso: Clustering and Optimization in Large Graphs

- Computer Science, MedicineKDD
- 2015

The network lasso is introduced, a generalization of the group lasso to a network setting that allows for simultaneous clustering and optimization on graphs and an algorithm based on the Alternating Direction Method of Multipliers (ADMM) to solve this problem in a distributed and scalable manner.

Shrink Globally, Act Locally: Sparse Bayesian Regularization and Prediction

- Mathematics
- 2012

We study the classic problem of choosing a prior distribution for a location parameter β = (β1, . . . , βp) as p grows large. First, we study the standard “global-local shrinkage” approach, based on…

Alternative prior distributions for variable selection with very many more variables than observations

- Mathematics
- 2005

The problem of variable selection in regression and the generalised linear model is addressed.
We adopt a Bayesian approach with priors for the regression coefficients that are
scale mixtures of…

Dirichlet–Laplace Priors for Optimal Shrinkage

- Mathematics, MedicineJournal of the American Statistical Association
- 2015

This article proposes a new class of Dirichlet–Laplace priors, which possess optimal posterior concentration and lead to efficient posterior computation.