# Selective Inference for Sparse Multitask Regression with Applications in Neuroimaging

arXiv: https://arxiv.org/abs/2205.14220 · HTML: https://mlsanity.com/paper/2205.14220/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 85 references that are in the map.
- First posted on arXiv 27 May 2022.

## Builds on (most cited first, 11 of 11)

- [A Survey on Multi-Task Learning](https://mlsanity.com/paper/1707.08114/) (2017)
- [Optimal Inference After Model Selection](https://mlsanity.com/paper/1410.2597/) (2014)
- [Computing Valid p-values for Image Segmentation by Selective Inference](https://mlsanity.com/paper/1906.00629/) (2019)
- [More powerful post-selection inference, with application to the Lasso](https://mlsanity.com/paper/1801.09037/) (2018)
- [Approximate selective inference via maximum likelihood](https://mlsanity.com/paper/1902.07884/) (2019)
- [On overfitting and post-selection uncertainty assessments](https://mlsanity.com/paper/1712.02379/) (2017)
- [Sparse Overlapping Sets Lasso for Multitask Learning and its Application to fMRI Analysis](https://mlsanity.com/paper/1311.5422/) (2013)
- [On Multiplicative Multitask Feature Learning](https://mlsanity.com/paper/1610.07563/) (2016)
- [Integrative Bayesian models using Post-selective Inference: a case study in Radiogenomics](https://mlsanity.com/paper/2004.12012/) (2020)
- [Scalable methods for Bayesian selective inference](https://mlsanity.com/paper/1703.06176/) (2017)
- [Treatment Effect Estimation with Efficient Data Aggregation](https://mlsanity.com/paper/2203.12726/) (2022)

## Built on by (most cited first, 1 of 1)

- [Statistical Testing for Multiple Instance Learning via Selective Inference with Applications to Computational Pathology](https://mlsanity.com/paper/2609.31712/) (2026)

## Abstract (arXiv)

Multi-task learning is frequently used to model a set of related response variables from the same set of features, improving predictive performance and modeling accuracy relative to methods that handle each response variable separately. Despite the potential of multi-task learning to yield more powerful inference than single-task alternatives, prior work in this area has largely omitted uncertainty quantification. Our focus in this paper is a common multi-task problem in neuroimaging, where the goal is to understand the relationship between multiple cognitive task scores (or other subject-level assessments) and brain connectome data collected from imaging. We propose a framework for selective inference to address this problem, with the flexibility to: (i) jointly identify the relevant covariates for each task through a sparsity-inducing penalty, and (ii) conduct valid inference in a model based on the estimated sparsity structure. Our framework offers a new conditional procedure for inference, based on a refinement of the selection event that yields a tractable selection-adjusted likelihood. This gives an approximate system of estimating equations for maximum likelihood inference, solvable via a single convex optimization problem, and enables us to efficiently form confidence intervals with approximately the correct coverage. Applied to both simulated data and data from the Adolescent Brain Cognitive Development (ABCD) study, our selective inference methods yield tighter confidence intervals than commonly used alternatives, such as data splitting. We also demonstrate through simulations that multi-task learning with selective inference can more accurately recover true signals than single-task methods.