# Bayesian functional linear regression with sparse step functions

arXiv: https://arxiv.org/abs/1604.08403 · HTML: https://mlsanity.com/paper/1604.08403/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Apr 2016.

## Built on by (most cited first, 2 of 2)

- [Non-stationary Gaussian process discriminant analysis with variable selection for high-dimensional functional data](https://mlsanity.com/paper/2109.14171/) (2021)
- [Bayesian adaptive and interpretable functional regression for exposure profiles](https://mlsanity.com/paper/2203.00784/) (2022)

## Abstract (arXiv)

The functional linear regression model is a common tool to determine the relationship between a scalar outcome and a functional predictor seen as a function of time. This paper focuses on the Bayesian estimation of the support of the coefficient function. To this aim we propose a parsimonious and adaptive decomposition of the coefficient function as a step function, and a model including a prior distribution that we name Bayesian functional Linear regression with Sparse Step functions (Bliss). The aim of the method is to recover areas of time which influences the most the outcome. A Bayes estimator of the support is built with a specific loss function, as well as two Bayes estimators of the coefficient function, a first one which is smooth and a second one which is a step function. The performance of the proposed methodology is analysed on various synthetic datasets and is illustrated on a black P'erigord truffle dataset to study the influence of rainfall on the production.