# Semiparametric Functional Factor Models with Bayesian Rank Selection

arXiv: https://arxiv.org/abs/2108.02151 · HTML: https://mlsanity.com/paper/2108.02151/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Aug 2021.

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

- [Overfitted high-dimensional matrix factorizations via adaptive spectral shrinkage](https://mlsanity.com/paper/2606.19540/) (2026)
- [Generalized Cumulative Shrinkage Process Priors with Applications to Sparse Bayesian Factor Analysis](https://mlsanity.com/paper/2303.00473/) (2023)

## Abstract (arXiv)

Functional data are frequently accompanied by a parametric template that describes the typical shapes of the functions. However, these parametric templates can incur significant bias, which undermines both utility and interpretability. To correct for model misspecification, we augment the parametric template with an infinite-dimensional nonparametric functional basis. The nonparametric basis functions are learned from the data and constrained to be orthogonal to the parametric template, which preserves distinctness between the parametric and nonparametric terms. This distinctness is essential to prevent functional confounding, which otherwise induces severe bias for the parametric terms. The nonparametric factors are regularized with an ordered spike-and-slab prior that provides consistent rank selection and satisfies several appealing theoretical properties. The versatility of the proposed approach is illustrated through applications to synthetic data, human motor control data, and dynamic yield curve data. Relative to parametric and semiparametric alternatives, the proposed semiparametric functional factor model eliminates bias, reduces excessive posterior and predictive uncertainty, and provides reliable inference on the effective number of nonparametric terms--all with minimal additional computational costs.