# Sequential Adaptive Priors for Orthogonal Functions

arXiv: https://arxiv.org/abs/2508.15552 · HTML: https://mlsanity.com/paper/2508.15552/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 27 references that are in the map.
- First posted on arXiv 21 Aug 2025.

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

- [Orthogonal Random Features](https://mlsanity.com/paper/1610.09072/) (2016)
- [Orthogonal Gaussian process models](https://mlsanity.com/paper/1611.00203/) (2016)
- [Bayesian Repulsive Gaussian Mixture Model](https://mlsanity.com/paper/1703.09061/) (2017)
- [Bayesian Monotone Regression using Gaussian Process Projection](https://mlsanity.com/paper/1306.4041/) (2013)
- [Bayesian Constraint Relaxation](https://mlsanity.com/paper/1801.01525/) (2018)
- [Bayesian Inference for Stationary Points in Gaussian Process Regression Models for Event-Related Potentials Analysis](https://mlsanity.com/paper/2009.07745/) (2020)
- [Bayesian Functional Principal Components Analysis via Variational Message Passing](https://mlsanity.com/paper/2104.00645/) (2021)
- [Bayesian modeling of nearly mutually orthogonal processes](https://mlsanity.com/paper/2205.12361/) (2022)
- [Spatiotemporal factor models for functional data with application to population map forecast](https://mlsanity.com/paper/2302.04412/) (2023)
- [Similarity-based Random Partition Distribution for Clustering Functional Data](https://mlsanity.com/paper/2308.01704/) (2023)
- [Prior distributions for structured semi-orthogonal matrices](https://mlsanity.com/paper/2501.10263/) (2025)

## Abstract (arXiv)

We propose a novel class of prior distributions for sequences of orthogonal functions, which are frequently required in various statistical models such as functional principal component analysis (FPCA). Our approach constructs priors sequentially by imposing adaptive orthogonality constraints through a hierarchical formulation of conditionally normal distributions. The orthogonality is controlled via hyperparameters, allowing for flexible trade-offs between exactness and smoothness, which can be learned from the observed data. We illustrate the properties of the proposed prior and show that it leads to nearly orthogonal posterior estimates. The proposed prior is employed in Bayesian FPCA, providing more interpretable principal functions and efficient low-rank representations. Through simulation studies and analysis of human mobility data in Tokyo, we demonstrate the superior performance of our approach in inducing orthogonality and improving functional component estimation.