# Probabilistic Functional Neural Networks

arXiv: https://arxiv.org/abs/2503.21585 · HTML: https://mlsanity.com/paper/2503.21585/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 27 references that are in the map.
- First posted on arXiv 27 Mar 2025.

## Builds on (most cited first, 12 of 12)

- [Sequence to Sequence Learning with Neural Networks](https://mlsanity.com/paper/1409.3215/) (2014)
- [An Introduction to Variational Autoencoders](https://mlsanity.com/paper/1906.02691/) (2019)
- [Recurrent Neural Networks for Time Series Forecasting: Current Status and Future Directions](https://mlsanity.com/paper/1909.00590/) (2019)
- [Structure Discovery in Nonparametric Regression through Compositional Kernel Search](https://mlsanity.com/paper/1302.4922/) (2013)
- [Multivariate Functional Principal Component Analysis for Data Observed on Different (Dimensional) Domains](https://mlsanity.com/paper/1509.02029/) (2015)
- [Functional time series prediction under partial observation of the future curve](https://mlsanity.com/paper/1906.00281/) (2019)
- [High-dimensional functional time series forecasting: An application to age-specific mortality rates](https://mlsanity.com/paper/1810.01195/) (2018)
- [Clustering and Forecasting Multiple Functional Time Series](https://mlsanity.com/paper/2201.01024/) (2022)
- [Sparsely Observed Functional Time Series: Estimation and Prediction](https://mlsanity.com/paper/1811.06340/) (2018)
- [On projection methods for functional time series forecasting](https://mlsanity.com/paper/2105.04399/) (2021)
- [Detection and Estimation of Structural Breaks in High-Dimensional Functional Time Series](https://mlsanity.com/paper/2304.07003/) (2023)
- [Forecasting density-valued functional panel data](https://mlsanity.com/paper/2403.13340/) (2024)

## Abstract (arXiv)

High-dimensional functional time series (HDFTS) are often characterized by nonlinear trends and high spatial dimensions. Such data poses unique challenges for modeling and forecasting due to the nonlinearity, nonstationarity, and high dimensionality. We propose a novel probabilistic functional neural network (ProFnet) to address these challenges. ProFnet integrates the strengths of feedforward and deep neural networks with probabilistic modeling. The model generates probabilistic forecasts using Monte Carlo sampling and also enables the quantification of uncertainty in predictions. While capturing both temporal and spatial dependencies across multiple regions, ProFnet offers a scalable and unified solution for large datasets. Applications to Japan's mortality rates demonstrate superior performance. This approach enhances predictive accuracy and provides interpretable uncertainty estimates, making it a valuable tool for forecasting complex high-dimensional functional data and HDFTS.