# Deep Functional Factor Models: Forecasting High-Dimensional Functional Time Series via Bayesian Nonparametric Factorization

arXiv: https://arxiv.org/abs/2305.14543 · HTML: https://mlsanity.com/paper/2305.14543/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 46 references that are in the map.
- First posted on arXiv 23 May 2023.

## Builds on (most cited first, 21 of 21)

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- [On the Properties of Neural Machine Translation: Encoder-Decoder Approaches](https://mlsanity.com/paper/1409.1259/) (2014)
- [Time Series Forecasting With Deep Learning: A Survey](https://mlsanity.com/paper/2004.13408/) (2020)
- [Deep Kernel Learning](https://mlsanity.com/paper/1511.02222/) (2015)
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- [Priors in Bayesian Deep Learning: A Review](https://mlsanity.com/paper/2105.06868/) (2021)
- [Learning deep kernels for exponential family densities](https://mlsanity.com/paper/1811.08357/) (2018)
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- [Heterogeneous Multi-output Gaussian Process Prediction](https://mlsanity.com/paper/1805.07633/) (2018)
- [Learning Scalable Deep Kernels with Recurrent Structure](https://mlsanity.com/paper/1610.08936/) (2016)
- [Deep Learning for Functional Data Analysis with Adaptive Basis Layers](https://mlsanity.com/paper/2106.10414/) (2021)
- [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)
- [EEGNN: Edge Enhanced Graph Neural Network with a Bayesian Nonparametric Graph Model](https://mlsanity.com/paper/2208.06322/) (2022)
- [CATVI: Conditional and Adaptively Truncated Variational Inference for Hierarchical Bayesian Nonparametric Models](https://mlsanity.com/paper/2001.04508/) (2020)
- [An autocovariance-based learning framework for high-dimensional functional time series](https://mlsanity.com/paper/2008.12885/) (2020)
- [Factor modelling for high-dimensional functional time series](https://mlsanity.com/paper/2112.13651/) (2021)

## Abstract (arXiv)

This paper introduces the Deep Functional Factor Model (DF2M), a Bayesian nonparametric model designed for analysis of high-dimensional functional time series. DF2M is built upon the Indian Buffet Process and the multi-task Gaussian Process, incorporating a deep kernel function that captures non-Markovian and nonlinear temporal dynamics. Unlike many black-box deep learning models, DF2M offers an explainable approach to utilizing neural networks by constructing a factor model and integrating deep neural networks within the kernel function. Additionally, we develop a computationally efficient variational inference algorithm to infer DF2M. Empirical results from four real-world datasets demonstrate that DF2M provides better explainability and superior predictive accuracy compared to conventional deep learning models for high-dimensional functional time series.