Spatiotemporal factor models for functional data with application to population map forecast

TL;DR

This paper introduces a Bayesian spatiotemporal factor model for functional data, specifically applied to forecasting hourly population changes in Tokyo, combining FDA and factor analysis for improved prediction and interpretability.

Contribution

The paper develops a novel Bayesian spatiotemporal factor model that incorporates functional data analysis and sparse factor loadings for population forecasting.

Findings

The model achieves high predictive accuracy on population data.

Sparse factor loadings enhance interpretability of spatial structures.

Flexibility allows incorporation of additional time series features.

Abstract

The proliferation of mobile devices has led to the collection of large amounts of population data. This situation has prompted the need to utilize this rich, multidimensional data in practical applications. In response to this trend, we have integrated functional data analysis (FDA) and factor analysis to address the challenge of predicting hourly population changes across various districts in Tokyo. Specifically, by assuming a Gaussian process, we avoided the large covariance matrix parameters of the multivariate normal distribution. In addition, the data were both time and spatially dependent between districts. To capture these characteristics, a Bayesian factor model was introduced, which modeled the time series of a small number of common factors and expressed the spatial structure through factor loading matrices. Furthermore, the factor loading matrices were made identifiable and sparse to ensure the interpretability of the model. We also proposed a Bayesian shrinkage method as a systematic approach for factor selection. Through numerical experiments and data analysis, we investigated the predictive accuracy and interpretability of our proposed method. We concluded that the flexibility of the method allows for the incorporation of additional time series features, thereby improving its accuracy.