Beyond Expectation: Deep Joint Mean and Quantile Regression for Spatiotemporal Problems.

Area of Science:

• Machine Learning
• Deep Learning
• Spatiotemporal Data Analysis

Background:

• Spatiotemporal problems are critical across many research domains.
• Existing deep learning models often focus only on conditional expectations, limiting predictive accuracy.
• A more complete understanding of predictive density is needed for complex spatiotemporal data.

Purpose of the Study:

• To propose a multioutput multiquantile deep learning approach for spatiotemporal problems.
• To jointly model conditional quantiles and the conditional expectation.
• To provide a more comprehensive predictive density for spatiotemporal data.

Main Methods:

• Developed a multioutput multiquantile deep learning framework.
• Applied a multitask learning perspective to quantile regression.
• Utilized two large-scale transportation datasets for empirical validation.

Main Results:

• Successfully addressed the quantile crossing problem in deep learning.
• Significantly outperformed state-of-the-art quantile regression methods.
• Demonstrated improved predictions for conditional expectations through joint modeling.

Conclusions:

• Jointly modeling quantiles and expectation offers a richer predictive density description.
• The proposed method effectively captures heteroscedasticity with minimal computational overhead.
• This approach enhances predictive performance by leveraging multitask learning and regularization effects.