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A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments

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Probability Forecast Combination via Entropy Regularized Wasserstein Distance.

Ryan Cumings-Menon¹, Minchul Shin²

¹The US Census Bureau, 4600 Silver Hill Rd, Suitland-Silver Hill, MD 20746, USA.

Entropy (Basel, Switzerland)

|December 8, 2020

Summary

This summary is machine-generated.

We introduce novel methods for combining probability and density forecasts using entropy regularized Wasserstein distance. This approach enhances predictive accuracy for economic indicators like U.S. inflation.

Keywords:

Wasserstein distance density forecasting entropy regularization forecast combination model combination optimal transport quantile aggregation

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Area of Science:

Econometrics
Statistical modeling
Machine learning

Background:

Combining forecasts is crucial for improving predictive accuracy.
Existing methods may not optimally leverage distributional information.
Wasserstein distance offers a powerful tool for comparing probability distributions.

Purpose of the Study:

To develop and theoretically characterize new probability and density forecast combination methods.
To demonstrate the benefits of entropy regularization in forecast combination.
To provide a practical method for parameter selection and apply it to U.S. inflation forecasting.

Main Methods:

Utilizing entropy regularized Wasserstein distance for forecast combination.
Theoretical analysis of the regularized Wasserstein barycenter for Gaussian densities.
Developing a method for selecting the regularization tuning parameter.
Empirical application to U.S. inflation rate density forecasting.

Main Results:

The regularized Wasserstein barycenter of Gaussian densities is shown to be Gaussian.
A method for computing the mean and variance-covariance matrix of the combined density is provided.
Entropy regularization is demonstrated to improve the predictive power of combined density forecasts.
The proposed method shows improved forecast quality for U.S. inflation compared to unregularized methods.

Conclusions:

Entropy regularized Wasserstein distance provides a robust framework for forecast combination.
The proposed methods offer theoretical and practical advantages for density forecasting.
Regularization enhances predictive accuracy, particularly in economic applications like inflation forecasting.