# Matrix Completion of World Trade

arXiv: https://arxiv.org/abs/2109.03930 · HTML: https://mlsanity.com/paper/2109.03930/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 45 references that are in the map.
- First posted on arXiv 8 Sep 2021.

## Builds on (most cited first, 7 of 7)

- [Matrix Completion and Low-Rank SVD via Fast Alternating Least Squares](https://mlsanity.com/paper/1410.2596/) (2014)
- [Sampling Permutations for Shapley Value Estimation](https://mlsanity.com/paper/2104.12199/) (2021)
- [Machine Learning Methods Economists Should Know About](https://mlsanity.com/paper/1903.10075/) (2019)
- [Missing Not at Random in Matrix Completion: The Effectiveness of Estimating Missingness Probabilities Under a Low Nuclear Norm Assumption](https://mlsanity.com/paper/1910.12774/) (2019)
- [Product Progression: a machine learning approach to forecasting industrial upgrading](https://mlsanity.com/paper/2105.15018/) (2021)
- [A change of perspective in network centrality](https://mlsanity.com/paper/1805.08740/) (2018)
- [Enhancing countries' fitness with recommender systems on the international trade network](https://mlsanity.com/paper/1904.02412/) (2019)

## Abstract (arXiv)

This work applies Matrix Completion (MC) -- a class of machine-learning methods commonly used in the context of recommendation systems -- to analyse economic complexity. MC is applied to reconstruct the Revealed Comparative Advantage (RCA) matrix, whose elements express the relative advantage of countries in given classes of products, as evidenced by yearly trade flows. A high-accuracy binary classifier is derived from the application of MC, with the aim of discriminating between elements of the RCA matrix that are, respectively, higher or lower than one. We introduce a novel Matrix cOmpletion iNdex of Economic complexitY (MONEY) based on MC, which is related to the predictability of countries' RCA (the lower the predictability, the higher the complexity). Differently from previously-developed indices of economic complexity, the MONEY index takes into account the various singular vectors of the matrix reconstructed by MC, whereas other indices are based only on one/two eigenvectors of a suitable symmetric matrix, derived from the RCA matrix. Finally, MC is compared with a state-of-the-art economic complexity index (GENEPY). We show that the false positive rate per country of a binary classifier constructed starting from the average entry-wise output of MC can be used as a proxy of GENEPY.