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We propose a novel latent factor model for recommending product size ts {Small, Fit, Large} to customers. Latent factors for customers and products in our model correspond to their physical true size, and are learnt from past product purchase and returns data. e outcome for a customer, product pair is predicted based on the di erence between customer and product true sizes, and e cient algorithms are proposed for computing customer and product true size values that minimize two loss function variants. In experiments with Amazon shoe datasets, we show that our latent factor models incorporating personas, and leveraging return codes show a 17-21% AUC improvement compared to baselines. In an online A/B test, our algorithms show an improvement of 0.49% in percentage of Fit transactions over control.

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