The paper introduces Deep Partial Least Squares (DPLS) for empirical asset pricing, a novel methodology that combines partial least squares (PLS) with deep learning to estimate non-linear factor models. DPLS addresses the limitation of traditional linear factor models by capturing non-linear risk factor structure, which arises when asset returns and factors are non-Gaussian. The method uses PLS to project both firm characteristics and asset returns onto a small set of latent factors, maximizing covariance between them. Then, a deep neural network learns the non-linear mapping from factor loadings to returns, enabling the model to capture interaction effects and higher-order terms. This approach advances deep learning in asset pricing by moving beyond linear stochastic discount factors and Gaussian assumptions.

Empirically, the DPLS factor model is applied to monthly returns and firm characteristics of 3290 Russell 1000 stocks from December 1989 to January 2018. The model demonstrates superior predictive performance compared to LASSO and plain deep learning, achieving information ratios approximately 1.2 times greater. Additionally, DPLS reduces network training times due to its more parsimonious architecture, as PLS effectively reduces dimensionality. The model also provides interpretability by identifying the most important latent factors and firm characteristics, and by characterizing anomalies through both linear risk exposures and interaction effects. Overall, DPLS offers a powerful and interpretable framework for empirical asset pricing that balances predictive accuracy with economic theory.