# Deep Learning in Characteristics-Sorted Factor Models

arXiv: https://arxiv.org/abs/1805.01104 · HTML: https://mlsanity.com/paper/1805.01104/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 May 2018.

## Built on by (most cited first, 7 of 7)

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- [Non-linear dimension reduction in factor-augmented vector autoregressions](https://mlsanity.com/paper/2309.04821/) (2023)
- [LambdaRankIC: Directly Optimizing Rank IC for Financial Prediction](https://mlsanity.com/paper/2605.00501/) (2026)
- [Natural Gradient Hybrid Variational Inference with Application to Deep Mixed Models](https://mlsanity.com/paper/2302.13536/) (2023)
- [High Dimensional Time Series Regression Models: Applications to Statistical Learning Methods](https://mlsanity.com/paper/2308.16192/) (2023)
- [PEARL: Performance-Enhanced Aggregated Representation Learning](https://mlsanity.com/paper/2509.24312/) (2025)
- [Portfolio Optimization Proxies under Label Scarcity and Regime Shifts via Bayesian and Deterministic Students under Semi-Supervised Sandwich Training](https://mlsanity.com/paper/2604.14206/) (2026)

## Abstract (arXiv)

This paper presents an augmented deep factor model that generates latent factors for cross-sectional asset pricing. The conventional security sorting on firm characteristics for constructing long-short factor portfolio weights is nonlinear modeling, while factors are treated as inputs in linear models. We provide a structural deep learning framework to generalize the complete mechanism for fitting cross-sectional returns by firm characteristics through generating risk factors -- hidden layers. Our model has an economic-guided objective function that minimizes aggregated realized pricing errors. Empirical results on high-dimensional characteristics demonstrate robust asset pricing performance and strong investment improvements by identifying important raw characteristic sources.