# Generative Machine Learning for Multivariate Equity Returns

arXiv: https://arxiv.org/abs/2311.14735 · HTML: https://mlsanity.com/paper/2311.14735/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 28 references that are in the map.
- First posted on arXiv 21 Nov 2023.

## Builds on (most cited first, 14 of 14)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [Pixel Recurrent Neural Networks](https://mlsanity.com/paper/1601.06759/) (2016)
- [Importance Weighted Autoencoders](https://mlsanity.com/paper/1509.00519/) (2015)
- [Accurate Uncertainties for Deep Learning Using Calibrated Regression](https://mlsanity.com/paper/1807.00263/) (2018)
- [Invertible Residual Networks](https://mlsanity.com/paper/1811.00995/) (2018)
- [Learning Likelihoods with Conditional Normalizing Flows](https://mlsanity.com/paper/1912.00042/) (2019)
- [Quant GANs: Deep Generation of Financial Time Series](https://mlsanity.com/paper/1907.06673/) (2019)
- [Multi-Asset Spot and Option Market Simulation](https://mlsanity.com/paper/2112.06823/) (2021)
- [Quasi-Autoregressive Residual (QuAR) Flows](https://mlsanity.com/paper/2009.07419/) (2020)

## Built on by (most cited first, 4 of 4)

- [Universal randomised signatures for generative time series modelling](https://mlsanity.com/paper/2406.10214/) (2024)
- [DELPHYNE: A Pre-Trained Model for General and Financial Time Series](https://mlsanity.com/paper/2506.06288/) (2025)
- [NeuralFactors: A Novel Factor Learning Approach to Generative Modeling of Equities](https://mlsanity.com/paper/2408.01499/) (2024)
- [Denoising ESG: quantifying data uncertainty from missing data with Machine Learning and prediction intervals](https://mlsanity.com/paper/2407.20047/) (2024)

## Abstract (arXiv)

The use of machine learning to generate synthetic data has grown in popularity with the proliferation of text-to-image models and especially large language models. The core methodology these models use is to learn the distribution of the underlying data, similar to the classical methods common in finance of fitting statistical models to data. In this work, we explore the efficacy of using modern machine learning methods, specifically conditional importance weighted autoencoders (a variant of variational autoencoders) and conditional normalizing flows, for the task of modeling the returns of equities. The main problem we work to address is modeling the joint distribution of all the members of the S&P 500, or, in other words, learning a 500-dimensional joint distribution. We show that this generative model has a broad range of applications in finance, including generating realistic synthetic data, volatility and correlation estimation, risk analysis (e.g., value at risk, or VaR, of portfolios), and portfolio optimization.