How deep generative models can help quants reduce the risk of overfitting?

1. How deep generative models can help quants reduce the risk of overﬁtting? Talk at QuantUniversity Autumn School 2020 Gautier Marti HKML Research 27 October 2020 Gautier Marti (HKML Research) Applications of GANs for Quants 27 October 2020 1 / 59

2. Table of contents 1 Introduction 2 GANs explained GANs Milestones & Major Achievements How do GANs work? 3 Applications of GANs for Quants Generating Synthetic Datasets to Avoid Strategy Overﬁtting Generating Alternative Realistic Historical Paths for Risk Estimation 4 Current State of the Art and Limitations 5 Conclusion and Questions? Gautier Marti (HKML Research) Applications of GANs for Quants 27 October 2020 2 / 59

3. Section 1 Introduction Gautier Marti (HKML Research) Applications of GANs for Quants 27 October 2020 3 / 59

4. Generative Adversarial Network’s Deﬁnition & Goal (Deep) generative models are a broad class of models. For the sake of clarity, we will only consider Generative Adversarial Networks in this presentation. Deﬁnition: Generative Adversarial Network (GAN) A generative adversarial network (GAN) is a class of machine learning frame- works where two neural networks (usually known as the generator and the discriminator) contest with each other in a zero-sum game (i.e. one agent’s gain is another agent’s loss). Main purpose of a GAN: Generating realistic synthetic data Given a training set, this technique learns to generate new data with the same statistics as the training set. Gautier Marti (HKML Research) Applications of GANs for Quants 27 October 2020 4 / 59

5. Introduction (3 min. video) https://www.youtube.com/watch?v=97B8tuHwLY0 Gautier Marti (HKML Research) Applications of GANs for Quants 27 October 2020 5 / 59

6. Scope of the presentation In this talk, we will focus on doing a review of GANs success so far (mostly image generation), explaining how Generative Adversarial Networks (GANs) work. Then, we will present applications of these models for quant researchers / traders use cases. Finally, we shall brieﬂy discuss the current limitations and challenges to be overcome for a broader adoption of these models in the industry. Gautier Marti (HKML Research) Applications of GANs for Quants 27 October 2020 6 / 59

7. Section 2 GANs explained Gautier Marti (HKML Research) Applications of GANs for Quants 27 October 2020 7 / 59

8. Subsection 1 GANs Milestones & Major Achievements Gautier Marti (HKML Research) Applications of GANs for Quants 27 October 2020 8 / 59

9. GANs: A relatively new Deep Learning model (2014) Goodfellow, Ian, et al. “Generative adversarial nets.” Advances in neural information processing systems. 2014. Cited by 22354 papers as of 18 September 2020. Gautier Marti (HKML Research) Applications of GANs for Quants 27 October 2020 9 / 59

10. Text to Photo-realistic Image Synthesis (2016) https://arxiv.org/pdf/1612.03242.pdf Gautier Marti (HKML Research) Applications of GANs for Quants 27 October 2020 10 / 59

11. Deepfakes (2017) Ctrl Shift Face (YouTube channel) https://www.youtube.com/channel/UCKpH0CKltc73e4wh0_pgL3g You Won’t Believe What Obama Says In This Video! https://www.youtube.com/watch?v=cQ54GDm1eL0 Gautier Marti (HKML Research) Applications of GANs for Quants 27 October 2020 11 / 59

12. Edmond de Belamy (2018) Created by 3 students First artwork created using Artiﬁcial Intelligence to be featured in a Christie’s auction Sold for USD 432,500 Signed minG maxD Ex [log(D(x))] + Ez [log(1 − D(G(z)))] In French, “bel ami” means “good fellow”, a pun-tribute to Ian Goodfellow, the creator of GANs Gautier Marti (HKML Research) Applications of GANs for Quants 27 October 2020 12 / 59

13. StyleGAN (2019) & StyleGAN2 (2020) GANs can generate realistic fake human faces: Give it a try: https://thispersondoesnotexist.com/ NVIDIA StyleGAN paper: https://arxiv.org/pdf/1812.04948.pdf NVIDIA StyleGAN2 paper: https://arxiv.org/pdf/1912.04958.pdf Remark. In December 2019, Facebook took down a network of accounts with false identities, and mentioned that some of them had used proﬁle pictures created with artiﬁcial intelligence. Gautier Marti (HKML Research) Applications of GANs for Quants 27 October 2020 13 / 59

14. Speech2Face & Wav2Pix (2019) GANs conditioned on speech of a person can output a realistic face with its correct gender, ethnicity, and approximate age: Relevant papers: Wav2Pix: https://arxiv.org/pdf/1903.10195.pdf Speech2Face: https://arxiv.org/pdf/1905.09773.pdf Gautier Marti (HKML Research) Applications of GANs for Quants 27 October 2020 14 / 59

15. GameGAN (2020) GameGAN is able to learn Pac-Man dynamics and produce a visually consistent simulation of the game: NVIDIA paper https://arxiv.org/pdf/2005.12126.pdf https://www.youtube.com/watch?v=4OzJUNsPx60 Gautier Marti (HKML Research) Applications of GANs for Quants 27 October 2020 15 / 59

16. Subsection 2 How do GANs work? Gautier Marti (HKML Research) Applications of GANs for Quants 27 October 2020 16 / 59

17. A GAN basic architecture Gautier Marti (HKML Research) Applications of GANs for Quants 27 October 2020 17 / 59

18. GAN training – step by step tutorial Gautier Marti (HKML Research) Applications of GANs for Quants 27 October 2020 18 / 59

40. Conditional Generative Adversarial Nets Seminal paper: https://arxiv.org/pdf/1411.1784.pdf Gautier Marti (HKML Research) Applications of GANs for Quants 27 October 2020 40 / 59

41. Conditional Generative Adversarial Nets Gautier Marti (HKML Research) Applications of GANs for Quants 27 October 2020 41 / 59

42. Section 3 Applications of GANs for Quants Gautier Marti (HKML Research) Applications of GANs for Quants 27 October 2020 42 / 59

43. Subsection 1 Generating Synthetic Datasets to Avoid Strategy Overﬁtting Gautier Marti (HKML Research) Applications of GANs for Quants 27 October 2020 43 / 59

44. Strategy Overfitting Scenario In September 2020, a naive or unscrupulous strat presents to his manager a new strategy: The strategy would have initiated a massive short in February 2020, and would have bet big on a rally starting late March 2020. The strat sells the strategy to his manager as able to pick-up early signals of market sell-offs and bounce-backs thanks to advanced machine learning and alternative data (obviously, what else?). The manager, excited, cannot wait but to deploy capital to it. How to fight against this industry-wide fallacy? Well-thought and carefully designed incentives schemes (e.g. reward a sound research framework rather than impressive in-sample backtests) Counterfactual thinking, realistic simulations of alternative paths Gautier Marti (HKML Research) Applications of GANs for Quants 27 October 2020 44 / 59

45. Strategy Overﬁtting – Simulations of Alternative Paths (1) Some alternative data: Second-hand car market in Hong Kong A tabular dataset X Gautier Marti (HKML Research) Applications of GANs for Quants 27 October 2020 45 / 59

46. Strategy Overﬁtting – Simulations of Alternative Paths (2) econ quant idea: When inventory builds up (more people are selling their cars than buying), then the HSI plummets over the next quarter. math quant idea: My black-box ML algorithm predicts that HSI decreases whenever two Ferraris are sold right after a Bugatti Veyron comes to market, based on the given dataset. Using GANs, we can sample new datasets ˆX ∼ X, or even ( ˆX, ˆy) ∼ (X, y), where y can be the HSI performance or any variable we aim at predicting (e.g. market+industry residualized returns of the respective carmakers). Gautier Marti (HKML Research) Applications of GANs for Quants 27 October 2020 46 / 59

47. Strategy Overﬁtting – Simulations of Alternative Paths (3) Method 1: Strategy stability Use a GAN to learn the distribution (X, y) of the tabular data (cf. https://arxiv.org/pdf/1907.00503.pdf) From the calibrated GAN, generate ˆX(n) , ˆy(n) N n=1 synthetic datasets Backtest the strategy on the N datasets, and collect perf. metrics Analyze the perf. metrics; Discard the strategy if not stable. Gautier Marti (HKML Research) Applications of GANs for Quants 27 October 2020 47 / 59

48. Strategy Overﬁtting – Simulations of Alternative Paths (4) Method 1bis: Find whether a strategy is robust and obvious given data As the strat-quant team manager, provide each one of the N quants with a GAN-generated copy of the original data. They have to work on it independently. Will they ﬁnd the same strategy? With roughly the same parameters? If so, the strategy is robust, but also likely to be crowded given the data. Test it, and run it in production, on the original data. Gautier Marti (HKML Research) Applications of GANs for Quants 27 October 2020 48 / 59

49. Strategy Overﬁtting – Simulations of Alternative Paths (5) In Koshiyama et al. (https://arxiv.org/pdf/1901.01751.pdf): Generate N synthetic datasets: Method 2: Strategy ﬁne-tuning Find the parameters which maximize the average perf. over the N datasets Method 2bis: Strategy combination (ensemble models) Fit a model on each of the N datasets Predict using an ensemble of the N trained models GAN vs. Stationary Bootstrap (for generating the N synthetic datasets) Gautier Marti (HKML Research) Applications of GANs for Quants 27 October 2020 49 / 59

50. Subsection 2 Generating Alternative Realistic Historical Paths for Risk Estimation Gautier Marti (HKML Research) Applications of GANs for Quants 27 October 2020 50 / 59

51. Risk-based Portfolio Allocation (1) Scenario You want to systematically allocate capital to your strategies. Literature claims that such or such method works better than all others by providing a dubious backtest. When you horse race the various allocation methods, results are not stable across periods and universes. How can we conclude anything useful? Realistic simulations! Gautier Marti (HKML Research) Applications of GANs for Quants 27 October 2020 51 / 59

52. CorrGAN: Sampling Realistic Financial Correlation Matrices Using Generative Adversarial Networks 6 stylized facts of empirical ﬁnancial correlation matrices Marchenko-Pastur-like distribution, except for: a very large ﬁrst eigenvalue, a couple of other large eigenvalues Perron-Frobenius property positive correlations Hierarchical structure of clusters Scale-free property of the degrees in MST Original paper: https://arxiv.org/pdf/ 1910.09504.pdf Implemented in the MlFinlab python package: https://hudsonthames. org/mlfinlab/ Gautier Marti (HKML Research) Applications of GANs for Quants 27 October 2020 52 / 59

53. Risk-based Portfolio Allocation (2) Method 3: Testing Portfolio Allocation on Alternative Historical Paths Use a GAN to generate realistic synthetic correlation matrices (cf. https://arxiv.org/pdf/1910.09504.pdf) Generate time series verifying the correlation structure Estimate portfolio weights (in-sample), measure out-of-sample risk Analyze performance of the portfolio allocation methods Gautier Marti (HKML Research) Applications of GANs for Quants 27 October 2020 53 / 59

54. Risk-based Portfolio Allocation (3) Question: Can we predict when a method (say the Hierarchical Risk Parity (HRP)) outperforms another one (say naive risk parity)? And why? Method 4: Understanding the outperformance of a method over another Extract features from the underlying correlation matrix Fit a ML model features → outperformance (using train, validation, test datasets) Verify if there is any good predictability Explain the predictions as a function of features Gautier Marti (HKML Research) Applications of GANs for Quants 27 October 2020 54 / 59

55. Risk-based Portfolio Allocation (4) Concrete example: HRP vs. naive risk parity High values for the cophenetic correlation coeﬃcient are characteristic of a strong hierarchical structure. Thus, HRP outperforms naive risk parity when the underlying DGP has a strong hierarchical structure (nested clusters). cf. Jochen Papenbrock recent work for similar applications of Explainable AI (XAI) in ﬁnance (https://firamis.de/) Gautier Marti (HKML Research) Applications of GANs for Quants 27 October 2020 55 / 59

56. Section 4 Current State of the Art and Limitations Gautier Marti (HKML Research) Applications of GANs for Quants 27 October 2020 56 / 59

57. Current State of the Art and Limitations This discussion is by nature technical, but we can highlight the following limitations which are relevant for quants: GANs can generate realistic tabular datasets (2019), but models trained on synthetic data only were shown inferior to the ones trained on the original data We know how to GAN-generate realistic synthetic financial time series (e.g. S&P 500 returns); We know how to GAN-generate realistic synthetic financial correlation matrices (of the S&P 500 constituents, for example); However, we do not know yet how to GAN-generate realistic multivariate financial time series, i.e. verifying both the time series and the cross-sectional stylized facts Gautier Marti (HKML Research) Applications of GANs for Quants 27 October 2020 57 / 59

58. Section 5 Conclusion and Questions? Gautier Marti (HKML Research) Applications of GANs for Quants 27 October 2020 58 / 59

59. Conclusion and Questions? Deep generative models and GANs in particular are an exciting new technology. In ﬁnance, they are actively researched in a few places but results are not widely advertised. We have to rely on top tech companies and academic labs to drive the fundamental understanding and improvements of these models. contact@hkml-research.com Gautier Marti (HKML Research) Applications of GANs for Quants 27 October 2020 59 / 59