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

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

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?

Section 1
Introduction

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.

Introduction (3 min. video)
https://www.youtube.com/watch?v=97B8tuHwLY0

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.

Section 2
GANs explained

Subsection 1
GANs Milestones & Major Achievements

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.

Text to Photo-realistic Image Synthesis (2016)
https://arxiv.org/pdf/1612.03242.pdf

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

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

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.

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

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

Subsection 2
How do GANs work?

A GAN basic architecture

GAN training – step by step tutorial

Conditional Generative Adversarial Nets
Seminal paper: https://arxiv.org/pdf/1411.1784.pdf

Conditional Generative Adversarial Nets

Section 3
Applications of GANs for Quants

Subsection 1
Generating Synthetic Datasets to Avoid Strategy Overﬁtting

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

Strategy Overﬁtting – Simulations of Alternative Paths (1)
Some alternative data: Second-hand car market in Hong Kong
A tabular dataset X

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).

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.

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.

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)

Subsection 2
Generating Alternative Realistic Historical Paths
for Risk Estimation

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!

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/

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

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

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/)

Section 4
Current State of the Art and Limitations

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

Section 5
Conclusion and Questions?

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

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