Machine Learning for Asset Managers Toolbox

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Introduction

I started this work with the personal goal to master and test the concepts described in the book Machine Learning for Asset Managers.

This repository contains the implementation of these concepts and answers to the exercises.

Disclaimers

• This work is licensed under the Apache License Version 2.0 unless specified otherwise.

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Getting Started

Clone this repository locally:

git clone https://github.com/samatix/ml-asset-managers.git
pip install -r requirements.txt
python setup.py build_ext --inplace

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Available Utilities

Entropy Calculation

• Initial inputs

import numpy as np 

from src import entropy

x = np.array([
            -1.068975469981432, 0.37745946782651796, -1.4503714157560206,
            -2.0189938521856945, -0.6720045848322777, 1.0585123584971843,
            0.10590926320793637, 2.8321554887980236, -1.6415040483953403,
            0.8256354839964547
        ]) 

e = np.array([
            -0.4355421091328046, 0.08072721876416557, -0.18228820347023844,
            0.1553520158613207, -0.07595958194802123, -1.5300711428677072,
            -1.482275653452137, -0.035086362949407486, -1.3101091248694603,
            -0.7693024441943448
        ])

• Calculate the marginal entropy

marginal = entropy.marginal(x, bins=10)
assert marginal == 1.8866967846580784

• Calculate the join entropy

joint = entropy.joint(x, e)
assert joint == 1.8343719702816235

• Calculate the mutual information (normalized as well) When the variables are independent

# Independent Variables
y = 0 * x + e
mi = entropy.mutual_info(x, y, bins=5)
nmi = entropy.mutual_info(x, y, bins=5, norm=True)
corr = np.corrcoef(x, y)[0, 1]

# No correlation and normalized mutual information is low (small
# observations set)
assert corr == -0.08756232304451231
assert nmi == 0.4175336691560972

When the variables are linearly correlated

# Linear Correlation
y = 100 * x + e
nmi = entropy.mutual_info(x, y, bins=5, norm=True)
corr = np.corrcoef(x, y)[0, 1]

# Linear correlation between x and y both the correlation and
# normalized mutual information are close to 1
assert corr == 0.9999901828471118
assert nmi, 1.0000000000000002

When the variables are non-linearly correlated

# Linear Correlation
y = 100 * abs(x) + e
nmi = entropy.mutual_info(x, y, bins=5, norm=True)
corr = np.corrcoef(x, y)[0, 1]

# Non linear correlation between x and y. Correlation is close to 0
# but the normalized mutual information detects correlation betweeen x and y
assert corr == 0.13607916658759206
assert nmi, 1.0000000000000002

• Calculate the conditional entropy

conditional = entropy.conditional(x, e)

# H(X) >= H(X|Y)
assert entropy.marginal(x) >= conditional

# H(X|X) = 0
assert entropy.conditional(x, x) == 0

assert conditional == 0.8047189562170498

• Calculate the variation of information (normalized as well) (similar to the previous example of mutual information)

• The possibility to use the optimal number of bins when calling the previous functions with bins=None

numb_bins = entropy.num_bins(n_obs=10)
assert numb_bins, 3

numb_bins = entropy.num_bins(n_obs=100)
assert numb_bins, 7

# For joint entropy with zero correlation
numb_bins = entropy.num_bins(n_obs=10, corr=0)
assert numb_bins, 3

# For joint entropy with total correlation
numb_bins = entropy.num_bins(n_obs=10, corr=1)
# In this case, we return the num_bins using corr=None 

# For joint entropy with 0.5 correlation
numb_bins = entropy.num_bins(n_obs=10, corr=0.99)
assert numb_bins, 7

Fixtures

• Generate a random block correlation matrix

from src.testing.fixtures import CorrelationFactory

cf = CorrelationFactory(
                        n_cols=10,
                        n_blocks=4,
                        sigma_b=0.5,
                        sigma_n=1,
                        seed=None
                    )

corr = cf.random_block_corr()

Notebooks

• Chapter 2 on distances summary and exercises tentative solutions

Bibliography

• López de Prado, M. (2020). Machine Learning for Asset Managers (Elements in Quantitative Finance). Cambridge: Cambridge University Press. doi:10.1017/9781108883658