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Presentation of a real use case at TAJ law firm (Deloitte Paris) of applying Machine learning on ...

Presentation of a real use case at TAJ law firm (Deloitte Paris) of applying Machine learning on accounting to help clients to prepare their tax audit.

- Preparation of a tax audit

with Machine Learning

“Feature Importance” analysis applied

to accounting using XGBoost R package

Meetup Paris Machine Learning Applications Group – Paris – May 13th, 2015 - Who am I?

Michaël Benesty

@pommedeterre33

@pommedeterresautee

fr.linkedin.com/in/mbenesty

• CPA (Paris): 4 years

• Financial auditor (NYC): 2 years

• Tax law associate @ Taj (Deloitte - Paris) since 2013

• Department TMC (Computerized tax audit)

• Co-author XGBoost R package with Tianqi Chen (main author) & Tong

He (package maintainer) - WARNING

Everything that will be presented

tonight is exclusively based

on open source software

Please try the same at home - Plan

1. Accounting & tax audit context

2. Machine learning application

3. Gradient boosting theory - Accounting crash course 101 (1/2)

Accounting is a way to transcribe economical operations.

• My company buys €10 worth of potatoes to cook delicious French

fries.

Account number

Account Name

Debit

Credit

601

Purchase

10.00

512

Bank

10.00

Description: Buy €10 of potatoes to XYZ - Accounting crash course 101 (2/2)

French Tax law requires many more information in my accounting:

• Who?

• Name of the potatoes provider

• Account of the potatoes provider

• When?

• When the accounting entry is posted

• Date of the invoice from the potatoes seller

• Payment date

• …

• What?

• Invoice ref

• Item description

• …

• How Much?

• Foreign currency

• …

• … - Tax audit context

Since 2014, companies audited by the French tax administration shall

provide their entire accounting as a CSV / XML file.

Simplified* example:

EcritureDate|CompteNum|CompteLib|PieceDate|EcritureLib|Debit|Credit

20110805|601|Purchase|20110701|Buy potatoes|10|0

20110805|512|Bank|20110701|Buy potatoes|0|10

*: usually there are 18 columns - Example of a trivial apparent anomaly

Article 39 of French tax code states that (simplified):

“For FY 2011, an expense is deductible from P&L 2011 when its

operative event happens in 2011”

In our audit software (ACL), we add a new Boolean feature to

the dataset: True if the invoice date is out of 2011, False

otherwise - Boring tasks to perform by a human

Find a pattern to predict if accounting entry will be tagged as an anomaly

regarding the way its fields are populated.

1. Take time to display lines marked as out of FY

demo dataset (1 500 000 lines) ≈ 100 000 lines marked having invoice out of FY

2. Take time to analyze 18 columns of the accounting

from 200 to >> 100 000 different values per column

3. Take time to find a pattern/rule by hand. Use filters. Iterate.

4. Take time to check that pattern found in selection is not in remaining

data - What Machine Learning can do to help?

1.

Look at whole dataset without human help

2.

Analyze each value in each column without human help

3.

Find a pattern without human help

4.

Generate a (R-Markdown) report without human help

Requirements:

• Interpretable

• Scalable

• Works (almost) out of the box - 2 tries for a success

1st try: Subgroup mining (Failed)

Find feature values common to a group of observations which are

different from the rest of the dataset.

2nd try: Feature importance on decision tree based

algorithm (Success)

Use predictive algorithm to describe the existing data. - 1st try: Subgroup mining algorithm

Find feature values common to a group of observations which are different from

the rest of the dataset.

1. Find an existing open source project

2. Check it gives interpretable results in reasonable time

3. Help project main author on:

• reducing memory footprint by 50%, fixing many small bugs (2 months)

• R interface (1 month)

• Find and fix a huge bug in the core algorithm just before going in production (1 week)

After the last bug fix, the algorithm was too slow to be used on real accounting… - 2nd try: XGBoost

Available on R, Python, Julia, CLI

Fast speed and memory efficient

• Can be more than 10 times faster than GBM in Sklearn and R (Benchmark on GitHub deposit)

• New external memory learning implementation (based on distributed computation implementation)

Distributed and Portable

• The distributed version runs on Hadoop (YARN), MPI, SGE etc.

• Scales to billions of examples (tested on 4 billions observations / 20 computers)

XGBoost won many Kaggle competitions, like:

• WWW2015 Microsoft Malware Classification Challenge (BIG 2015)

• Tradeshift Text Classification

• HEP meets ML Award in Higgs Boson Challenge

• XGBoost is by far the most discussed tool in ongoing Otto competition - Iterative feature importance with XGBoost (1/3)

Shows which features are the most important to predict if an entry has

its field PieceDate (invoice date) out of the Fiscal Year.

In this example, FY is from 2010/12/01

to 2011/11/30

It is not surprising to have PieceDate

among the most important features

because the label is based on this

feature! But the distribution of

important invoice date is interesting

here.

Most entries out of the FY have the

same invoice date:

20111201 - Iterative feature importance with XGBoost (2/3)

Since in previous slide, one feature represents > 99% of the gain we

remove it from the dataset and we run a new analysis.

Most entries

are related to

the same

JournalCode

(nature of

operation) - Iterative feature importance with XGBoost (3/3)

Entries marked as out of FY have the same invoice date, and are related

to the same JournalCode. We run a new analysis without JournalCode:

Most of the

entries with an

invoice date

issue are

related to

Inventory

accounts!

That’s the kind

of pattern we

were looking

for - XGBoost explained in 2 pics (1/2)

Classification And Regression Tree (CART)

Decision tree is about learning a set of rules:

if 𝑋1 ≤ 𝑡1 & if 𝑋2 ≤ 𝑡2 then 𝑅1

if 𝑋1 ≤ 𝑡1 & if 𝑋2 > 𝑡2 then 𝑅2

…

Advantages:

• Interpretable

• Robust

• Non linear link

Drawbacks:

• Weak Learner

• High variance - XGBoost explained in 2 pics (2/2)

Gradient boosting on CART

• One more tree = loss mean decreases = more data explained

• Each tree captures some parts of the model

• Original data points in tree 1 are replaced by the loss points for tree 2 and 3 - Learning a model ≃ Minimizing the loss

function

Given a prediction

𝑦 and a label 𝑦, a loss function ℓ measures the

discrepancy between the algorithm's 𝑛 prediction and the desired 𝑛 output.

• Loss on training data:

𝑛

𝐿 =

ℓ(𝑦𝑖, 𝑦𝑖)

𝑖=1

• Logistic loss for binary classification:

1

𝑛

ℓ 𝑦𝑖, 𝑦𝑖 = −

𝑦

𝑛

𝑖 log

𝑦𝑖 + 1 − 𝑦𝑖 log(1 − 𝑦𝑖)

𝑖=1

Logistic loss punishes by the infinity* a false certainty in prediction 0; 1

*: lim log 𝑥 = −∞

𝑥→0+ - Growing a tree

In practice, we grow the tree greedily:

• Start from tree with depth 0

• For each leaf node of the tree, try to add a split. The change of objective after adding the

split is:

𝐺2

𝐺2

𝐺

2

Complexity cost by

𝐺𝑎𝑖𝑛 =

𝐿

+

𝑅

−

𝐿 + 𝐺𝑅

− 𝛾

introducing

𝐻𝐿 + 𝜆

𝐻𝑅 + 𝜆

𝐻𝑅 + 𝐻𝐿 + 𝜆

Additional leaf

Score of

left child

Score of right child

Score if we don’t split

G is called sum of residual which means the general mean direction of the residual we

want to fit.

H corresponds to the sum of weights in all the instances.

𝛾 and 𝜆 are 2 regularization parameters.

Tianqi Chen. (Oct. 2014) Learning about the model: Introduction to Boosted Trees - Gradient Boosting

Iteratively learning weak classifiers with respect to a distribution and

adding them to a final strong classifier.

• Each round we learn a new tree to approximate the negative gradient

and minimize the loss

Whole model prediction

𝑦(𝑡) =

𝑦(𝑡−1) + 𝑓

𝑖

𝑖

𝑡(𝑥𝑖)

Tree t prediction

• Loss:

𝑛

𝑂𝑏𝑗(𝑡) =

ℓ 𝑦𝑖, 𝑦 𝑡−1 + 𝑓𝑡(𝑥𝑖)

+ Ω(𝑓𝑡)

𝑖=1

Friedman, J. H. (March 1999) Stochastic Gradient Boosting.

Complexity cost

by introducing

additional tree - Gradient descent

“Gradient Boosting is a special case of the functional gradient descent

view of boosting.”

Mason, L.; Baxter, J.; Bartlett, P. L.; Frean, Marcus (May 1999). Boosting Algorithms as Gradient Descent in Function Space.

Loss

Usually you finish here

Sometimes

you are lucky

2D View - Building a good model for feature importance

For feature importance analysis, in Simplicity Vs Accuracy trade-off,

choose the first. Few rule of thumbs (empiric):

• nrounds: number of trees. Keep it low (< 20 trees)

• max.depth: deepness of each tree. Keep it low (< 7)

• Run iteratively the feature importance analysis and remove the most

important features until the 3 most important features represent less

than 70% of the whole gain. - Love XGBoost? Vote XGBoost!

Otto challenge

Help XGBoost open source project to spread knowledge by voting for

our script explaining how to use our tool (no prize to win)

https://www.kaggle.com/users/32300/tianqi-chen/otto-group-product-classification-

challenge/understanding-xgboost-model-on-otto-data - Too much time in your life?

• General papers about gradient boosting:

• Greedy function approximation a gradient boosting machine. J.H. Friedman

• Stochastic Gradient Boosting. J.H. Friedman

• Tricks used by XGBoost

• Additive logistic regression a statistical view of boosting. J.H. Friedman T. Hastie R. Tibshirani (for the second-order statistics for tree

splitting)

• Learning Nonlinear Functions Using Regularized Greedy Forest. R. Johnson and T. Zhang (proposes to do fully corrective step, as well

as regularizing the tree complexity)

• Learning about the model: Introduction to Boosted Trees. Tianqi Chen. (from the author of XGBoost)