Feature Importance Analysis with XGBoost in 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
• …
• …

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

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)

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:
𝐿 =
𝑖=1
𝑛
ℓ(𝑦𝑖, 𝑦𝑖)
• Logistic loss for binary classification:
ℓ 𝑦𝑖, 𝑦𝑖 = −
1
𝑛 𝑖=1
𝑛
𝑦𝑖 log 𝑦𝑖 + 1 − 𝑦𝑖 log(1 − 𝑦𝑖)
Logistic loss punishes by the infinity* a false certainty in prediction 0; 1
*: lim
𝑥→0+
log 𝑥 = −∞

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:
𝐺𝑎𝑖𝑛 =
𝐺 𝐿
2
𝐻𝐿 + 𝜆
+
𝐺 𝑅
2
𝐻 𝑅 + 𝜆
−
𝐺 𝐿 + 𝐺 𝑅
2
𝐻 𝑅 + 𝐻𝐿 + 𝜆
− 𝛾
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.
Score of
left child Score of right child Score if we don’t split
Complexity cost by
introducing
Additional leaf
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
𝑦𝑖
(𝑡)
= 𝑦𝑖
(𝑡−1)
+ 𝑓𝑡(𝑥𝑖)
• Loss:
𝑂𝑏𝑗(𝑡)
=
𝑖=1
𝑛
ℓ 𝑦𝑖, 𝑦 𝑡−1
+ 𝑓𝑡(𝑥𝑖) + Ω(𝑓𝑡)
Friedman, J. H. (March 1999) Stochastic Gradient Boosting. Complexity cost
by introducing
additional tree
Tree t predictionWhole model prediction

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.
2D View
Loss
Sometimes
you are lucky
Usually you finish here

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)

Feature Importance Analysis with XGBoost in Tax audit

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