Big Data and Machine Learning with an Actuarial Perspective

178 Pages·2015·42.84 MB·English

Arthur CHARPENTIER - Big Data and Machine Learning with an Actuarial Perspective - IA|BE
Big Data and Machine Learning with an Actuarial Perspective
A. Charpentier (UQAM & Université de Rennes 1)
IA | BE Summer School, Louvain-la-Neuve, September 2015.
http://freakonometrics.hypotheses.org
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Arthur CHARPENTIER - Big Data and Machine Learning with an Actuarial Perspective - IA|BE
A Brief Introduction to Machine Learning and Data Science for Actuaries
A. Charpentier (UQAM & Université de Rennes 1)
Professor of Actuarial Sciences, Mathematics Department, UQàM
(previously Economics Department, Univ. Rennes 1 & ENSAE Paristech
actuary in Hong Kong, IT & Stats FFSA)
PhD in Statistics (KU Leuven), Fellow Institute of Actuaries
MSc in Financial Mathematics (Paris Dauphine) & ENSAE
Editor of the freakonometrics.hypotheses.org’s blog
Editor of Computational Actuarial Science, CRC
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Arthur CHARPENTIER - Big Data and Machine Learning with an Actuarial Perspective - IA|BE
Agenda
1. Introduction to Statistical Learning
2. Classification y ∈ {0, 1}, or y ∈ {•, •}
i i
R N
3. Regression y ∈ (possibly y ∈ )
i i
4. Model selection, feature engineering, etc
All those topics are related to computational issues, so codes will be mentioned
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Arthur CHARPENTIER - Big Data and Machine Learning with an Actuarial Perspective - IA|BE
Inside Black boxes
The goal of the course is to describe philosophical difference
between machine learning techniques, and standard statistical
/ econometric ones, to describe algorithms used in machine
learning, but also to see them in action.
A machine learning technique is
• an algorithm
• a code (implementation of the algorithm)
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Arthur CHARPENTIER - Big Data and Machine Learning with an Actuarial Perspective - IA|BE
Prose and Verse (Spoiler)
MAÎTRE DE PHILOSOPHIE: Sans doute. Sont-ce des vers que vous lui voulez écrire?
MONSIEUR JOURDAIN: Non, non, point de vers.
MAÎTRE DE PHILOSOPHIE: Vous ne voulez que de la prose?
MONSIEUR JOURDAIN: Non, je ne veux ni prose ni vers.
MAÎTRE DE PHILOSOPHIE: Il faut bien que ce soit l’un, ou l’autre.
MONSIEUR JOURDAIN: Pourquoi?
MAÎTRE DE PHILOSOPHIE: Par la raison, Monsieur, qu’il n’y a pour s’exprimer que la prose, ou
les vers.
MONSIEUR JOURDAIN: Il n’y a que la prose ou les vers?
MAÎTRE DE PHILOSOPHIE: Non, Monsieur: tout ce qui n’est point prose est vers; et tout ce qui
n’est point vers est prose.
MONSIEUR JOURDAIN: Et comme l’on parle qu’est-ce que c’est donc que cela?
MAÎTRE DE PHILOSOPHIE: De la prose.
MONSIEURJOURDAIN: Quoi? quand je dis: "Nicole, apportez-moi mes pantoufles, et me donnez
mon bonnet de nuit" , c’est de la prose?
MAÎTRE DE PHILOSOPHIE: Oui, Monsieur.
MONSIEUR JOURDAIN: Par ma foi! il y a plus de quarante ans que je dis de la prose sans que
j’en susse rien, et je vous suis le plus obligé du monde de m’avoir appris cela. Je voudrais
donc lui mettre dans un billet: Belle Marquise, vos beaux yeux me font mourir d’amour;
mais je voudrais que cela fût mis d’une manière galante, que cela fût tourné gentiment.
‘Le Bourgeois Gentilhomme ’, Molière (1670)
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Arthur CHARPENTIER - Big Data and Machine Learning with an Actuarial Perspective - IA|BE
Part 1.
Statistical/Machine Learning
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Arthur CHARPENTIER - Big Data and Machine Learning with an Actuarial Perspective - IA|BE
Statistical Learning and Philosophical Issues
From Machine Learning and Econometrics, by Hal Varian :
“Machine learning use data to predict some variable as a function of other
covariables,
• may, or may not, care about insight, importance, patterns
• may, or may not, care about inference (how y changes as some x change)
Econometrics use statistical methodes for prediction, inference and causal
modeling of economic relationships
• hope for some sort of insight (inference is a goal)
• in particular, causal inference is goal for decision making.”
→ machine learning, ‘new tricks for econometrics’
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Arthur CHARPENTIER - Big Data and Machine Learning with an Actuarial Perspective - IA|BE
Statistical Learning and Philosophical Issues
Remark machine learning can also learn from econometrics, especially with non
i.i.d. data (time series and panel data)
Remark machine learning can help to get better predictive models, given good
datasets. No use on several data science issues (e.g. selection bias).
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Arthur CHARPENTIER - Big Data and Machine Learning with an Actuarial Perspective - IA|BE
Statistical Learning and Philosophical Issues
“Ceteris Paribus: causal effect with other things being held constant; partial
derivative
Mutatis mutandis: correlation effect with other things changing as they will; total
derivative
Passive observation: If I observe price change of dx , how do I expect quantity
j
sold y to change?
Explicit manipulation: If I explicitly change price by dx , how do I expect
j
quantity sold y to change?”
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Arthur CHARPENTIER - Big Data and Machine Learning with an Actuarial Perspective - IA|BE
Non-Supervised and Supervised Techniques
Just x ’s, here, no y : unsupervised.
i i
Use principal components to reduce dimension: we want d vectors z , · · · , z
1 d
such that
d
X 4 1911941ll5ll
x ∼ ω z or X ∼ ZΩT −2 1916ll
i i,j j 3 1914941ll7ll1918ll
where Ω is a k × dj=m1atrix, with d < k. Log Mortality Rate −8−6−4 PC score 2 −1012 llllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll 19ll4lllllllllll2lllllllll1llllllllllll9llllllll4l11lllll39ll9llllllll1l4ll90lllll
0 20 40 60 80 −10 −5 0 5 10 15
Age PC score 1
First Compoment is z = Xω where
1 1
3 l
−2
ω1 = akrωgmk=a1x (cid:8)kX · ωk2(cid:9) = akrωgmk=a1x nωTXTXωo Log Mortality Rate −6−4 PC score 2 012 lllllllllllllllllllllllllllllllllllllllllll llllll llllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll
−10−8 −1 lllllllllllllllllllllllllllllllllllllllll
0 20 40 60 80 −10 −5 0 5 10 15
Age PC score 1
Second Compoment is z = Xω where
2 2
(cid:26) (cid:27)
(1) (1)
2 T
ω = argmax kX · ωk where X = X − Xω ω
f f
2 1 1
| {z }
kωk=1
z
1
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