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Discrete choice and machine learning: two peas in apod?
Michel Bierlaire
Transport and Mobility LaboratorySchool of Architecture, Civil and Environmental Engineering
Ecole Polytechnique Federale de Lausanne
October 17, 2018
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Introduction
Outline
1 Introduction
2 A little exercise
3 ML and discrete choice
4 Looking back
5 Data collection6 Model output7 Estimation8 Cross-validation9 Conclusions
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Introduction
Future mobility
Trends
Mobility as a service
Shared mobility
Demand patterns are more and morecomplex
New sources of data
Travel demand
Traditional methodology: discretechoice
Emergence of machine learning
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Introduction
IATBR 2018
Session 3E: Machine Learning –FundamentalsSession 6E: More Machine Learning
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Introduction
Interest from young researchers
My PhD topic is “Understanding
Multi-Modal Passenger Behaviour at City
Scale.” I have used trip diary data to
compare the performance of multiple
discrete choice models, including various
multinomial logistic regression models,
random forests, support vector
machines and neural networks.”
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A little exercise
Outline
1 Introduction
2 A little exercise
3 ML and discrete choice
4 Looking back
5 Data collection6 Model output7 Estimation8 Cross-validation9 Conclusions
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A little exercise
Journal of choice modelling
Issues
22 to 29
2017 and 2018
Procedure
Download HTML
Write Python script to extract words.
Calculate the occurrences of words.
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A little exercise
Some counts
logit 4948utility 8326machine 99learning 1459statistics 634pattern 383classification 0
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A little exercise
Visual representation: first attempt
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A little exercise
Manual cleaning
Remove common words
the is in and of with to for a that are as each et al on by
this we be can from it has where such also may pp not all
an their one other was than two at only when use table our
how new at or they but using both were using if three no
more which these have then given into while over used
because section based there will about you some many been
did between who same would its any among under could
Remove patterns
Keep only real words — no digits, no special character
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A little exercise
Visual representation: second attempt
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A little exercise
Manual cleaning
Remove obvious words
model models choice data
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A little exercise
Visual representation: third attempt
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A little exercise
Machine learning
Manual intervention is common
“A great deal of manual work goes into building and training
intelligent machine learning algorithms.” Sascha Schubert, businesssolutions manager at SAS, May 22, 2017.
“Whenever new learning is involved in ML, the human programmer
has to intervene and adapt the programming algorithm to make the
learning happen.” Paramita Ghosh, Dataversity.net, April 13, 2017.
Hyperparameter tuning.
Learning rate tuning.
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ML and discrete choice
Outline
1 Introduction
2 A little exercise
3 ML and discrete choice
4 Looking back
5 Data collection6 Model output7 Estimation8 Cross-validation9 Conclusions
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ML and discrete choice
Definitions
Machine learning is
an interdisciplinary field
that uses statistical techniques
to give computer systems the ability to”learn” from data,
without being explicitly programmed.
[Wikipedia]
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ML and discrete choice
Definitions
Applications of machine learning
classification
regression
clustering
density estimation
dimensionality reduction
[Wikipedia]
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ML and discrete choice
Discrete choice and classification
Discrete choice from a ML perspective
dependent variable is discrete
supervised learning
logistic regression
Introduction to Discrete Choice Models www.edx.org
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Looking back
Outline
1 Introduction
2 A little exercise
3 ML and discrete choice
4 Looking back
5 Data collection6 Model output7 Estimation8 Cross-validation9 Conclusions
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Looking back
10 years ago: Automatic Facial Expression Recognition
“The face is the most extraordinary
communicator, capable of accurately
signaling emotion in a bare blink of a
second, capable of concealing
emotion equally well”
Deborah Blum
Typical machine learning application
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Looking back
Choice experiment
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Looking back
Choice model
[Sorci et al., 2010]
Vi = ASCi +∑
k
IikβFACSik AUk
︸ ︷︷ ︸+∑
h
IihβEDUih EDUh
︸ ︷︷ ︸+∑
ℓ
IiℓβAAMiℓ AAM
︸ ︷︷ ︸
Ingredients
Facial Action Coding System (FACS) [Ekman and Friesen, 1978]
Expression Descriptive Units (EDU) [Antonini et al., 2006]
Active Appearance Model (AAM) [Edwards et al., 1998]
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Looking back
Main conclusions of this work
Quality of classification similar to neuralnetworks and Bayesian networks.
Behavioral insights of the discretechoice model.
Interpretation of the parameters.
Possibility to exploit know-how in thespecification.
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Data collection
Outline
1 Introduction
2 A little exercise
3 ML and discrete choice
4 Looking back
5 Data collection6 Model output7 Estimation8 Cross-validation9 Conclusions
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Data collection
Data universe
Machine Learning: data processing
Dataset is the universe
Data generation process is usuallyignored
Representativity is assumed
Main argument: the size of the datasetis very large
Discrete choice: inference
A population is identified
Data collection strategies are designed
Data sets are rebalanced to representthe population
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Data collection
Potential implications
Classification
Results from statistics: bias of theparameters
Not necessarily an issue ifcross-validation is applied
Aggregation
Counting
Aggregation biases may be severe
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Data collection
Example
City of Geneva
Data for March 2, 2017.
Phone data: boundary flows, between adjacent zones.
ML: results of the ML learning algorithm of the phone company.
Compared with loop detectors: flows of cars
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Data collection
Results
Source: Montesinos Ferrer, Lamotte, Geroliminis
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Model output
Outline
1 Introduction
2 A little exercise
3 ML and discrete choice
4 Looking back
5 Data collection6 Model output7 Estimation8 Cross-validation9 Conclusions
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Model output
Model output
Probability that an item n belongs to a class i
Choice models
Probability is used in applications
Classification
Class with highest probability is selected
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Model output
Severe aggregation bias
Example: classify 1000 items in two classes.
Data generation process
51% class 1 / 49% class 2
Perfect ML model
After projection: always predicts class 1
Total number of items in class 1
In reality: 510
Predicted: 1000
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Model output
Aggregation bias increases with the number of classes
Example: classify N items in K classes.
Data generation process
1+εK
class 1 / K−1−εK(K−1) class i
Perfect ML model
After projection: always predicts class 1
Total number of items in class 1
In reality: N 1+εK
Predicted: N
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Estimation
Outline
1 Introduction
2 A little exercise
3 ML and discrete choice
4 Looking back
5 Data collection6 Model output7 Estimation8 Cross-validation9 Conclusions
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Estimation
Loss function/goodness of fit
Formalism
Class i , item n
Independent variables/features :xn = (xin)
Ji=1
Choice / class: yn = (yin)Ji=1 ∈ {0, 1}J
Unknown parameters: β ∈ RK
Model: f (xn;β) ∈ [0, 1]
Loss function: finite sums
L(β) =N∑
n=1
L(f (xn;β), yn)
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Estimation
Loss function/goodness of fit
L(f (xn;β), yn) =
-Log likelihood / crossentropy
−J∑
i=1
yin ln f (xn;β)
Square loss
J∑
i=1
(1− yinf (xn;β))2
Hinge loss
J∑
i=1
|1− yinf (xn;β)|+
Exponential loss
J∑
i=1
exp(−γyinf (xn;β))
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Estimation
Stochastic gradient descent
Loss function
L(β) =N∑
n=1
L(f (xn;β), yn)
Key ingredient for optimization
Gradient:∇L(β) =
∑n∈{1,...,N}∇L(f (xn;β), yn)
Big data
Approx.:∑
n∈B⊆{1,...,N}∇L(f (xn;β), yn).
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Estimation
Stochastic gradient on choice data [Lederrey et al., 2018]
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Cross-validation
Outline
1 Introduction
2 A little exercise
3 ML and discrete choice
4 Looking back
5 Data collection6 Model output7 Estimation8 Cross-validation9 Conclusions
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Cross-validation
Cross-validation
Main ideas
How to select the best model?
It should be the one that predicts best
Example: leave-one-out
If =1
N
N∑
n=1
L(f (xn; βn−), yn)
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Conclusions
Outline
1 Introduction
2 A little exercise
3 ML and discrete choice
4 Looking back
5 Data collection6 Model output7 Estimation8 Cross-validation9 Conclusions
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Conclusions
Summary
DCM ML
Manual intervention Model spec. AlgorithmInterpretability Yes Not quiteSampling issues Handled Mainly IgnoredModel output Probability Mostly 0/1
Estimation standard NL opt. stochastic gradientCross-validation Mainly ignored Yes
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Conclusions
Conclusions
Two different communities
Two different state-of-practice
Similar objectives
Research agenda
Bring the best from each world
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Conclusions
Bibliography I
Antonini, G., Sorci, M., Bierlaire, M., and Thiran, J.-P. (2006).Discrete choice models for static facial expression recognition.In Blanc-Talon, J., Philips, W., Popescu, D., and Scheunders, P.,editors, Advanced Concepts for Intelligent Vision Systems, volume4179 of Lecture Notes in Computer Science, pages 710–721. SpringerBerlin / Heidelberg.ISBN:978-3-540-44630-9.
Edwards, G. J., Cootes, T. F., and Taylor, C. J. (1998).Face recognition using active appearance models.In European conference on computer vision, pages 581–595. Springer.
Ekman, P. and Friesen, W. (1978).Facial coding action system (facs): A technique for the measurementof facial actions.
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Conclusions
Bibliography II
Lederrey, G., Lurkin, V., and Bierlaire, M. (2018).SNM: Stochastic newton method for optimization of discrete choicemodels.In Proceedings of the 21st IEEE International Conference on
Intelligent Transportation Systems, Maui, Hawaii.
Sorci, M., Antonini, G., Cruz, J., Robin, T., Bierlaire, M., and Thiran,J.-P. (2010).Modelling human perception of static facial expressions.Image and Vision Computing, 28(5):790–806.
Michel Bierlaire (EPFL) Discrete Choice/Machine Learning October 17, 2018 44 / 44