are you the beatles or the rolling stones? · are you the beatles or the rolling stones? virginie...
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Are You The Beatles Or The Rolling Stones?
Virginie Lurkin and Brian Sifringer
N. Ortelli, G. Lederrey, A. Alahi, M. Bierlaire
Transport and Mobility LaboratorySchool of Architecture, Civil, and Environmental Engineering ENAC
Ecole Polytechnique Federale de Lausanne
13th Workshop on Discrete Choice Models
June 21-23, 2018
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“The new and good ideas come from having a very broad andmultidisciplinary range of interests.”
Robin Chase
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Are You The Beatles Or The Rolling Stones? Virginie Lurkin and Brian Sifringer
Discrete choice models
Understand and predict individual choice behaviorusing mathematical models
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Are You The Beatles Or The Rolling Stones? Virginie Lurkin and Brian Sifringer
Discrete choice models
Understand and predict individual choice behaviorusing mathematical models
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Are You The Beatles Or The Rolling Stones? Virginie Lurkin and Brian Sifringer
Discrete choice models
Uin = Vin + εin
Pin = eVin∑j∈Cn eVjn
Vin = ...+ βcCostin + βtTimein + ...︸ ︷︷ ︸linear in parameters
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Are You The Beatles Or The Rolling Stones? Virginie Lurkin and Brian Sifringer
Discrete choice models
Uin = Vin + εin
Pin = eVin∑j∈Cn eVjn
Vin = ...+ βcCostin + βtTimein + ...︸ ︷︷ ︸linear in parameters
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Are You The Beatles Or The Rolling Stones? Virginie Lurkin and Brian Sifringer
Discrete choice models
Uin = Vin + εin
Pin = eVin∑j∈Cn eVjn
Vin = ...+ βcCostin + βtTimein + ...
Vin = ...+ βcCostin + βtTimein + ...︸ ︷︷ ︸linear in parameters
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Are You The Beatles Or The Rolling Stones? Virginie Lurkin and Brian Sifringer
Discrete choice models
Uin = Vin + εin
Pin = eVin∑j∈Cn eVjn
Vin = ...+ βcCostin + βtTimein + ...︸ ︷︷ ︸linear in parameters
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Are You The Beatles Or The Rolling Stones? Virginie Lurkin and Brian Sifringer
Discrete choice models
Uin = Vin + εin
Pin = eVin∑j∈Cn eVjn
Vin = ...+ βcCostin + βtTimein + ...︸ ︷︷ ︸linear in parameters
Prediction accuracy + Interpretability
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Are You The Beatles Or The Rolling Stones? Virginie Lurkin and Brian Sifringer
Machine learning
Neural networks
Very good prediction accuracy
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Are You The Beatles Or The Rolling Stones? Virginie Lurkin and Brian Sifringer
Machine learning
Neural networks
Very good prediction accuracy
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Are You The Beatles Or The Rolling Stones? Virginie Lurkin and Brian Sifringer
Machine learning
Neural networks
Very good prediction accuracy
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Are You The Beatles Or The Rolling Stones? Virginie Lurkin and Brian Sifringer
Machine learning
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Are You The Beatles Or The Rolling Stones? Virginie Lurkin and Brian Sifringer
Machine learning
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Enhancing Discrete Choice Models withNeural Networks
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Are You The Beatles Or The Rolling Stones? Virginie Lurkin and Brian Sifringer
General idea
Bringing the predictive strength of Neural Networks, a powerfulmachine learning-based technique, to the field of Discrete Choice Models
without compromising the interpretability of these models
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Are You The Beatles Or The Rolling Stones? Virginie Lurkin and Brian Sifringer
Multinomial Logit as Convolution NN
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Are You The Beatles Or The Rolling Stones? Virginie Lurkin and Brian Sifringer
Multinomial Logit as Convolution NN
Activation Function: Softmax
Loss: Categorical Cross-Entropy
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Are You The Beatles Or The Rolling Stones? Virginie Lurkin and Brian Sifringer
Multinomial Logit as Convolution NN
A single convolution gives us the utility functions
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Are You The Beatles Or The Rolling Stones? Virginie Lurkin and Brian Sifringer
Model and Validation on Swissmetro
Stated Preference Survey
Simple utilities for validation purposes:
Vcar = ASCcar + βcost · Costcar + βtime · Timecar
Vtrain = ASCtrain + βcost · Costtrain + βtime · Timetrain
VSM = ASCSM + βcost · CostSM + βtime · TimeSM
Biogeme betas Convolution Kernel weights
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Are You The Beatles Or The Rolling Stones? Virginie Lurkin and Brian Sifringer
Neural Network enhanced DCM
Case 1: same inputs
The new term from the NN overruns the MNL linear parameters
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Are You The Beatles Or The Rolling Stones? Virginie Lurkin and Brian Sifringer
Neural Network enhanced DCM
Case 2: different inputs
New term in the utility specification coming from a NN using all unusedfeatures
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Are You The Beatles Or The Rolling Stones? Virginie Lurkin and Brian Sifringer
Neural Network enhanced DCM
Case 2: different inputs
Uin = ASCi + βcost · Costin + βtime · Timein + βNN · NNin + εin
Interpretation: NNin = uncaptured information of MNL model
MNL estimates keep their significance
Increase in log-likelihood
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Are You The Beatles Or The Rolling Stones? Virginie Lurkin and Brian Sifringer
Swissmetro case
Utility Functions
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Are You The Beatles Or The Rolling Stones? Virginie Lurkin and Brian Sifringer
Swissmetro case
Unused Features
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Are You The Beatles Or The Rolling Stones? Virginie Lurkin and Brian Sifringer
Results
Benchmark - standard MNL
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Are You The Beatles Or The Rolling Stones? Virginie Lurkin and Brian Sifringer
Results
Benchmark - standard MNL
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Are You The Beatles Or The Rolling Stones? Virginie Lurkin and Brian Sifringer
Results
Hybrid model
++ Increased Likelihood
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Are You The Beatles Or The Rolling Stones? Virginie Lurkin and Brian Sifringer
Results
Hybrid model
++ Increased likelihood
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Are You The Beatles Or The Rolling Stones? Virginie Lurkin and Brian Sifringer
Results
Hybrid model
++ Keeps important parameters significant
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Are You The Beatles Or The Rolling Stones? Virginie Lurkin and Brian Sifringer
Results
Hybrid model
– Some parameters loose significance
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Are You The Beatles Or The Rolling Stones? Virginie Lurkin and Brian Sifringer
Results
Simple hybrid model - only key parameters
++ Keeps important parameters significant
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Are You The Beatles Or The Rolling Stones? Virginie Lurkin and Brian Sifringer
Results
Simple hybrid model - only key parameters
Increased likelihood + significant parameters
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Are You The Beatles Or The Rolling Stones? Virginie Lurkin and Brian Sifringer
Results
Comparison
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Are You The Beatles Or The Rolling Stones? Virginie Lurkin and Brian Sifringer
Conclusions
Enhancing DCM greatly increases likelihood
Same input or correlated input
- Breaks original parameter significance
Independent Input
- Best performances for likelihood
- All parameters have good sign and significance
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Are You The Beatles Or The Rolling Stones? Virginie Lurkin and Brian Sifringer
Future work
Interpretability: what is really happening?
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What do you think?
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Automatic Utility Specification Using MachineLearning Techniques
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Are You The Beatles Or The Rolling Stones? Virginie Lurkin and Brian Sifringer
Credit
Nicola Ortelli
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Are You The Beatles Or The Rolling Stones? Virginie Lurkin and Brian Sifringer
Motivation
Determining the appropriate utility specification for a particularapplication is a difficult task
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Are You The Beatles Or The Rolling Stones? Virginie Lurkin and Brian Sifringer
Motivation
Determining the appropriate utility specification for a particularapplication is a difficult task
Expertise + Intuition
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Are You The Beatles Or The Rolling Stones? Virginie Lurkin and Brian Sifringer
Motivation
Determining the appropriate utility specification for a particularapplication is a difficult task
Inspiration + Experience
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Are You The Beatles Or The Rolling Stones? Virginie Lurkin and Brian Sifringer
Motivation
Determining the appropriate utility specification for a particularapplication is a difficult task
Trial-and-error
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Are You The Beatles Or The Rolling Stones? Virginie Lurkin and Brian Sifringer
Motivation
Determining the appropriate utility specification for a particularapplication is a difficult task
Time consuming
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Are You The Beatles Or The Rolling Stones? Virginie Lurkin and Brian Sifringer
Objective
Build a procedure that automatically finds a good utilityspecification based on the data
Define neighborhood relations between specifications and useclassical local search algorithms
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Are You The Beatles Or The Rolling Stones? Virginie Lurkin and Brian Sifringer
Automatic utility specification framework
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Are You The Beatles Or The Rolling Stones? Virginie Lurkin and Brian Sifringer
Data partition
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Are You The Beatles Or The Rolling Stones? Virginie Lurkin and Brian Sifringer
Data partition
Data set separated into train set and test set
Train set separated into K folds
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Are You The Beatles Or The Rolling Stones? Virginie Lurkin and Brian Sifringer
Specifications and neighborhood structure
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Are You The Beatles Or The Rolling Stones? Virginie Lurkin and Brian Sifringer
Specifications and neighborhood structure
Current assumptions:
Only continuous and binary variables
Each continuous variable is included either on its own or ininteraction with one binary variable
All parameters are alternative specific
Example:
V = ...+ βx · x + ...
V = ...+ βx,b1=0 · x · (1 − b1) + βx,b1=1 · x · b1 + ...
V = ...+ βx,b2=0 · x · (1 − b2) + βx,b2=1 · x · b2 + ...
V = ...+ βx,b1=0,b2=0 · x · (1 − b1) · (1 − b2) + βx,b1=1,b2=0 · x · b1 · (1 − b2)
+ βx,b1=0,b2=1 · x · (1 − b1) · b2 + βx,b1=1,b2=1 · x · b1 · b2 + ...
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Are You The Beatles Or The Rolling Stones? Virginie Lurkin and Brian Sifringer
Specifications and neighborhood structure
Neighbors of a particular specification = all specifications that are asingle change away from it
Four possible changes: add, remove, interact, un-interact
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Are You The Beatles Or The Rolling Stones? Virginie Lurkin and Brian Sifringer
Measure of performance
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Are You The Beatles Or The Rolling Stones? Virginie Lurkin and Brian Sifringer
Measure of performance
Current assumptions:
Performance of a specification is measured as the log-likelihood ityields on new data
Cross-validation is used to avoid overfitting or favorizing models witha large number of parameters
The global performance Pm of model m is defined as the sum of thelog-likelihoods obtained on each fold after estimation on the K-1others:
Pm =K∑
k=1
Lmk
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Are You The Beatles Or The Rolling Stones? Virginie Lurkin and Brian Sifringer
Neighbor validation
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Are You The Beatles Or The Rolling Stones? Virginie Lurkin and Brian Sifringer
Neighbor validation
Conditions of acceptance of a model m :
A neighbor that performs better than the baseline is always accepted
P(accept m) = 1 if Pm ≥ Pmb
One that performs worse might still get accepted, depending on thedifference of performance Pm −Pmb and the current iteration number
P(accept m) =exp(Pm − Pmb )
Ttif Pm < Pmb
The algorithm ends when all neighbors of a model are rejected
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Case study 1: Optima
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Are You The Beatles Or The Rolling Stones? Virginie Lurkin and Brian Sifringer
Case study: Optima
Revealed preference survey conducted in Switzerland for CarPostal:
Three alternatives: public transports, car and soft modes
1’814 observations left after discarding incomplete ones
Two binary and six continuous variables are considered
250’000 different specifications can be obtained
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Are You The Beatles Or The Rolling Stones? Virginie Lurkin and Brian Sifringer
Best specification
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Are You The Beatles Or The Rolling Stones? Virginie Lurkin and Brian Sifringer
Comparison with an existing model
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Case study 2: SwissMetro
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Are You The Beatles Or The Rolling Stones? Virginie Lurkin and Brian Sifringer
Case study: SwissMetro
Stated choice survey to analyze the impact of the Swissmetro:
Three alternatives: train, Swissmetro and car
Nine different situations for each of the 1’192 respondents
Two binary and eight continuous variables are considered
6’250’000 different specifications can be obtained
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Are You The Beatles Or The Rolling Stones? Virginie Lurkin and Brian Sifringer
Best specification
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Are You The Beatles Or The Rolling Stones? Virginie Lurkin and Brian Sifringer
Comparison with an existing model
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Conclusions
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Are You The Beatles Or The Rolling Stones? Virginie Lurkin and Brian Sifringer
Conclusions
Despite a certain number of restrictions, results show that this topicis worth further investigation
The procedure reaches very good specifications in a matter ofminutes
In some cases, the obtained model outperforms the benchmark withless variables under consideration
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Are You The Beatles Or The Rolling Stones? Virginie Lurkin and Brian Sifringer
Future work
VNS –> neighborhood structures + relax assumptions
What is a good utility specification ?
Predictability
Parameters significance
Behavioral interpretation
....
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