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Volodymyrk
Bayesian Model Averaging
Bayesian Mixer, 27.09.2016
London, UK
Volodymyrk
Bayesian Model Averaging (BMA) - 1 minute version
New Project - how much does it worth?
CFO VP of Growth
Net Present Value: $50m $100m
Model M1
Model M2
30%CEO belief:
after evaluating both
models and market
data
70%
$15m + $70m = $85m
K = 2
Volodymyrk
Bayesian Model Averaging (BMA) - 3 minute version
VP of Growth
CLV assumptions
$10 $12 $15
CAC
$4 72 129 149
$6 62 112 133
$8 51 92 101
Average= $100.11m
Sensitivity Analysis for M2
DATA
Volodymyrk
Bayesian Model Averaging (BMA) - 5 minute version
Bayesian Model Averaging: A Tutorial
Jennifer A. Hoeting, David Madigan, Adrian E. Raftery and Chris T. Volinsky
How much do you trust your
VP and CFO, before you look
at models?
Scary normalising term
that you can ignore
Prior probability for
model parameter
Volodymyrk
Bayesian answer to overfitting
Frequentist:
- model selection
- regularisation
Bayesian:
- BMA
- marginalisation
Volodymyrk
Case Study
You just get the best job in the galaxy
Volodymyrk
Your new Boss Business domain Modelling case
Always test your models on synthetic data that you understand and control
Volodymyrk
Use Cases:
- Fraud Detection
- Inventory Sourcing
Data
Volodymyrk
Modelling goals
- Prediction range is needed, so that you can identify fraudulent transactions
(sand people under-reporting real transaction size and pocketing profit)
- Sale price should be easily explainable, as a function of various Droid Features
so that Jabba can invest in appropriate scavenging/sourcing projects
- You want lowest prediction error possible
so that you are not feeded to Sarlacc
Volodymyrk
Data Generation
Class-1
Class-2
Class-3
Class-4
durability
circuitry
height
weight
price
...
age
Volodymyrk
Data Collection
Volodymyrk
Model Selection - classical method
credits ~ height + weight + power + dents + rad + wheels + legs + red + blue + black + temperature + lat + long + ir_emit + dents_log + height_log + weight_log + power_log + rad_log
Adj. R2: 0.884974385182
Volodymyrk
Model Selection - backward elimination
Volodymyrk
Final Model
credits ~ weight + power + dents + rad + wheels + blue + black + temperature + lat + dents_log + height_log + weight_log + power_log
Adj. R2: 0.903544333611
Volodymyrk
Model Evaluation (out-of-sample)
Volodymyrk
Ridge regression (L2 regularisation)
Volodymyrk
Bayesian Model Averaging for Linear Models - a special case
Inclusion probability for (regression coefficients) are weighted across all possible models
Number of models = combinations of all K features (include/exclude) = 2K
Volodymyrk
How to actually do BMA? (in R)
cran.r-project.org/web/packages/BMA cran.r-project.org/web/packages/BAScran.r-project.org/web/packages/BMS
Mature. A.k.a. “the original”
Developed by PhD duringresearch. Not maintained
Newest. Maintained by Chair
of the Department ofStatistical Science at Duke
Volodymyrk
BMA using BMS (R) package
Model Selection L2 Regularisation BMA
MSE 9736.49 7782.21 7329.44
It worked!
But you can find inputs into data generator script that will not work as well!
Volodymyrk
Nice things you get from BMA
Posterior Inclusion Probability!
How cool is that!
Volodymyrk
Model ranking!
MCMC can beused, if number of
features is large
Best model, according toBMA
Volodymyrk
Can we use it for more complex models?
normalising term
that you can ignore
http://www.ssc.wisc.edu/~bhansen/718/NonParametrics15.pdf
http://www.ejwagenmakers.com/2004/aic.pdf
Warning:Very questionable math.
Does not work
Volodymyrk
Can we use BMA to combine complex (incl. hierarchical) models?
1
3
2
Model order is somewhat similar. Relative probabilities are not.
We need working Reverse-Jump MCMC or something more sophisticated.
Not available in common bayesian MCMC packages yet.
Volodymyrk
In Summary
- BMA is a Bayesian version of ML Model Ensembles
- Math behind is quite beautiful
- Model Averaging is useful for interpretation, not only prediction
- Invest in synthetic data generation,
- before applying new modelling techniques to real-world data
- Even if you are not using BMA, fit different models
- And combine them, if your goal is prediction
- BMA works very well for common GLMs, but does not work yet for arbitrary
models
- Do try it next time you need to fit OLS, though!
Volodymyrk
Of course we are hiring!
● (Snr, Mid) Data Scientists
● Solutions Architect
● Ruby Developer
● Data Engineer
● Senior Artist
● Technical Artist
● Unity Developers
● Senior Product Manager
● Product Director
http://jobs.productmadness.com/

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Bayesian model averaging

  • 1. Volodymyrk Bayesian Model Averaging Bayesian Mixer, 27.09.2016 London, UK
  • 2. Volodymyrk Bayesian Model Averaging (BMA) - 1 minute version New Project - how much does it worth? CFO VP of Growth Net Present Value: $50m $100m Model M1 Model M2 30%CEO belief: after evaluating both models and market data 70% $15m + $70m = $85m K = 2
  • 3. Volodymyrk Bayesian Model Averaging (BMA) - 3 minute version VP of Growth CLV assumptions $10 $12 $15 CAC $4 72 129 149 $6 62 112 133 $8 51 92 101 Average= $100.11m Sensitivity Analysis for M2 DATA
  • 4. Volodymyrk Bayesian Model Averaging (BMA) - 5 minute version Bayesian Model Averaging: A Tutorial Jennifer A. Hoeting, David Madigan, Adrian E. Raftery and Chris T. Volinsky How much do you trust your VP and CFO, before you look at models? Scary normalising term that you can ignore Prior probability for model parameter
  • 5. Volodymyrk Bayesian answer to overfitting Frequentist: - model selection - regularisation Bayesian: - BMA - marginalisation
  • 6. Volodymyrk Case Study You just get the best job in the galaxy
  • 7. Volodymyrk Your new Boss Business domain Modelling case Always test your models on synthetic data that you understand and control
  • 8. Volodymyrk Use Cases: - Fraud Detection - Inventory Sourcing Data
  • 9. Volodymyrk Modelling goals - Prediction range is needed, so that you can identify fraudulent transactions (sand people under-reporting real transaction size and pocketing profit) - Sale price should be easily explainable, as a function of various Droid Features so that Jabba can invest in appropriate scavenging/sourcing projects - You want lowest prediction error possible so that you are not feeded to Sarlacc
  • 12. Volodymyrk Model Selection - classical method credits ~ height + weight + power + dents + rad + wheels + legs + red + blue + black + temperature + lat + long + ir_emit + dents_log + height_log + weight_log + power_log + rad_log Adj. R2: 0.884974385182
  • 13. Volodymyrk Model Selection - backward elimination
  • 14. Volodymyrk Final Model credits ~ weight + power + dents + rad + wheels + blue + black + temperature + lat + dents_log + height_log + weight_log + power_log Adj. R2: 0.903544333611
  • 17. Volodymyrk Bayesian Model Averaging for Linear Models - a special case Inclusion probability for (regression coefficients) are weighted across all possible models Number of models = combinations of all K features (include/exclude) = 2K
  • 18. Volodymyrk How to actually do BMA? (in R) cran.r-project.org/web/packages/BMA cran.r-project.org/web/packages/BAScran.r-project.org/web/packages/BMS Mature. A.k.a. “the original” Developed by PhD duringresearch. Not maintained Newest. Maintained by Chair of the Department ofStatistical Science at Duke
  • 19. Volodymyrk BMA using BMS (R) package Model Selection L2 Regularisation BMA MSE 9736.49 7782.21 7329.44 It worked! But you can find inputs into data generator script that will not work as well!
  • 20. Volodymyrk Nice things you get from BMA Posterior Inclusion Probability! How cool is that!
  • 21. Volodymyrk Model ranking! MCMC can beused, if number of features is large Best model, according toBMA
  • 22. Volodymyrk Can we use it for more complex models? normalising term that you can ignore http://www.ssc.wisc.edu/~bhansen/718/NonParametrics15.pdf http://www.ejwagenmakers.com/2004/aic.pdf Warning:Very questionable math. Does not work
  • 23. Volodymyrk Can we use BMA to combine complex (incl. hierarchical) models? 1 3 2 Model order is somewhat similar. Relative probabilities are not. We need working Reverse-Jump MCMC or something more sophisticated. Not available in common bayesian MCMC packages yet.
  • 24. Volodymyrk In Summary - BMA is a Bayesian version of ML Model Ensembles - Math behind is quite beautiful - Model Averaging is useful for interpretation, not only prediction - Invest in synthetic data generation, - before applying new modelling techniques to real-world data - Even if you are not using BMA, fit different models - And combine them, if your goal is prediction - BMA works very well for common GLMs, but does not work yet for arbitrary models - Do try it next time you need to fit OLS, though!
  • 25. Volodymyrk Of course we are hiring! ● (Snr, Mid) Data Scientists ● Solutions Architect ● Ruby Developer ● Data Engineer ● Senior Artist ● Technical Artist ● Unity Developers ● Senior Product Manager ● Product Director http://jobs.productmadness.com/