This document discusses using machine learning techniques like EM algorithms, MCMC sampling, and Dirichlet process mixture models to model transit and dwell times for Tesla vehicle deliveries based on interval-censored data from multiple sources. The models are used to estimate probability distributions of transit times and schedule optimal pickup dates to minimize expected losses from late deliveries.

1. USING MACHINE LEARNING TO DELIVER TESLAUSING MACHINE LEARNING TO DELIVER TESLA
MODEL 3'SMODEL 3'S
Michael Lindon

2. DISCLAIMER!DISCLAIMER!
[not real data]

3. SUPPLY CHAIN AUTOMATIONSUPPLY CHAIN AUTOMATION
Michael Lindon Charles Freundlich
Sr. Data Scientist Sr. Manager

4. (mock)

5. source: https://www. ickr.com/photos/steevithak/34209933664

6. (mock)

7. DATADATA

8. DATA STRUCTUREDATA STRUCTURE

9. SOURCES OF MEASUREMENTSOURCES OF MEASUREMENT
Mobile App
Carrier Portal
Hub Logistics Worker
Tesla Logistics Worker

10. FEATURESFEATURES
Driver Type: Single Driver/Team Driver
Service Level: Standard/Expedited
Driver ID
Company
Weather Information
Tra c Information
Temporal Features

11. FIRST PASS MODEL: XGBOOSTFIRST PASS MODEL: XGBOOST

12. "These features aren't available at
runtime..."

13. Features are not known for future predictions
Regression Density Estimation→

14. "These transit and dwell times don't
make sense"

15. Mobile App - Human Error
Carrier Portal - Human Error
Hub Logistics Worker - Human Error
Tesla Logistics Worker - Human Error
Data Processing - Logical Errors

16. DESIGNING OUR OWN EXPERIMENTDESIGNING OUR OWN EXPERIMENT

17. DATA SCIENCE SUPERPOWERSDATA SCIENCE SUPERPOWERS
Experimental Design
Data Engineering
Statistics + ML

18. GEOFENCESGEOFENCES

19. GEOFENCES + CAR GPSGEOFENCES + CAR GPS

20. RAW TRAINING DATARAW TRAINING DATA

21. Transit/Dwell Times are "interval censored"

22. BASIC MODELLINGBASIC MODELLING

23. Observe:
, … ,z1 zn
yi
(μ, )σ
2
∼ LogNormal(μ, )σ
2
= log zi
∼ NI ( , λ, , )χ
2
μ0 ν0 σ
2
0
∈ [ , ] :=yi Li Ui Ii

24. Joint has tractable conditional distributions:
π(μ, |I) =
∫
π(y, μ, |I)dyσ
2
σ
2
|μ, ,yi σ
2
Ii
(μ, )|y, Iσ
2
∼ T N(μ, , , )σ
2
Li Ui
∼ NI ( , , , )χ
2
μ̃ λ̃ ν̃ σ
2
~

25. OPTIMIZATION: EM ALGORITHM [1]OPTIMIZATION: EM ALGORITHM [1]
Expectation w.r.t. truncated-normal
Mode of Normal-inverse-
Computes the MAP estimate of and
Q(μ, | , )σ
2
μ
(t)
σ
2(t)
,μ
(t+1)
σ
2(t+1)
:= [log π(μ, , y|I)| , ]σ
2
μ
(t)
σ
2(t)
← argmax Q(μ, | , )σ
2
μ
(t)
σ
2(t)
χ
2
⇒ μ σ
2

26. MCMC: GIBBS SAMPLING [2]MCMC: GIBBS SAMPLING [2]
Generate
Generate
∼ π( | , , )y
(t+1)
i
yi μ
(t)
σ
2(t)
Ii
(μ, ∼ π(μ, | , I)σ
2
)
(t+1)
σ
2
y
(t+1)

27. TRANSIT EXAMPLE:TRANSIT EXAMPLE:

28. EXPECTATION MAXIMIZATIONEXPECTATION MAXIMIZATION
= 1.946μ̂ = 0.003σ̂
2
⇒ [z] = 7.01 [z] = 0.15

29. MARKOV CHAIN MONTE CARLOMARKOV CHAIN MONTE CARLO

30. NONPARAMETRIC DENSITY ESTIMATIONNONPARAMETRIC DENSITY ESTIMATION

31. DIRICHLET PROCESS MIXTURE MODEL [3,4]DIRICHLET PROCESS MIXTURE MODEL [3,4]
Censored Observations:
| ,yi μi σ
2
i
( , )μi σ
2
i
G
∼ N( , )μi σ
2
i
∼ G
∼ (NI ( , λ, , ), α)χ
2
μ0 ν0 σ
2
0
∈ [ , ]yi Li Ui

32. ESTIMATED SURVIVAL FUNCTIONESTIMATED SURVIVAL FUNCTION

33. ESTIMATED DENSITYESTIMATED DENSITY

34. DECISION THEORYDECISION THEORY

35. Point Estimate "ETA" Neglects Uncertainty
Model Output is Posterior Predictive Distribution
Need to schedule car pickup date
p( |Data) =
∫
p( |θ)p(θ|Data)dθy
⋆
y
⋆

36. customer pickup date (action)
car arrival time at service center (rv)
Loss function
Late Arrivals Damage Brand
Storage Costs
Working Capital Costs
a ∈ 
y
⋆
L(a, )y
⋆

37. MINIMIZING EXPECTED LOSSMINIMIZING EXPECTED LOSS
R(a)
â
=
∫
L(a, )p( |Data)dy
⋆
y
⋆
y
⋆
← argmin R(a)

38. References
1. Dempster, A., Laird, N., & Rubin, D. (1977). Maximum Likelihood from Incomplete Data via the EM Algorithm. Journal of the Royal Statistical Society. Series B
(Methodological), 39(1), 1-38.
2. Kuo L., Smith A.F.M., MacEachern S., West M. (1992) Bayesian Computations in Survival Models Via the Gibbs Sampler. In: Klein J.P., Goel P.K. (eds) Survival Analysis:
State of the Art. Nato Science (Series E: Applied Sciences), vol 211. Springer, Dordrecht
3. Michael D. Escobar & Mike West (1995) Bayesian Density Estimation and Inference Using Mixtures, Journal of the American Statistical Association, 90:430, 577-588,
DOI: 10.1080/01621459.1995.10476550
4. Radford M. Neal (2000) Markov Chain Sampling Methods for Dirichlet Process Mixture Models, Journal of Computational and Graphical Statistics, 9:2, 249-265, DOI:
10.1080/10618600.2000.10474879