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Demand Forecasting with Machine Learning
Colin Ard

2. © 2016 Micron Technology, Inc. |
Agenda
- Demand Forecasting at Micron
- Classical Time Series Analysis
- Building Predictive Models for Time Series with Machine Learning
- Demand Forecasting with Machine Learning Ensembles
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A Bit About Micron
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- Founded in 1978 in Boise, ID
- First fabrication unit completed in 1980
- Growth through expansion and acquisition
- Global company with over 30,000 employees

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Demand Forecasting at Micron
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5. - Scope: Tens of thousands of series requiring forecasting
- Scale: Consistent high demand vs sparse low demand
- Structure…
Data Complexities

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Univariate Time Series Analysis
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𝑌𝑡 = 𝛼 + 𝛽𝑡 + 𝑒𝑡, 𝑒𝑡 ~Normal 0, 𝜎2
Solve by minimizing loss function: 𝐿 𝑌, 𝛼, 𝛽
Residual
𝐿 𝑌, 𝛼, 𝛽 = 𝑌𝑡 − 𝛼 − 𝛽𝑡 2
𝑇
𝑡=1
Squared error loss

7. © 2016 Micron Technology, Inc. |
Univariate Time Series Analysis
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ACFℎ = Correlation 𝑌𝑡, 𝑌𝑡−ℎ
Partial ACFℎ = Correlation 𝑌𝑡, 𝑌𝑡−ℎ|𝑌𝑡−1, … 𝑌𝑡−ℎ+1
Residual
𝐿 𝑌, 𝛼, 𝛽 = 𝑌𝑡 − 𝛼 − 𝛽𝑡 2
𝑇
𝑡=1
Squared error loss
𝑌𝑡 = 𝛼 + 𝛽𝑡 + 𝑒𝑡, 𝑒𝑡 ~Normal 0, 𝜎2
Solve by minimizing loss function: 𝐿 𝑌, 𝛼, 𝛽

8. © 2016 Micron Technology, Inc. |
Auto-regression (AR): 𝑌𝑡 = 𝛿 + 𝜑𝑌𝑡−1 + 𝑤𝑡
Univariate Time Series Analysis
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Differencing: ∆𝑌𝑡 = 𝑌𝑡 − 𝑌𝑡−1
Moving average (MA): 𝑌𝑡 = 𝜇 + 𝜃𝑤𝑡−1 + 𝑤𝑡
Non-stationary series
Difference: 𝑌𝑡 → ∆𝑌𝑡
AR 1
MA 1
Residuals from Differenced Series

9. © 2016 Micron Technology, Inc. |
Univariate Time Series Analysis
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Non-stationary series
Difference: 𝑌𝑡 → ∆𝑌𝑡
Residuals from ARIMA (1, 1, 1)
Auto-regression (AR): 𝑌𝑡 = 𝛿 + 𝜑𝑌𝑡−1 + 𝑤𝑡
Differencing: ∆𝑌𝑡 = 𝑌𝑡 − 𝑌𝑡−1
Moving average (MA): 𝑌𝑡 = 𝜇 + 𝜃𝑤𝑡−1 + 𝑤𝑡

10. © 2016 Micron Technology, Inc. |
Univariate Time Series Analysis
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Non-stationary series
Difference: 𝑌𝑡 → ∆𝑌𝑡
Forecasted Value
Expected Value
Residuals from ARIMA (1, 1, 1)
Auto-regression (AR): 𝑌𝑡 = 𝛿 + 𝜑𝑌𝑡−1 + 𝑤𝑡
Differencing: ∆𝑌𝑡 = 𝑌𝑡 − 𝑌𝑡−1
Moving average (MA): 𝑌𝑡 = 𝜇 + 𝜃𝑤𝑡−1 + 𝑤𝑡

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A Machine Learning Approach

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A Machine Learning Approach

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A Machine Learning Approach

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A Machine Learning Approach

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A Machine Learning Approach

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The Bias-Variance Tradeoff
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𝐿 𝑌, 𝑓; 𝛾 = 𝑌𝑖 − 𝑓 𝑋𝑖
2
𝑁
𝑖=1
+ 𝛾 𝑓′′
𝑠 2
𝑑𝑠
𝛾 = ∞ 𝛾 = 00 < 𝛾 < ∞
Squared error loss Complexity penalty
𝛾 ≥ 0: Tuning Parameter

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Demand History
Naïve Forecast
Alternate Forecasts
Ensemble Forecast
Machine Learning

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Ensembling Methods Pt. 1
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Final pre-processing steps:
- Cumulative forecasts totals
- Model demand over the next 3 months, as opposed to demand
3 months from now
- Separate ensemble models trained for each cumulative
forecast span
- Feature sorting for suitability in modeling:
- linear associations
- interaction-dependent associations
- Feature/Outcome transformation and scaling…
Outcome𝑖 =
Actual𝑖 − Naive𝑖
𝑐 + Actual𝑖 + Naive𝑖
Feature𝑖𝑚 =
Forecast 𝑖𝑚 − Naive𝑖
𝑐 + Forecast 𝑖𝑚 + Naive𝑖
∆𝑌𝑖
Stacked Generalization
𝑓1 𝑋𝑖
…
𝑌𝑖 = 𝐹 𝑋𝑖
𝑓2 𝑋𝑖 𝑓3 𝑋𝑖 𝑓 𝑀 𝑋𝑖
𝐹 ∆𝑌𝑖 1
, ∆𝑌𝑖 2
, … , ∆𝑌𝑖 𝑀
, …
~

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Ensembling Methods Pt. 2
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Naïve Forecast: Qty
∆𝑌 ARIMA
100K
-0.2
1M
R1
R2
R3 R4
∆𝑌𝑖 = 𝐿 𝑹, ∆𝑌𝑖 1
, ∆𝑌𝑖 2
, … , ∆𝑌𝑖 𝑀
, …
…
Boosting Algorithms
𝑌0
∗
= 𝑌
ℎ0 𝑋
𝑌1
∗
ℎ1 𝑋
𝑌 𝑀
∗
ℎ 𝑀 𝑋 𝑌 = 𝐹 𝑀 𝑋

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Ensemble Methods Pt. 3
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Training Data
T1 T2 T3 TB
…
Bootstrap Aggregation
Bagged Estimate
𝑌𝑖 =
1
𝐵
𝑌𝑖
𝑏
𝐵
𝑏=1
𝑋𝑖1, 𝑌𝑖1 𝑋𝑖2, 𝑌𝑖2 … 𝑋𝑖,𝑇−ℎ, 𝑌𝑖,𝑇−ℎ 𝑋𝑖𝑠 𝑖
, 𝑌𝑖𝑠 𝑖
𝑋1𝑠1
, 𝑌1𝑠1
𝑋2𝑠2
, 𝑌2𝑠2
…
Candidate model inputs for Product i
Full sample at bth training iteration
Goal:
- A generalizable model for change in demand
Challenges:
- Have to assume the fundamentals that drove historical
demand are likely to fluctuate over time
- Limited to validation of the algorithm rather than
testing of predictions from a specific trained model
𝑆𝑎𝑚𝑝𝑙𝑒
Forecasting h months ahead from month T
𝑋𝑖𝑠 𝑖
, 𝑌𝑖𝑠 𝑖
… 𝑋 𝑁𝑠 𝑁
, 𝑌𝑁𝑠 𝑁

21. © 2016 Micron Technology, Inc. |
Forecast Accuracy Metrics and Validation
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𝑤𝑀𝐴𝑃𝐸 = 100 ×
Actual − Forecast
Actual
𝐴𝑐𝑐𝑢𝑟𝑎𝑐𝑦 = 100 − 𝑤𝑀𝐴𝑃𝐸
Training Data:
𝑋𝑖𝑠, 𝑌𝑖𝑠 , 𝑠 ∈ 1, … , 𝑇 − ℎ
Validation Data:
𝑋𝑖𝑇, 𝑌𝑖𝑇
𝑃𝑟𝑒𝑑𝑖𝑐𝑡
Training Data:
𝑋𝑖𝑠, 𝑌𝑖𝑠 , 𝑠 ∈ 2, … , 𝑇 − ℎ + 1
Validation Data:
𝑋𝑖,𝑇+1, 𝑌𝑖,𝑇+1
𝑃𝑟𝑒𝑑𝑖𝑐𝑡
…
Training Data:
𝑋𝑖𝑠, 𝑌𝑖𝑠 , 𝑠 ∈ 𝐾 + 1, … , 𝑇 − ℎ + 𝐾
Validation Data:
𝑋𝑖,𝑇+𝐾, 𝑌𝑖,𝑇+𝐾
𝑃𝑟𝑒𝑑𝑖𝑐𝑡
Training Data:
𝑋𝑖𝑠, 𝑌𝑖𝑠 , 𝑠 ∈ 3, … , 𝑇 − ℎ + 2
Validation Data:
𝑋𝑖,𝑇+2, 𝑌𝑖,𝑇+2
𝑃𝑟𝑒𝑑𝑖𝑐𝑡

22. © 2016 Micron Technology, Inc. |
Forecast Accuracy Validation
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Lag-1 Lag-2 (Cumulative) Lag-3 (Cumulative)

23. © 2016 Micron Technology, Inc. |
Conclusions
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- Significant gains in forecast accuracy across lags
- Understand the challenge and play to your strengths
- Business processes, available data, and goals of the analysis
- Institutional knowledge and human expertise
- Acknowledgements
- Micron Enterprise Data Science and Demand Management Teams