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Chris Campbell Gaussian Processes

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Page 1: Gaussian Processes · Gaussian Processes. Forecasting Processes Agenda Gaussian Processes Profit Code Speed. Forecasting Processes. Project Structure & Docs. Packaging & Testing

Chris Campbell

Gaussian Processes

Page 2: Gaussian Processes · Gaussian Processes. Forecasting Processes Agenda Gaussian Processes Profit Code Speed. Forecasting Processes. Project Structure & Docs. Packaging & Testing

Forecasting Processes

Agenda

Gaussian Processes

Profit

Code Speed

Page 3: Gaussian Processes · Gaussian Processes. Forecasting Processes Agenda Gaussian Processes Profit Code Speed. Forecasting Processes. Project Structure & Docs. Packaging & Testing

Forecasting Processes

Page 4: Gaussian Processes · Gaussian Processes. Forecasting Processes Agenda Gaussian Processes Profit Code Speed. Forecasting Processes. Project Structure & Docs. Packaging & Testing

Project Structure & Docs

Page 5: Gaussian Processes · Gaussian Processes. Forecasting Processes Agenda Gaussian Processes Profit Code Speed. Forecasting Processes. Project Structure & Docs. Packaging & Testing

Packaging & Testing

Page 6: Gaussian Processes · Gaussian Processes. Forecasting Processes Agenda Gaussian Processes Profit Code Speed. Forecasting Processes. Project Structure & Docs. Packaging & Testing

Reproducible Data

Page 7: Gaussian Processes · Gaussian Processes. Forecasting Processes Agenda Gaussian Processes Profit Code Speed. Forecasting Processes. Project Structure & Docs. Packaging & Testing

Reproducible Data

Raw Data

1 run_all.R

CommitScripts

f34d20 sales

Data Checksum

02ec42

2 run_all.R 932a45 sales 563b3e

3 run_all.R 932a45 sales 74a10d

Page 8: Gaussian Processes · Gaussian Processes. Forecasting Processes Agenda Gaussian Processes Profit Code Speed. Forecasting Processes. Project Structure & Docs. Packaging & Testing

Agile Planning & Tickets

Page 9: Gaussian Processes · Gaussian Processes. Forecasting Processes Agenda Gaussian Processes Profit Code Speed. Forecasting Processes. Project Structure & Docs. Packaging & Testing

Cross-Validation

Page 10: Gaussian Processes · Gaussian Processes. Forecasting Processes Agenda Gaussian Processes Profit Code Speed. Forecasting Processes. Project Structure & Docs. Packaging & Testing

Model Ensemble

Page 11: Gaussian Processes · Gaussian Processes. Forecasting Processes Agenda Gaussian Processes Profit Code Speed. Forecasting Processes. Project Structure & Docs. Packaging & Testing

Gaussian Processes

Page 12: Gaussian Processes · Gaussian Processes. Forecasting Processes Agenda Gaussian Processes Profit Code Speed. Forecasting Processes. Project Structure & Docs. Packaging & Testing

Joint Distribution

Page 13: Gaussian Processes · Gaussian Processes. Forecasting Processes Agenda Gaussian Processes Profit Code Speed. Forecasting Processes. Project Structure & Docs. Packaging & Testing

Conditional Probability

Page 14: Gaussian Processes · Gaussian Processes. Forecasting Processes Agenda Gaussian Processes Profit Code Speed. Forecasting Processes. Project Structure & Docs. Packaging & Testing

Time Series

Page 15: Gaussian Processes · Gaussian Processes. Forecasting Processes Agenda Gaussian Processes Profit Code Speed. Forecasting Processes. Project Structure & Docs. Packaging & Testing

Distribution Next Point

Page 16: Gaussian Processes · Gaussian Processes. Forecasting Processes Agenda Gaussian Processes Profit Code Speed. Forecasting Processes. Project Structure & Docs. Packaging & Testing

package:GPfit

library(GPfit)gp2 <- GP_fit(

X = xm1, Y = y1)

Page 17: Gaussian Processes · Gaussian Processes. Forecasting Processes Agenda Gaussian Processes Profit Code Speed. Forecasting Processes. Project Structure & Docs. Packaging & Testing

Points in Time

Page 18: Gaussian Processes · Gaussian Processes. Forecasting Processes Agenda Gaussian Processes Profit Code Speed. Forecasting Processes. Project Structure & Docs. Packaging & Testing

Kernel

𝐾(𝑥, 𝑥) =

𝑘(𝑥1, 𝑥1 ) 𝑘(𝑥1, 𝑥2 ) 𝑘(𝑥1, 𝑥𝑛 )𝑘(𝑥2, 𝑥1 ) 𝑘(𝑥2, 𝑥2 ) 𝑘(𝑥2, 𝑥𝑛 )𝑘(𝑥𝑛, 𝑥1 ) 𝑘(𝑥𝑛, 𝑥2 ) 𝑘(𝑥𝑛, 𝑥𝑛 )

Page 19: Gaussian Processes · Gaussian Processes. Forecasting Processes Agenda Gaussian Processes Profit Code Speed. Forecasting Processes. Project Structure & Docs. Packaging & Testing

Slow in High Dimensions

Page 20: Gaussian Processes · Gaussian Processes. Forecasting Processes Agenda Gaussian Processes Profit Code Speed. Forecasting Processes. Project Structure & Docs. Packaging & Testing

Code Speed

Page 21: Gaussian Processes · Gaussian Processes. Forecasting Processes Agenda Gaussian Processes Profit Code Speed. Forecasting Processes. Project Structure & Docs. Packaging & Testing

What is taking longest?

library(profvis)profvis(gp2 <- GP_fit(X = xm1, Y = y1))

Page 22: Gaussian Processes · Gaussian Processes. Forecasting Processes Agenda Gaussian Processes Profit Code Speed. Forecasting Processes. Project Structure & Docs. Packaging & Testing

Timing Hierarchy by Function

Page 23: Gaussian Processes · Gaussian Processes. Forecasting Processes Agenda Gaussian Processes Profit Code Speed. Forecasting Processes. Project Structure & Docs. Packaging & Testing

Flame Graph

Page 24: Gaussian Processes · Gaussian Processes. Forecasting Processes Agenda Gaussian Processes Profit Code Speed. Forecasting Processes. Project Structure & Docs. Packaging & Testing

Replace Slower Code

Page 25: Gaussian Processes · Gaussian Processes. Forecasting Processes Agenda Gaussian Processes Profit Code Speed. Forecasting Processes. Project Structure & Docs. Packaging & Testing

Profit

Page 26: Gaussian Processes · Gaussian Processes. Forecasting Processes Agenda Gaussian Processes Profit Code Speed. Forecasting Processes. Project Structure & Docs. Packaging & Testing

Forecasts aggregatedmonthly

Page 27: Gaussian Processes · Gaussian Processes. Forecasting Processes Agenda Gaussian Processes Profit Code Speed. Forecasting Processes. Project Structure & Docs. Packaging & Testing

GitHub & CRAN

Page 28: Gaussian Processes · Gaussian Processes. Forecasting Processes Agenda Gaussian Processes Profit Code Speed. Forecasting Processes. Project Structure & Docs. Packaging & Testing

https://builder.r-hub.io/

Page 29: Gaussian Processes · Gaussian Processes. Forecasting Processes Agenda Gaussian Processes Profit Code Speed. Forecasting Processes. Project Structure & Docs. Packaging & Testing

Uncertainty

Page 30: Gaussian Processes · Gaussian Processes. Forecasting Processes Agenda Gaussian Processes Profit Code Speed. Forecasting Processes. Project Structure & Docs. Packaging & Testing

Gaussian Processes

Derive non-linear relationships from observed data

Excellent for interpolation

Allow estimation of forecast error

Poor performance for higher dimensionality

Kernel, RKHS, and Gaussian Processes

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Forecasting and Trading Commodity Contract Spreads with Gaussian Processes

Forecasting and Trading Commodity Contract Spreads with ... · Forecasting and Trading Commodity Contract Spreads with Gaussian Processes Abstract This paper examines the use of Gaussian

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Gaussian Processes - All Facultypeople.ee.duke.edu/~lcarin/David1.27.06.pdf · Gaussian Distributions and Gaussian Processes • A Gaussian distribution is a distribution over vectors

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