Deep Factors for Forecasting Yuyang Wang, Alex Smola, Danielle C. - PowerPoint PPT Presentation

Deep Factors for Forecasting Yuyang Wang, Alex Smola, Danielle C. Maddix, Jan Gasthaus, Dean Foster, Tim Januschowski

Time Series Prediction … at Amazon weekly units 
 servers 
 shipped forecast and forecast and used years ahead Capacity planning Market entry Topology Planning

Time Series Prediction … at Amazon • Predict demand for each product available at Amazon • Problem • How many items to order • Where to order • When to mark down (ugly sweaters after Christmas)

Forecasting predictions sample paths zt xt Estimate future observations (univariate case) p ( z t +1 | ( x 1 , z 1 ), …( x t , z t ), x t +1 ) Make optimal decisions argmin a 𝔽 z t +1 | past [ l ( a , z t +1 , past)]

But in reality …

Two old ideas predictions sample paths zt xt • Model each time series • Model all time series locally and individually jointly and globally • Easy to add more • Works better • Simple models • Impossible to add more • Doesn’t work so well • Complex model

… make a good one • Local model • Global model • Reads from global model • Nonlinear backbone • Updates local state • Nonparametric • Theorem (deFinetti for time series) 
 For an exchangeable distribution over time series the joint distribution can be written as a local/global model. 1,…, T for i ∈ {1,… N }) = ∫ dg T N ∏ ∏ p ( x i p ( x i t | x i t − 1 , …, x i p ( g t | g t − 1 , … g 1 ) t , g t , … g 1 ) t =1 i =1 • Corresponding result for trees, too (via Tree-deFinetti)