Automatic Forecasting at Scale

Sean J. Taylor 12 Aug 2015

Joint Statistical Meetings

Many Forecasting Problems at Facebook

• capacity planning: servers, switches, people, even food

• user / advertiser growth

• revenue

• goal setting for teams (with respect to forecast)

• detecting anomalies

• “trending” units

Business Time Series Have Similar Attributes• comprised by multiple “units”

(e.g. countries, users, advertisers, hardware units)

• units are “born” at different times, can exit the sample

• growth curves are common (e.g. saturating a market)

• complex, human-scale seasonality, holidays and events

• structural breaks as exogenous changes happen(e.g. new products, redesigns, site outages)

• missing data

Thousands or millions of forecasts?

Mo’ Data, Mo’ Problems

A second (and third) kind of scale: many people and problems

Goal is to create technology: people who are not experts can use it easily with few decisions and trust the output

Technology?

Results of my search for forecasting advice

▪ carefully clean, scale, and fix missingness in data

▪ try many kinds of models

▪ use model selection procedures based on (penalized) goodness-of-fit or just ocular goodness-of-fit

▪ lots of tacit knowledge involved — experienced forecasters have earned a lot of credibility

Why is building a forecaster harder than building a classifier?

How most people build a classifier:

1. Choose a loss function.

2. Gather as much data as possible and construct potentially useful features.

3. Train models using different amounts of regularization.

4. Choose the one that predicts the best out-of-sample using some cross-validation procedure.

With a flexible enough learner, the only time a human needs to intervene is during feature construction!

Forecasting as (special) supervised learningFeatures

▪ state-features constructed from historical data

▪ time-based features for seasonality, events, etc.

Training

▪ off-the-shelf regularized regression (glmnet, VW)

Model selection

▪ use simulated forecasts to estimate expected loss

When you have a really awesome

hammer, make everything

look like a regularized regression.

argmin�

ky �X�k2 + �1k�k1 + �2k�k2

A flexible extrapolation model

Fixed-Horizon Forecasting Regression

Regressors are generated from paste state:

yt+H = f(yt, yt�1, yt�2, . . .)

yt+H = ↵yt + �1

t

tX

i=1

yi

Last ValueMean Value

State features from one-sided kernel-weighted statistics

t

Can use any weighted statistic to generate features: mean, variance, quantiles, etc.

past data

Assumption: local smoothnessAssume parameters vary smoothly over forecast horizon (same as assuming forecast is locally smooth).

yt+H = ↵H · yt + �H · 1t

tX

i=1

yi

Different model for each horizon

↵H

H0 Max Horizon

Adding Seasonality FeaturesAdd components to the model that represent deterministic functions of time:

▪ trend

▪ cyclic cubic splines for yearly seasonality

▪ day-of-week, day-of-year, hour-of-day dummy variables

▪ smooth curves around known holidays

yt+H = f(yt, yt�1, yt�2, . . .) + g(t+H)

t y1/1 51/2 91/3 16

t last mean1/1 - -1/2 5 51/3 9 7

t+H y Mon Tue1/1 5 1 01/2 9 0 11/3 14 0 0

State Features

Target + Time Features

t+H t H y last mean Mon Tues

1/2 1/1 1 5 - - 0 1

1/3 1/1 2 9 - - 0 0

1/3 1/2 1 14 5 5 0 0

Input Data for TrainingSeries

Making it hierarchicalWe want to borrow information about processes across units. Huge opportunity because:

1. We know more about “new” time series than we think if we are willing to assume they are generated from a similar process.

2. The more examples from a family of time series processes we have, the better we are able to learn about its structure. Example: stock market.

3. Precision gains from borrowing information.

One weird trick for hierarchical models

Common Features

United States

Canada

Mexico

Global parameters Unit-specific

yi,t+H = ↵yt + �1

t

tX

i=1

yi + ↵iyt + �i1

t

tX

i=1

yi

Training

▪ BIG DATA: optimization-based techniques are difficult to use here because

▪ Online learning using SGD/Adagrad/Adadelta work well here AND we can update parameters for different loss functions and regularization parameters at the same time.

▪ Other bonus for online learning: incremental learning on data sorted by time!

Model Selection via Forward Cross-ValidationWe have two sets of hyper-parameters:

1. regularization of the model coefficients.

2. amount of differencing we do before fitting.

Just like in the classification version of the problem, we choose the model that empirically forecasts the best by selecting K simulated forecast dates.

Training stream

Testing stream

Checkpoint Model

1

2 1

23

Predictive Intervals with Quantile Regression

Very important to quantify uncertainty about a forecast. Often we’d prefer that people not even look at the point estimates.

Once you’re in the land of regularized linear regression, we can get predictive intervals simply by changing loss function to quantile loss.

Directly optimizing the model for the correct amount of empirical coverage!

Computational Tricks

▪ online feature scaling

▪ feature hashing

▪ stochastic gradient descent (and Adagrad, Adadelta)

▪ fitting several models simultaneously on the same data stream

Scaling to More People/Problems

1. Start with a single use-case and nail it.

2. Parameterize that solution — adding new problems should simple be configuration.

3. Work on model/fitting procedure, then run all previous models for diagnostics.

4. Provide easy tools for model criticism — top predictive errors, examples with under/over coverage, etc.

Conclusions▪ Different kinds of “at scale” — people and problems are

more important than size of data

▪ If a model/technique is hard to use, it’s worth thinking about what it would take for a non-expert to use it.

▪ Making problems look like regularized linear regression is GREAT.

▪ Forecasting can be made into a very special kind of supervised learning.

▪ Email me with comments/feedback: sjt@fb.com