Forecasting Space-time Events Jeremy Heffner Senior Data Scientist jheffner@azavea.com

340 N 12th St, Suite 402 Philadelphia, PA 19107 215.295.2600 www.azavea.com

37 people using geodata

to do stuff that matters

B Corporation •  Civic/Social impact •  Donate share of profits

Research-Driven •  10% Research Program •  Academic Collaborations •  Open Source •  Open Data

Land Water People

It’s the third Thursday in February and school is in session. There were 3 burglaries and 2 robberies yesterday. Six bars, three take-out stores, and a school are in the neighborhood. The forecast is 63°. Where do you focus your 2 vehicles?

It’s the third Thursday in February and school is in session. There were 3 burglaries and 2 robberies yesterday. Six bars, three take-out stores, and a school are in the neighborhood. The forecast is 63°. Where do you focus your 2 vehicles?

Geographic Data Geoprocessing

Forecasting Results

Geographic Data

(x, y, t)

Map Algebra

{local, focal, zonal, global} operations

Geoprocessing

a geographic data processing engine for high performance applications

6183 x 4992 4598 x 4867 118 MB 86 MB

1770271 x 910139

5.8 TB

a geographic data processing engine for high performance applications

Demos at geotrellis.io

Example GeoTrellis Operation

Forecasting Crime

~ 250 m cells & 1+ hour time slices

Data Volume

•  Space –  Chicago IL is 234 sq miles –  250 m cell size creates 10,000 cells

•  Time –  3 years of data –  1 hour resolution –  26,000 hour blocks

•  Space x Time –  260,000,000 hour block cells (examples)

Data Volume

•  Sampling FTW! –  Outcomes are sparse (small % of examples have crimes) –  Sampling strategy preserves crime events –  Use models that can utilize example weights

–  Baseline crime levels •  Similar to traditional hotspot maps

–  Near repeat patterns •  Event recency (contagion)

–  Risk Terrain Modeling •  Proximity and density of geographic features •  Points, Lines, Polygons (bars, bus stops, etc.)

–  Collective Efficacy •  Socioeconomic indicators (poverty, unemployment, etc.)

–  Natural Terrain •  Slope, aspect, elevation, roughness

Features

–  Routine Activity Theory •  Offender: proximity and concentration of known offenders •  Guardianship: police presence (AVL / GPS) •  Targets: measures of exposure (population, parcels, vehicles)

–  Temporal cycles •  Seasonality, time of month, day of week, time of day

–  Recurring temporal events •  Holidays, sporting events, etc.

–  Weather •  Temperature, wind, precipitation

Features

Gun shootings example Source: Rutgers, http://www.rutgerscps.org/rtm/irvrtmgoogearth.htm

crimes prior7 prior364 dayssincelast bardist dow

0 0 0 365 >2000ft Monday

0 0 1 234 >2000ft Monday

1 1 3 3 750ft Tuesday

0 0 2 43 500ft Wednesday

2 0 2 74 500ft Friday

crimes probability

0 0

1 a

2 b

3 c

4 d

Aoristic Analysis

Event 1

Event 2

Event 3

Event 4

crimes weights prior7 prior364 dayssincelast bardist dow

0 1 0 0 365 >2000ft Monday

0 1 0 1 234 >2000ft Monday

0 0.5 1 3 3 750ft Tuesday

1 0.5 1 3 3 750ft Tuesday

0 0 0 2 43 500ft Wednesday

0 0.13 0 2 74 500ft Friday

1 0.32 0 2 74 500ft Friday

2 0.55 0 2 74 500ft Friday

Models •  Baseline models (6)

–  {28, 56, 364} day counts –  {28, 56, 364} day kernel densities

•  HunchLab models –  Variations of a stacked ensemble:

•  examples è gradient boosting machine (gbm) è y/n probabilities •  y/n probabilities è generalized additive model (gam) è counts

gradient boosting machine (GBM)

Build Decision Tree 1

Predict with 1

Calculate errors

1 Build Decision Tree 2

Predict with 1 & 2

Calculate errors

2 Build Decision Tree 3

Predict with 1-3

Calculate errors

3 …

312 million

4 million

1 mil 1 mil 1 mil 1 mil

Sampling

4 folds

GBM

}

1 mil

Evaluate

43

200

312 million

4 million

Sampling

GBM 43

Model Building

1.  Build a GBM –  examples è gradient boosting machine è y/n probabilities

•  Segment examples into several folds –  For each fold build a GBM model on the rest of the data –  For each iteration in the GBMs:

»  Randomly sample a portion of the data (stochastic) »  Adjust weights of observations (adaptive boosting)

•  Determine how many iterations result in the most accurate model •  Build a GBM on all of the data for that many iterations

generalized additive model (GAM)

Model Building

2.  Build a GAM –  y/n probabilities è generalized additive model è counts

•  Transforms (“bends”) GBM output into counts •  Calibrates count levels with key variables

Using the Forecasts

# Assaults x

$87,238 x

0%

# Burglary x

$13,096 x

25%

# MVT x

$9,079 x

50%

# Rape x

$217,866 x

0%

# Robbery x

$67,277 x

10%

Sum to Predicted Cost of Preventable Crime

Patrol Benefit (Predicted Crime)

Patrol Effort (Road Length)

÷ =

Patrol Benefit / Effort

Patrol Benefit / Effort

Patrol Effort (Budget)

Select Best Areas Subject to ‘Budget’

Is always patrolling today’s highest risk locations the best strategy?

101 100 2

2 2 50

1 1 1

101 100 2

2 2 50

1 1 1

75 30 2

2 2 60

1 1 1

101 100 2

2 2 50

1 1 1

80 60 2

2 2 40

1 1 1

1.65 1.63 -0.61

-0.61 -0.61 0.48

-0.64 -0.64 -0.64

101 100 2

2 2 50

1 1 1

1.65 1.63 0

0 0 0.48

0 0 0

Weighted Forecast Z-score Filter

4.52 4.34 0

0 0 0.11

0 0 0

1.65 1.63 0

0 0 0.48

0 0 0

4.52 4.34 0

0 0 0.11

0 0 0

Filter Raise to Power

Probabilistic Selection

4.52 4.34 0

0 0 0.11

0 0 0

1.65 1.63 0

0 0 0.48

0 0 0

4.52 4.34 0

0 0 0.11

0 0 0

Filter Raise to Power

Probabilistic Selection

4.52 4.34 0

0 0 0.11

0 0 0

1.65 1.63 0

0 0 0.48

0 0 0

4.52 4.34 0

0 0 0.11

0 0 0

Filter Raise to Power

Probabilistic Selection

Results

So what forecasts crime?

Crime Data -  Cities: Chicago, Philadelphia, Seattle, Washington DC -  Crime Types: Aggravated Assault, Burglary (Residential &

Non-residential), Homicide, Motor Vehicle Theft, Theft from Motor Vehicle, Robbery

Geographic Data -  POIs / Roads: OpenStreetMap -  Terrain: USGS

Temporal Data -  Weather: Forecast IO API

Theory Group Example Variables Built Geography Density/Distance from schools, police, fire stations,

etc. ...

Historic Levels Counts & Kernel Density for prior events, time periods >= 14 days

Temporal Cycles Day of Week, phases of moon, sunlight hours

Time Since Last (Near-Repeat) Number of periods since last event

Weather Pressure, Min/Max temperature, wind speed

Natural Terrain Aspect, elevation, roughness, slope

Row & Column Raster cell row and column (ideally unused)

Variation across Crime Types

Variation across Cities

Wind Speed & Aggravated Assault (Chicago)

Time Since Last & Theft From Vehicles (Seattle)

MVT and Distance from School (Philadelphia)

Measuring Accuracy

Measuring Accuracy

Accuracy Results

Questions? Jeremy Heffner Senior Data Scientist jheffner@azavea.com

340 N 12th St, Suite 402 Philadelphia, PA 19107 215.295.2600 www.azavea.com