Ishanu Chattopadhyay
Assistant Professor of
Data Science
University of Chicago
Rare Events in Complex Systems:
A Unified Framework To Model and Forecast Extreme
Weather, Seismic Events, Urban Crime and Global Terrorism
AI Awakens
Explains better than human students taking an introductory course
End
of
Theory?
https://chat.openai.com/chat
Urban Crime
Conflicts & Terrorism
Extreme weather phenomena
Seismic events
Irreducible
Complexity
Long-range memory
Non-trivial stochastic effects
No point learning individual sample paths
Can we learn stochastic phenomena non-parametrically?
Can we learn stochastic phenomena non-parametrically?
?
Chattopadhyay, Ishanu, and Hod Lipson. "Abductive learning of quantized stochastic processes with probabilistic finite automata." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 371, no. 1984 (2013): 20110543.
State structure :
self-similarity in dynamical systems
Modern AI algorithms are inspired by the computational units of the brain
Approximation by superpositions of a sigmoidal function
G. Cybenko, 1989
All neural networks are trained via "backpropagation"
Error gradients tend to decay fast as they are back propagated.
Deep Learning without Neural Networks
Gradient Propagation
Causality across two processes
Causality across time delays
Fractal Net: Information gradient doe not decay from the computation
Fractal Net
Neural Net
fixed non-linear activation
The Fractal Net architecture
No back-propagation
Deep Learning without Neural Networks
Lets Predict Crime
Rotaru, V., Huang, Y., Li, T. et al.
Event-level prediction of urban crime reveals a signature of enforcement bias in US cities. Nature Human Behavior 6, 1056–1068 (2022).
ID,Case Number,Date,Block,IUCR,Primary Type,Description,Location Description,Arrest,Domestic,Beat,District,Ward,Community Area,FBI Code,X Coordinate,Y Coordinate,Year,Updated On,Latitude,Longitude,Location\\
8316800,HT550945,08/11/2011 11:00:00 AM,086XX S MARQUETTE AVE,1120,DECEPTIVE PRACTICE,FORGERY,RESIDENCE,false,false,0423,004,7,46,10,1195654,1848294,2011,02/04/2016 06:33:39 AM,41.738615478,-87.558741896\\
8316805,HT550781,10/20/2011 05:00:00 AM,056XX S ABERDEEN ST,0890,THEFT,FROM BUILDING,RESIDENCE,false,false,0712,007,16,68,06,1169943,1867457,2011,02/04/2016 06:33:39 AM,41.791797599,-87.652385205\\
8316806,HT550706,10/20/2011 05:45:00 AM,079XX S LOOMIS BLVD,031A,ROBBERY,ARMED: HANDGUN,STREET,false,false,0612,006,21,71,03,1168370,1852331,2011,02/04/2016 06:33:39 AM,41.750323974,-87.658588247\\
8316811,HT539324,10/12/2011 12:23:52 PM,003XX E 75TH ST,2027,NARCOTICS,POSS: CRACK,SMALL RETAIL STORE,true,false,0323,003,6,69,18,1179641,1855355,2011,02/04/2016 06:33:39 AM,41.758372192,-87.61719416\\
8316822,HT551031,10/19/2011 02:00:00 AM,071XX W DICKENS AVE,0910,MOTOR VEHICLE THEFT,AUTOMOBILE,SIDEWALK,false,false,2512,025,36,25,07,1127877,1913161,2011,02/04/2016 06:33:39 AM,41.918027518,-87.805606689\\
8316824,HT551032,10/20/2011 12:00:00 AM,034XX N NATCHEZ AVE,2825,OTHER OFFENSE,HARASSMENT BY TELEPHONE,RESIDENCE,false,false,1632,016,36,17,26,1132429,1922272,2011,02/04/2016 06:33:39 AM,41.94295109,-87.788669409\\
8316825,HT549690,10/19/2011 12:51:00 PM,079XX S ADA ST,2820,OTHER OFFENSE,TELEPHONE THREAT,APARTMENT,false,false,0612,006,21,71,26,1168711,1852015,2011,02/04/2016 06:33:39 AM,41.749449482,-87.657347764\\
8316826,HT549865,10/19/2011 06:00:00 AM,011XX N LEAMINGTON AVE,0810,THEFT,OVER \$500,RESIDENTIAL YARD (FRONT/BACK),false,false,1531,015,37,25,06,1141821,1907155,2011,02/04/2016 06:33:39 AM,41.9012995,-87.754523767\\
8316827,HT550963,09/01/2011 04:00:00 PM,079XX S LOOMIS BLVD,0610,BURGLARY,FORCIBLE ENTRY,RESIDENCE-GARAGE,false,false,0612,006,21,71,05,1168380,1851969,2011,02/04/2016 06:33:39 AM,41.749330381,-87.658562005\\
8316838,HT548010,10/17/2011 03:20:00 PM,055XX N KEDZIE AVE,0820,THEFT,\$500 AND UNDER,"SCHOOL, PUBLIC, GROUNDS",true,false,1712,017,40,13,06,1154047,1936545,2011,02/04/2016 06:33:39 AM,41.981712678,-87.708829703\\
8316839,HT551049,10/20/2011 08:50:00 AM,102XX S AVENUE N,0430,BATTERY,AGGRAVATED: OTHER DANG WEAPON,STREET,false,false,0432,004,10,52,04B,1201166,1837763,2011,02/04/2016 06:33:39 AM,41.709579698,-87.538903651\\
8316871,HT549680,10/19/2011 01:03:00 PM,044XX N BROADWAY,0460,BATTERY,SIMPLE,DEPARTMENT STORE,false,false,2313,019,46,3,08B,1168460,1929880,2011,02/04/2016 06:33:39 AM,41.963123126,-87.65601675\\
8316872,HT551071,10/19/2011 03:10:00 PM,053XX S CALUMET AVE,0810,THEFT,OVER \$500,RESIDENCE,false,false,0234,002,3,40,06,1179390,1869685,2011,02/04/2016 06:33:39 AM,41.797700881,-87.617676981\\
8316873,HT551063,10/20/2011 11:10:00 AM,003XX E 47TH ST,1811,NARCOTICS,POSS: CANNABIS 30GMS OR LESS,SIDEWALK,true,false,0222,002,3,38,18,1178980,1873925,2011,02/04/2016 06:33:39 AM,41.809345175,-87.619051287\\
8316874,HT550901,10/20/2011 09:11:00 AM,033XX W OGDEN AVE,2022,NARCOTICS,POSS: COCAINE,POLICE FACILITY/VEH PARKING LOT,true,false,1024,010,24,29,18,1154489,1891024,2011,02/04/2016 06:33:39 AM,41.856790413,-87.708424071\\
8316875,HT549739,10/19/2011 01:30:00 PM,002XX E GARFIELD BLVD,0820,THEFT,\$500 AND UNDER,CTA BUS,false,false,0232,002,3,40,06,1178645,1868596,2011,02/04/2016 06:33:39 AM,41.794729551,-87.620442108\\
8316880,HT549802,10/19/2011 12:00:00 PM,011XX W WILSON AVE,0460,BATTERY,SIMPLE,COLLEGE/UNIVERSITY GROUNDS,false,false,2311,019,46,3,08B,1167612,1930696,2011,02/04/2016 06:33:39 AM,41.96538061,-87.659110921\\
8316881,HT431449,08/04/2011 11:00:00 AM,027XX W CHICAGO AVE,0820,THEFT,\$500 AND UNDER,STREET,false,false,1313,012,26,24,06,1157782,1905211,2011,02/04/2016 06:33:39 AM,41.895654523,-87.69595021\\
8316882,HT549162,10/19/2011 06:42:00 AM,105XX S WESTERN AVE,0610,BURGLARY,FORCIBLE ENTRY,TAVERN/LIQUOR STORE,false,false,2211,022,19,72,05,1162255,1834721,2011,02/04/2016 06:33:39 AM,41.702128701,-87.681485145\\
8316884,HT544972,10/16/2011 04:30:00 AM,103XX S HALSTED ST,1310,CRIMINAL DAMAGE,TO PROPERTY,SMALL RETAIL STORE,false,false,2232,022,34,73,14,1172807,1836192,2011,02/04/2016 06:33:39 AM,41.705939683,-87.642803521\\
8316886,HT549777,10/19/2011 02:10:00 PM,014XX W PRATT BLVD,0850,THEFT,ATTEMPT THEFT,SMALL RETAIL STORE,false,false,2431,024,49,1,06,1165565,1945281,2011,02/04/2016 06:33:39 AM,42.005446228,-87.666219555\\
8316887,HT551046,10/20/2011 11:10:00 AM,050XX N WINTHROP AVE,2820,OTHER OFFENSE,TELEPHONE THREAT,RESIDENCE,false,false,2033,020,48,3,26,1167955,1933907,2011,02/04/2016 06:33:39 AM,41.974184283,-87.657756697\\
8316889,HT550997,10/20/2011 09:10:00 AM,041XX N DICKINSON AVE,1121,DECEPTIVE PRACTICE,COUNTERFEITING DOCUMENT,STREET,true,false,1624,016,45,15,10,1142513,1926900,2011,02/04/2016 06:33:39 AM,41.955468935,-87.751489799\\
8316890,HT532649,10/07/2011 11:46:00 PM,062XX S VERNON AVE,2092,NARCOTICS,SOLICIT NARCOTICS ON PUBLICWAY,SIDEWALK,true,false,0313,003,20,42,26,1180324,1863694,2011,02/04/2016 06:33:39 AM,41.781239632,-87.614435596\\
8316893,HT551023,10/20/2011 02:00:00 AM,081XX S STEWART AVE,0810,THEFT,OVER \$500,STREET,false,false,0622,006,21,44,06,1175042,1850896,2011,02/04/2016 06:33:39 AM,41.746239973,-87.634181801\\
8316894,HT550772,10/20/2011 07:10:00 AM,048XX N TALMAN AVE,1320,CRIMINAL DAMAGE,TO VEHICLE,STREET,false,false,2031,020,40,4,14,1157831,1931974,2011,02/04/2016 06:33:39 AM,41.969093078,-87.695038453\\
8316898,HT551055,10/16/2011 09:00:00 AM,018XX S LAFLIN ST,1365,CRIMINAL TRESPASS,TO RESIDENCE,APARTMENT,false,false,1222,012,25,31,26,1166665,1891065,2011,02/04/2016 06:33:39 AM,41.856651049,-87.663730374\\
8316899,HT550695,10/20/2011 05:30:00 AM,122XX S HALSTED ST,1310,CRIMINAL DAMAGE,TO PROPERTY,RESIDENCE PORCH/HALLWAY,false,false,0524,005,34,53,14,1173210,1823636,2011,02/04/2016 06:33:39 AM,41.671475169,-87.641696924\\
8316901,HT549052,10/19/2011 12:01:00 AM,064XX S DR MARTIN LUTHER KING JR DR,1811,NARCOTICS,POSS: CANNABIS 30GMS OR LESS,STREET,true,false,0312,003,20,42,18,1180027,1862432,2011,02/04/2016 06:33:39 AM,41.777783389,-87.615563072\\
8316902,HT550988,10/20/2011 10:25:00 AM,066XX S KENNETH AVE,0486,BATTERY,DOMESTIC BATTERY SIMPLE,RESIDENCE,false,false,0833,008,13,65,08B,1147854,1860166,2011,02/04/2016 06:33:39 AM,41.772241474,-87.733568892\\
8316909,HT550957,10/20/2011 04:45:00 AM,051XX S MONITOR AVE,2825,OTHER OFFENSE,HARASSMENT BY TELEPHONE,RESIDENCE,false,true,0811,008,23,56,26,1138234,1869952,2011,02/04/2016 06:33:39 AM,41.79927468,-87.768598031\\
Input: Event Log (What happened, When and Where)
No manual selection of features!
Input: Event Log (What happened, When and Where)
variables: <location,category>
arrests | |
violent crimes | |
nonviolent crimes |
~3000 location tiles
~9000 variables
~40 million binary interactions
> 1 billion possible models of interaction
Generating Event Streams
Focusing on dynamics of observables
unmodeled factors
Observable future is a function of the observable past
Why no "features" ?
Philadelphia
The Problem:
>3 days in advance
Within ~2 city blocks
ONLY Past eventlog as input
Mean AUC
Property crime: 81%
Violent crime: 84%
Spatial tiles:
0.003 deg latitude, 0.003 deg longitude
0.25 miles across
Time-period:
Training: Jan 1 2016 - Dec 31 2018
Out-of-sample test: Jan 1 2019 - April 1 2019
Prediction Performance (Philadelphia)
sensitivity 0.90
ppv 0.87
100 crimes
Raise 103 flags
90 correct flags
13 false positives
10 missed
3 day ahead prediction
Jan 1 2019
to
April 1 2019
Play Movie
Triangles: actual events
heatmap: predicted risk 3 days ahead
Could we have predicted this?
Double homicide
Jan 7 2019
Triple homicide incident
Jan 7 2019
https://www.inquirer.com/crime/kensington-triple-shooting-homicide-philadelphia-police-20190107.html
Triangles: actual events
heatmap: predicted risk 3 days ahead
2019, Jan - 2022, Mar: Training
2022, Apr - 2022 Sep: Testing
Property and Violent Crimes
Every 10 events, about 8 flags are raised, with almost no false alarms
Rates of different crimes
Spatial Resolution
(~1000 yards)
Average sensitivity: 0.85
Average positive predictive value: 1.0
Horizon: 7 days +/- 1 Day
142 spatial tiles (~1000 yards tile size)
2020 - 2022, May: Training
2022, June - 2022 Dec: Testing
Property and Violent Crimes
Rates of different crimes
Out-of-sample Prediction
Average sensitivity: 0.83
Average positive predictive value: 0.98
Horizon: 7 days +/- 1 Day
220 spatial tiles
Training: Jan 1 2021 - March 31 2022
Out-of-sample test: Apr 1 2022 - July 22 2022
Spatial tiles:
0.0028 deg latitude, 0.0019 deg longitude
0.2 miles across
(100 x 300 yds)
Boston Districts: B2 B3 C1
Jan 1 2021 - July 22 2022
Total # of events: 7419
Boston MA, USA
fp 1.840708
tp 21.530973
fn 2.946903
sens 0.878993
ppv 0.909565
fp 0.106195
tp 3.982301
fn 0.522124
sens 0.881521
ppv 0.960446
property
violent
Property:
Other_Larceny-Larceny_from_MV-Auto_Theft-Residential_Burglary-Robbery-Commercial_Burglary
Violent:
Aggravated_Assault-Rape_&_Attempted-Homicide
Mean AUC
Property crime: 81%
Violent crime: 84%
Predicting
extreme weather
Predicting
extreme weather
Outperforms pure physics-based models at longer horizons
Predicting World Events
Temporal resolution: 1 day
Spatial Resolution: \(1^\circ \times 2^\circ\)
Global Terrorism DataBase
ishanu@uchicago.edu
Physics Introduction as structural and other constraints
Nearly
Hands-free
No feature-engineering
Next:
Model and predict world events
Extra Slides
Next:
Model and predict world events
Next:
Model and predict world events
The Issue with Neural Networks
only certain specific structures may be identified