Ishanu Chattopadhyay

Assistant Professor of

Data Science

University of Chicago

zed.uchicago.edu

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

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?

\sigma_0:0

\sigma_1:1

Can be more complicated...

A lot more complicated...

Algorithm genESeSS

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.

What do the states mean?

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

https://link.springer.com/article/10.1007/BF02551274

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

\gamma^A_{A_\delta} = 1 - \frac{\mathbb{E}_{x \in \Sigma^\star}h(\phi_x^{\mathcal{H}_A,\mathcal{H}_{A_\delta}})}{h(\phi_\lambda^{\mathcal{H}_A,\mathcal{H}_{A_\delta}})}

Causality across two processes

Causality across time delays

Fractal Net: Information gradient doe not decay from the computation

\gamma^A_{A_\delta} = 1 - \frac{\mathbb{E}_{x \in \Sigma^\star}h(\phi_x^{\mathcal{H}_A,\mathcal{H}_{A_\delta}})}{h(\phi_\lambda^{\mathcal{H}_A,\mathcal{H}_{A_\delta}})}

a^{l}_j = \sigma\left( \sum_k w^{l}_{jk} a^{l-1}_k + b^l_j \right)

Fractal Net

Neural Net

fixed non-linear activation

The Fractal Net architecture

No back-propagation

Deep Learning without Neural Networks

Lets Predict Crime

No manual selection of factors
No creation of "lists"
Uses only de-identified data

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).

https://doi.org/10.1038/s41562-022-01372-0

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

An adversarial game dynamic
Initial distributions are not well-mixed
Socio-economic factors affect dynamics
Dynamics shaped by physical geometric connectivity

\mathcal{E}(x,y,t) \in \{ \mathcal{C}_{NV},\mathcal{C}_V,\mathcal{A},\varnothing \}

\mathcal{E}: \mathcal{S}\times T \times \mathcal{F} \rightarrow \mathbb{E}

unmodeled factors

\mathcal{E}: \mathcal{S}\times T \times \mathcal{F} \rightarrow \mathbb{E}

\mathcal{E}(x,y,t) = f(\mathcal{E}(x_1,y_1,t_1),\cdots,\mathcal{E}(x_n,y_n,t_n))\\ \textrm{where } t_i \leqq t

Observable future is a function of the observable past

Why no "features" ?

Philadelphia

The Problem:

Predicting crime sufficiently ahead of time to be actionable
Prediction precise enough in time and space to be actionable
Use ONLY data that is realistically and cheaply available

>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

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

Wauwatosa, WI

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)

Chihuahua, Mexico

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

Boston, MA

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%