THE G LOBAL R ISK N ETWORK , P ART II Boleslaw Szymanski Xin Lin, - - PowerPoint PPT Presentation

FAILURES, DYNAMICS, EVOLUTION AND CONTROL OF

THE GLOBAL RISK NETWORK, PART II

Boleslaw Szymanski Xin Lin, Xiang Niu, Noemi Derzsy, Alaa Moussawi, Jianxi Gao, and Gyorgy Korniss

NeST Center & SCNARC Department of Computer Science Department of Physics, Applied Physics and Astronomy Rensselaer Polytechnic Institute, Troy, NY

Failures, Dynamics, Evolution and Control of the Global Risk Network *email: szymab@rpi.edu

Contagion Potentials Versus Internal Vulnerability

Network visualization showing the contagion potentials (indicated by color) and the internal failure probabilities (indicated by size) with the optimal parameters.

Five risks with the highest contagion potential in 2013 were: 8 ‐‐ Severe income disparity 25 – Global government failure 1 – Chronic fiscal imbalances 27 – Pervasive entrenched corruption 12 ‐‐ Failure of climate change adaptation

Failures, Dynamics, Evolution and Control of the Global Risk Network 2

Asymptotic (Steady State) Risk‐Persistence for 2013

3

• For 2013 data, we rank order the persistence of various risks

during the lifetime of a cascade. Strikingly, risk 8 ‐ “Severe income disparity” ‐ was active for about 80% of the lifetime of a cascade on average, while in comparison, the second most persistently active risk ‐ “Chronic fiscal imbalances” ‐ was active for about 33% of the lifetime of a cascade on average.

• Decreasing the internal failure and external influence

probabilities of global risks both contribute to the stability of the global economy, with reduction of internal failure probabilities contributing more effectively.

Conclusions Based on the Network Model

Failures, Dynamics, Evolution and Control of the Global Risk Network 4

Measuring Quality of Predictions

• In the global risk network, we recover latent (hidden) and explicit

parameters of the model from historical data and predict future activation of global risks, including cascades of such risk activations.

• The question arises how reliable such parameter recovery is and

how the recovery precision depends on the complexity of the model and the length of its historical data.

• Here, this model is applied to fire propagation in an artificial city

with modular blocks that can be assembled into a complex system.

• We simulate the fires in such cities of varying size, over varying

periods of times and use the Maximum Likelihood Estimation to recover the parameters and compare them with the values assigned to them in simulations.

• * X. Lin, A. Moussawi, G. Korniss, J.Z. Bakdash, and B.K. Szymanski, Limits of Risk Predictability
• In a Cascading Alternating Renewal Process Model, Scientific Reports 7:6699, (2017)

5 Failures, Dynamics, Evolution and Control of the Global Risk Network

Model Details

In the firehouse model, three types of houses are defined: small, medium and large. For each house, the quality of its building material and size of its lot are proportional to its size (type). Each house fire worthiness properties, such as resistance to fires, ability to spread fire,

• etc. are determined by its type and the housing density in its neighborhood.

Large houses have a low probability of catching fire and a high ability to recover from burning, while medium and small houses have increasingly lower characteristics. Each house has an influencing circle with a fixed radius, in which all the neighbors inside the circle are at risk of being catching fire from this house. We can expand the city by adding blocks horizontally and vertically.

6 Failures, Dynamics, Evolution and Control of the Global Risk Network

Failures, Dynamics, Evolution and Control of the Global Risk Network 7

Model Dynamics ‐ Probabilities

At time t, a house is in one of three states: susceptible (0), on‐fire (1), recovery(‐1) The dynamics progresses at each time step t > 0 as follows:

• 1. House i susceptible at time t–1 catches fire internally at time t with probability:
• 2. House i that was susceptible at time t–1 catches fire externally from on‐fire

neighbor j at time t with probability:

• 3. House i on‐fire at time t–1 is extinguished and enter the recovery state at time t

with probability:

• 4. House i in‐recovery at time t–1 becomes susceptible at time t with probability:

pi

int 1e i

int

p ji

ext 1e i

ext  pi

ext

pi

fire 1e i

fire

pi

rec 1e i

rec

Three state comparisons in torus model Three state comparisons in fully connected model

Model Comparison – Discrete vs. ODE

8

The higher the model connectivity, the better the match between discrete and ODE results. s(t) r(t) f(t)

Failures, Dynamics, Evolution and Control of the Global Risk Network

s(t) r(t) f(t)

Fraction of On‐fire Time in Simulation

• Time steps of simulation: 10,000
• Counts at how many time steps each house is on fire
• Averaged 20 independent realizations

9 Failures, Dynamics, Evolution and Control of the Global Risk Network

Measuring Performance of Estimated Parameters

• We generate 125 sets of time series for 6400 steps using ground truth

parameters: 𝛽 0.008, 𝛾 0.012, 𝛿 0.016, 𝜀 0.032 and compute estimated parameters from each of time series using Maximum Likelihood Estimation.

• Using sets of estimated parameters, we simulate multiple lengths of future

periods: 400, 800, 1600, 3200 and 6400 and record the length of normal, on‐ fire and recovery state as well as the number of emerging fires during the period; results are averaged over 20 realizations.

• We compute the difference between these estimated parameters and the

ground truth parameters and, determine, using Kolmogorov‐Smirnov metric the 𝜏 distance between estimated parameters and ground truth parameters.

• Finally, we find the 𝜏 boundary of each set of estimated parameters by

removing the largest 39 sets of results; the remaining results contain 68% of all sets of estimated parameter values, that are closest to the ground truth.

10 Failures, Dynamics, Evolution and Control of the Global Risk Network

Performance of Estimated Parameters

11 Failures, Dynamics, Evolution and Control of the Global Risk Network

Parameter Recovery in Global Risk Network

• Ground truth parameters: 𝛽 0.364, 𝛾 0.140, 𝛿 427
• For each case, there are 50 realizations.

12 Failures, Dynamics, Evolution and Control of the Global Risk Network

Parameter Recovery in Global Risk Network

• 125 sets of estimated parameters.
• Number of realizations is 20 in each scenario.

13 Failures, Dynamics, Evolution and Control of the Global Risk Network

Conclusions and Future Plan

Studying the prediction limit of an interconnected network of risks using Alternative Renewal Process, we find that:

• Simulations of discrete and continuous (ODE) risk models match each other

with precision improving with the increasing model connectivity.

• The parameter recovery performance improves and its error decreases when

the volume of training data grows.

• The relative error reduces asymptotically to zero with unlimited growth of

training data.

Future Plans Conclusions

14 Failures, Dynamics, Evolution and Control of the Global Risk Network

• Implementing parameter recovery for more complex models
• Measuring the prediction accuracy using statistical metrics
• Studying applications combining human expert assessment with the

stochastic computer predictions based on MLE recovered parameters for regional models.

Global Network Evolution: Transition Fraction

• Probability and fraction of transitions
• They depend on the (initial) system state; we assume below the state S∞ which is the

steady state at which each risk is active with stable probability pi

• Internal activation:
• External activation:
• Internal recovery:
• For small Ni from the Taylor’s approximation we get:

Ai

int  (1 pi)pi int

A

i ext  (1 pi)[1(1 pi ext) p j

jNi

 ] Ai

rec  pipi rec

ai

int 

Ai

int

Ai

int  Ai ext  Ai rec

2013 network 2017 network 2.69 3.07

ai

ext 

Ai

ext

Ai

int  Ai ext  Ai rec

ai

rec 

Ai

rec

Ai

int  Ai ext  Ai rec

15 Failures, Dynamics, Evolution and Control of the Global Risk Network

ai

ext

a i

int  1(1 Ni)  p j

jNeighbori

 1(1 Ni)   p j

jNeighbor

i





Evolution of Transition Fractions

0.1 0.2 0.3 0.4 0.5 1 11 21 31 41 Internal Fraction Risk (a) 2013 network 0.1 0.2 0.3 0.4 0.5 1 10 15 21 27 Internal Fraction Risk (b) 2017 network 0.1 0.2 0.3 0.4 0.5 1 11 21 31 41 External Fraction Risk (c) 2013 network 0.1 0.2 0.3 0.4 0.5 1 10 15 21 27 External Fraction Risk (d) 2017 network 16 Failures, Dynamics, Evolution and Control of the Global Risk Network

Influence Among Risks

Economic Environmental Geopolitical Societal Technological Economic Environmental Geopolitical Societal Technological Source Target (a) 2013 network 1.00 0.85 0.84 0.88 0.79 0.43 0.85 0.29 0.56 0.62 0.56 0.47 0.87 0.56 0.77 0.41 0.49 0.43 0.49 0.72 0.00 0.03 0.08 0.01 0.19 0.2 0.4 0.6 0.8 1 Normalized Influence Economic Environmental Geopolitical Societal Technological Economic Environmental Geopolitical Societal Technological Source Target (b) 2017 network 0.30 0.08 0.16 0.08 0.23 0.30 1.00 0.26 0.70 0.30 0.60 0.30 0.55 0.40 0.75 0.40 0.59 0.37 0.45 0.22 0.24 0.04 0.26 0.00 0.64 0.2 0.4 0.6 0.8 1 Normalized Influence 17 Failures, Dynamics, Evolution and Control of the Global Risk Network

Groups impacting three

• r more other groups

Background Information

The spread of cascades could be affected by the topology of an interconnected network.

“A cascading failure is a failure in a system of interconnected parts in which

the failure of a part can trigger the failure of successive parts. Such a failure may happen in many types of systems, including power transmission, computer networking, finance, human bodily systems, and bridges.”

Source: Wikipedia

“A global risk is defined as an occurrence that causes significant negative impact for several countries and industries over a time frame of up to 10

• years. A key characteristic of global risks is their potentially systemic nature –

they have the potential to affect an entire system, as opposed to individual parts and components. ”

Source: Wikipedia

18 Failures, Dynamics, Evolution and Control of the Global Risk Network

The report contains also an assessment of the risks potential impact, interconnectivity and likelihood of materialization in the next 10 years prepared by

• ver

1000 business, industry, government, international

• rganization and academic experts.
• Likelihood of a risk to occur over the next 10 years:

Each expert defines these likelihoods by numerical value ranging from 1 (lowest likelihood) to 5 (highest likelihood) using integers and mid‐points between integers within this range. Average all the experts’ rates and get the final value of likelihood.

• Connections between pairs of risks:

Each expert selects at least 3 and up to 10 combinations. There are 515 bidirectional edges defined that way, thus, the average degree of each node is relatively high, 20.6 per node.

• Impact:

If one risk were to occur, what is the rate of impact from 1 (lowest likelihood) to 5 (highest likelihood).

Expert Assessments

19 Failures, Dynamics, Evolution and Control of the Global Risk Network

• Five risks with high contagion potentials were chosen.
• The linear nature of the curves on the linear‐logarithmic scale

indicates that survival probabilities decay exponentially with time.

• These long cascade lifetimes, even in the absence of internal

failures, demonstrates the profound disadvantage

• f

interconnectivity of global risks.

• Interestingly, the lists of top five most persistent risks observed in

the cascades and seen in the full dynamics of activation are identical.

Cascades due to Single Risk Materializations

Failures, Dynamics, Evolution and Control of the Global Risk Network 20

Model Evaluation

• We use Likelihood Ratio test to evaluate our global risk network (null model)

with other alternative models.

• Since we know the likelihood of observed historical data of one model, we

can compute the likelihood ratio D.

• After getting LR and degree of freedom, we can compute the p‐value of a

significance level and determine which model is a better fit of data.

• According to the LR test, the disconnected and expert data based models

cannot be distinguished from each other with any reasonable significance level.

• The network model outperforms all other models in explaining the
• bserved data with the significance level of 0.01 or lower.

Failures, Dynamics, Evolution and Control of the Global Risk Network 21

Parameter Recovery in Various Scenarios

22 Failures, Dynamics, Evolution and Control of the Global Risk Network

• In (a)(b), the length of recovery dataset is 1600.
• N1,i=0.4 for large, 0.3 for medium and 0.2 for small houses.
• There are 20 realizations in each scenario

Monte Carlo Simulation (2013 risk network)

• The global risk network constantly

evolves and causes continuous changes in the current state of the global risks and their probabilities.

• However, if left unabated, the global risk

network would move from the current state to the steady state.

• This is why, we compare the steady states

to which these current states would move if no changes to the system had been introduced.

pi  pi

01

pi

01 1 pi 11

At steady state S฀:

0.2 0.4 0.6 0.8 1 1 10 102 103 104 105 inf frequency time (a) Economic

1 2 3 4 5 6 7 8 9 10

23 Failures, Dynamics, Evolution and Control of the Global Risk Network

Monte Carlo Simulation (2013 risk network)

24 Failures, Dynamics, Evolution and Control of the Global Risk Network

0.2 0.4 0.6 0.8 1 1 10 102 103 104 105 inf frequency time (b) Environmental

11 12 13 14 15 16 17 18 19 20

0.2 0.4 0.6 0.8 1 1 10 102 103 104 105 inf frequency time (c) Geopolitical

21 22 23 24 25 26 27 28 29 30

0.2 0.4 0.6 0.8 1 1 10 102 103 104 105 inf frequency time (d) Societal

31 32 33 34 35 36 37 38 39 40

0.2 0.4 0.6 0.8 1 1 10 102 103 104 105 inf frequency time (e) Technological

41 42 43 44 45 46 47 48 49 50

Evolution of Economic Risks

25 Failures, Dynamics, Evolution and Control of the Global Risk Network

Evolution of Environmental Risks

26 Failures, Dynamics, Evolution and Control of the Global Risk Network

Evolution of Geopolitical Risks

27 Failures, Dynamics, Evolution and Control of the Global Risk Network

Evolution of Societal Risks

28 Failures, Dynamics, Evolution and Control of the Global Risk Network

Evolution of Technological Risks

29 Failures, Dynamics, Evolution and Control of the Global Risk Network

Risk Influence

• Two initial states and likelihoods

for Monte Caro simulations are needed:

• Sj;0 in which risk j and all other risks i are initially

zero, si=0, sj=0; risk j is deactivated by setting normalized likelihood value to zero, Nj=0

• Sj;1 in which risk j is initially 1 and all other risks i

are zero, si=0, sj=1.

• The fraction of activation with these states

are denoted and respectively

• Influence of risk j on i:
• Influence of risk j on its neighbor layer k

Lk, where k={1,2}:

0.1 0.2 0.3 1 10 100 1000 (1000, 0.0096) (1000, 0.0027) Influence time step first layer second layer

The plot below shows the influence of a single risk on their two nearest layers of neighbors in 2017 network averaged over all 30 risks. Plotted values are averaged over 1000 runs. Initially large, the difference in influence between the first and second layer decays from large to small ratio near the stable point

ext i j ext i j i j

a a I

   

 

; 1 ;

I jLk  I ji

iLk



Close to steady state S฀ ext i j

a

 ;

ext i j

a

 1 ;

30 Failures, Dynamics, Evolution and Control of the Global Risk Network

Global Risks Discovery

• We lack an automatic tool to discover risk events.
• We want to learn from the Web media which risks

were active and when.

• We also use the Web media to learn with which

risks the public is concerned the most.

• Finally, we are interested in regional effects of risks.

31 Failures, Dynamics, Evolution and Control of the Global Risk Network

mwm14@cornell.edu

31

Wikipedia Current Event Portal (WCEP)

32

We take advantage of the WCEP, one of many knowledge networks created from the Web media content

Failures, Dynamics, Evolution and Control of the Global Risk Network 32

Story: 2004 Atlantic hurricane season

33

• event4571: At least nine deaths in Florida, two deaths

in the Bahamas, and one death in Georgia are blamed

• n the storm. Damage estimates range widely from

US$2 to US$15 billion. (9/7/04)

• event4571:
• in risks of: “storm”, “death by weather”,

“economic loss by weather”

• in location of: “Florida”, “Bahamas”, “Georgia”
• at date of: 9/7/04

Failures, Dynamics, Evolution and Control of the Global Risk Network 33

Step1:

• Prepares a few keywords and tags for each risk

according to the description

• Example:
• Risk: “10. Extreme weather event”
• Tag: “storm”
• Keyword: “storm”

34 Failures, Dynamics, Evolution and Control of the Global Risk Network 34

Step 2:

• Merges keywords list
• Example:
• 𝑡𝑢𝑝𝑠𝑛 ∪ ∅ 𝑡𝑢𝑝𝑠𝑛

35 Failures, Dynamics, Evolution and Control of the Global Risk Network 35

Step 3

• Creates for each event a

positive or a negative instance.

• Example of class “storm”:
• Positive instance:
• Tropical Storm Gaston

douses Richmond, Virginia, with up to 14 inches of rain, causing widespread flooding.

• Negative instance:
• Australia's Qantas Airways

announces plans to cut 1,500 jobs worldwide

36 Failures, Dynamics, Evolution and Control of the Global Risk Network 36

Step 4

• Trains classifier using bag‐of‐words representations
• f event descriptions
• Example:
• Positive instances:

storm: 𝑢𝑠𝑝𝑞𝑗𝑑𝑏𝑚, 𝑡𝑢𝑝𝑠𝑛, 𝑠𝑏𝑗𝑜, 𝑔𝑚𝑝𝑝𝑒𝑗𝑜𝑕, … , …

• Negative instances:

storm: 𝑏𝑗𝑠𝑥𝑏𝑧𝑡, 𝑞𝑚𝑏𝑜, 𝑘𝑝𝑐, 𝑥𝑝𝑠𝑚𝑒𝑥𝑗𝑒𝑓, … , …

37 Failures, Dynamics, Evolution and Control of the Global Risk Network 37

Step 5

• Ranks featured keywords of the trained classifier by

their entropy

• Example:
• Entropy ranking:

s𝑢𝑝𝑠𝑛: 1: 𝑡𝑢𝑝𝑠𝑛, 2: 𝑠𝑏𝑗𝑜, 3: 𝑔𝑚𝑝𝑝𝑒𝑗𝑜𝑕, …

• Adding two new keywords in the list: “rain” and

“flooding”

38 Failures, Dynamics, Evolution and Control of the Global Risk Network 38

Risk event filtering tool

• This process is continued until it eventually achieves all related keywords

for the risk events.

• Over 90% of events are not related to global risks and do not contain any

corresponding keywords.

39 Failures, Dynamics, Evolution and Control of the Global Risk Network 39

Story: 2004 Atlantic hurricane season

40

• event4571: in risks of “10. Extreme weather event”

and “11. Failure of climate‐change mitigation and adaptation”

• event4622: in risks of: “23. Large‐ scale involuntary

migration”

10 11 23

Failures, Dynamics, Evolution and Control of the Global Risk Network 40

Relational dependencies

41

170 edges 201 edges 108 common edges Asset bubble Extreme weather event Private data leak Biodiversity loss Risks that directly impact everyday life Risks with future (potential) impact on humanity

Failures, Dynamics, Evolution and Control of the Global Risk Network 41

Story: 2004 Atlantic hurricane season

42

• event4359
• ‐ in risk of: “10. Extreme weather event”
• ‐ in location of: “Virginia”

Risk category Country Count Environmental risk United States Risk category Country Count Environmental risk United States Societal risk Cuba 1 +1 +1 = 2

• event4571:
• ‐ in risk of: “10. Extreme weather event” and “11. Failure of climate‐

change mitigation and adaptation”

• ‐ in location of: “Florida”, and “Georgia”
• event4622:
• ‐ in risk of: “23. Large‐ scale involuntary migration”
• ‐ in location of: “Cuba”

Failures, Dynamics, Evolution and Control of the Global Risk Network 42

Political heat‐map (Economic)

43

Russia (1.00) U.S. (0.95) Mexico (0.72) Japan (0.75) Greece (0.61)

Failures, Dynamics, Evolution and Control of the Global Risk Network 43

Political heat‐map (Environmental)

44

U.S. (1.00) Mexico (0.90) Japan (0.91) China (0.97) India (0.91)

Failures, Dynamics, Evolution and Control of the Global Risk Network 44

Political heat‐map (Geopolitical)

45

Syria (0.62) North Korea (1.00)

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Political heat‐map (Societal)

46

Syria (0.98)

Failures, Dynamics, Evolution and Control of the Global Risk Network 46

Political heat‐map (Technological)

47

U.S. (1.00) U.K. (0.51)

47

Contributions:

• Built an automatic detection tool for risk events collection
• Reconstructed relational dependencies from risk events in the WCEP.
• The experts show concern about yet unseen risks that may arise in the future or have an

enormous impact on all humanity

• The public tends to focus on risks that matter to everyday life
• Discovered spatial characteristic of risks by analyzing local information extracted

from events.

• Economic risks are in trade developed countries
• Environmental risks are in coastal areas
• Geopolitical risks are in unstable nations
• Social risks are the consequence of geopolitical risks
• Technological risks are in technologically advanced countries

48 Failures, Dynamics, Evolution and Control of the Global Risk Network 48