Casper van Elteren
Dynamic importance of nodes is poorly predicted by static topological features
Complex systems are ubiquitous
Most approaches are not applicable to complex systems:
What is the most important node?
> What node drives the system?
Wang et al. (2016)
However we have a many-to-one mapping
1. Simplified dynamics
"Well-connected nodes are dynamically important"
2. Which feature to select?
N.B. implicit dynamics assumption!
Harush et al. (2017)
2. Dynamic importance interacts with structure
3. The size of intervention matters
Mechanism driving behavior are different under overwhelming interventions!
We have seen:
Possible solution: information theory
Information theory and complex systems
Traditional approaches are domain specific but all ask similar questions, e.g.:
Quax et al. (2016)
How to achieve universal approach to study various complex behavior?
There is a need for a universal language that decouples syntax from semantics
Quax et al. (2016)
Quantify in terms of "information"
Information Entropy: "Amount of uncertainty"
Mutual information: "Shared information"
N.B. No assumption on what generates P
Information in complex systems
Given ergodic system S
Information will always decrease as function of time
Driver-node will share the most information with the system over time
Diminishing role of hubs
Quax & Sloot (2013)
Goal: identify driver-node in real-world systems
Fried et al. (2015)
Ising spin dynamics
Used to model variety of behavior
Causal influence forms the ground truth
Advantages of KullBack-Leibler divergence:
|Name||What does it measure?|
|Current flow||Least resistance|
|Ind. var max(x)||Dep. var|
|- Degree centrality
- Betweenness centrality
- Current flow centrality
- Eigenvector centrality
- Information impact
Classification with random forest:
RNF classifier with high prediction accuracy
Information impact captures driver-node change
Information impact varies linearly with low causal impact
Structural connectedness != dynamic importance
Low causal impact
High causal impact
P(B | A = a)
m = amount of regressors
N = number of samples
My talk at the TU delft and IAS. Preprint can be found at https://arxiv.org/abs/1904.06654