Understanding Advanced Concepts in Temporal Point Processes for Human-Centered Machine Learning

Explore advanced concepts in temporal point processes through the lens of human-centered machine learning. Topics include marked temporal point processes, independent identically distributed marks, dependent marks, and mutually exciting marks. Learn about stochastic dynamical systems such as the Susceptible-Infected-Susceptible model. Dive into the nuances of temporal dynamics, event influences, and uncertain distributions in temporal point processes.

• Temporal Point Processes
• Machine Learning
• Human-Centered
• Stochastic Systems
• Advanced Concepts

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1. Advanced concepts in Temporal Point Processes HUMAN-CENTERED MACHINE LEARNING http://courses.mpi-sws.org/hcml-ws18/

2. Temporal Point Processes: Marks and SDEs with jumps 2

3. Marked temporal point processes Marked temporal point process: A random process whose realization consists of discrete marked events localized in time time time 3 History,

4. Independent identically distributed marks time Distribution for the marks: Observations: 1. Marks independent of the temporal dynamics 2. Independent identically distributed (I.I.D.) 4

5. Dependent marks: SDEs with jumps time History, Marks given by stochastic differential equation with jumps: Observations: Drift Event influence 1. Marks dependent of the temporal dynamics 2. Defined for all values of t 5

6. Dependent marks: distribution + SDE with jumps time History, Distribution for the marks: Drift Event influence Observations: 1. Marks dependent on the temporal dynamics 2. Distribution represents additional source of uncertainty 6

7. Mutuallyexciting + marks Bob time Christine Marks affected by neighbors 7 Drift Neighbor influence

8. Marked TPPs as stochastic dynamical systems Example: Susceptible-Infected-Susceptible (SIS) SDE with jumps Susceptible Infected Susceptible It gets infected It recovers Node is susceptible Infection rate If friends are infected, higher infection rate SDE with jumps Recovery rate Self-recovery rate when node gets infected If node recovers, rate to zero Rate increases if node gets treated 8