Advanced Concepts in Temporal Point Processes for Human-Centered Machine Learning
H
UMAN
-
CENTERED
M
ACHINE
L
EARNING
Advanced concepts in
Temporal Point Processes
http://courses.mpi-sws.org/hcml-ws18/
2
Temporal Point Processes
:
Marks and SDEs with jumps
3
Marked temporal point processes
Marked temporal point process:
A random process whose realization
consists of
discrete
marked
events localized in time
History,
time
time
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.)
5
Dependent marks: SDEs with jumps
Observations:
1.
Marks dependent of the temporal dynamics
2.
Defined for all values of t
Marks given by stochastic differential equation with jumps:
Drift
Event influence
History,
time
6
Dependent marks: distribution + SDE with jumps
1.
Marks dependent on the temporal dynamics
2.
Distribution represents additional source of uncertainty
Distribution for the marks:
Event influence
Drift
Observations:
History,
time
7
Mutually
exciting + marks
Neighbor influence
Drift
Marks affected by neighbors
time
Christine
Bob
8
Marked TPPs as stochastic dynamical systems
It gets
infected
Example:
Susceptible-Infected-Susceptible (SIS)
It recovers
Susceptible
Infected
Susceptible
SDE with jumps
If friends are infected, higher infection rate
Node is susceptible
Infection
rate
Recovery
rate
SDE with jumps
Self-recovery rate when
node gets infected
If node recovers,
rate to zero
Rate increases if
node gets treated
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.
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Presentation Transcript
Advanced concepts in Temporal Point Processes HUMAN-CENTERED MACHINE LEARNING http://courses.mpi-sws.org/hcml-ws18/
Temporal Point Processes: Marks and SDEs with jumps 2
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,
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
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
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
Mutuallyexciting + marks Bob time Christine Marks affected by neighbors 7 Drift Neighbor influence
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
