Sequential Inference for Evolving Groups of Objects
-
Upload
josephine-fischer -
Category
Documents
-
view
13 -
download
0
description
Transcript of Sequential Inference for Evolving Groups of Objects
Sequential Inference for Evolving Groups of Objects
2012-07-19
이범진Biointelligence Lab
Seoul National University
What are we going to do?
Think about dynamically evolving groups of objects¨ Ex)
flocks of birds Schools of fish Group of aircraft
However...
Difficulties on this research¨ 1. recognizing groups are hard¨ 2. incorporating new members into the groups,
Ex) splitting and merging of groups
How many groups?
Merging
Spliting
Proposed solution
Implementation rule¨ 1. Targets themselves are dynamic¨ 2. Targets’ grouping can change overtime¨ 3. Assignment of a target to a group affects the probabilistic
properties of the target dynamics¨ 4. Group statistics belong to a second hidden layer, target
statistics belong to the first hidden layer and the observation process usually depends only on the targets
¨ 5. Number of targets is typically unknown
Framework (1)
Dynamic group tracking model
𝒑 (𝑿𝟏: 𝒕 ,𝑮𝟏: 𝒕 ,𝒁𝟏 :𝒕 )=𝒑 (𝑿𝟏|𝑮𝟏 )𝒑 (𝑮𝟏)𝒑 (𝒁𝟏|𝑿𝟏)×∏𝒕 ′=𝟐
𝒕
𝒑 (𝑿 𝒕|𝑿 𝒕 −𝟏 ,𝑮 𝒕 ,𝑮𝒕 −𝟏 )𝒑 (𝑮𝒕|𝑮𝒕 −𝟏 , 𝑿 𝒕 −𝟏 )𝒑 (𝒁 𝒕∨𝑿 𝒕 )
G1
X1
Z1
G2
X2
Z2
Gt
Xt
Zt
Gt+1
Xt+1
Zt+1
Framework (2)
Main components of the group tracking model¨ 1. group dynamical model :
Describes motion of members in a group
¨ 2. group structure transition model Describes the way the group membership or group matic
states Xt
Markovian assumption
𝑝 (𝑋 𝑡∨𝑋 𝑡− 1 ,𝐺𝑡 ,𝐺𝑡− 1)
𝑝 (𝐺𝑡∨𝐺𝑡 −1 ,𝑋 𝑡− 1)
Why is it better!?
No resampling is required ¨ Particle filters use MCMC to rejuvenate degenerate samples
after resampling
Less computationally intensive than the MCMC-based particle filter¨ Because avoids numerical integration of the predictive den-
sity at every MCMC iteration
Consider the general joint distribution of St and St-1
¨
,
Framework (2)
Main components of the group tracking model¨ 1. group dynamical model :
Describes motion of members in a group
¨ 2. group structure transition model Describes the way the group membership or group matic
states Xt
Markovian assumption
𝑝 (𝑋 𝑡∨𝑋 𝑡− 1 ,𝐺𝑡 ,𝐺𝑡− 1)
𝑝 (𝐺𝑡∨𝐺𝑡 −1 ,𝑋 𝑡− 1)
Experiments(1)
Ground target tracking¨ For group dynamical model(with repulsive force, virtual
leader) Use stochastic differential equations (SDEs) and Itô stochastic
calculus– Using velocity, position, acceleration, restoring force, etc.
¨ For state-dependent group structure transition model
¨ For observation model Using single discretized sensor model which scans a fixed rec-
tangular region, and track-before-detect approach(TBD)
𝑝 (𝐺𝑡|𝑋 𝑡− 1,𝑒𝑡−1 ,𝐺𝑡 −1 )={ 𝑃𝑁𝐶
(1−𝑃𝑁𝐶)�̂� (𝐺𝑡∨𝐺𝑡 −1 ,𝑋 𝑡 −1 ,𝑒𝑡− 1)If ) otherwise
Experiments(1) result
MCMC-particles algorithm is used to detect and track the group targets
Nburn = 1000 iteration for burn-in
Experiments(2)
Group stock selection¨ For group stock mean reversion model (dynamical model)
Use stochastic differential equations (SDEs) Formulation with ‘force’ which changes stock prices that
brings the stocks back into equilibrium¨ For state-independent group structure transition model
K possible groups G = group assignment πt = models the underlying proportion of targets in various
groups at time t |
Experiments(2) cont.
Dynamic Dirichlet distribution ¨ Assumption
All the stocks are independent Stock prices starts at Z1,i = 0
¨ Transition is obtained from the log-distribution of the group stock mean
reversion model
Experiments(2) result
MCMC-particles algorithm is used to inference {Gt, πt}
These models can identify groupings of stock based only on their stock price behaviour