Sequential Inference for Evolving Groups of Objects

1. Sequential Inference for Evolving Groups of Objects 2012-07-19 이범진 Biointelligence Lab Seoul National University

2. What are we going to do? • Think about dynamically evolving groups of objects • Ex) • flocks of birds • Schools of fish • Group of aircraft

3. 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

4. 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 layerand the observation process usually depends only on the targets • 5. Number of targets is typically unknown

5. Framework (1) • Dynamic group tracking model G1 G2 Gt Gt+1 X2 Xt+1 X1 Xt Z1 Z2 Zt Zt+1

6. 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 • Describesthe way the group membership or group matic states Xt • Markovian assumption

7. How do we inference? • Proposed MCMC-particle algorithm

8. 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 density at every MCMC iteration • Consider the general joint distribution of St and St-1 ,

9. How good is it?

10. How good is it?

11. 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 • Describesthe way the group membership or group matic states Xt • Markovian assumption

12. 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 rectangular region, and track-before-detect approach(TBD) If ) otherwise

13. Experiments(1)

14. Experiments(1) result • MCMC-particles algorithm is used to detect and track the group targets • Nburn= 1000 iteration for burn-in

15. Experiments(1) result cont.

16. 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 • |

17. Experiments(2) cont.

18. 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

19. 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

20. Thank you