1 / 9

Construction of Dependent Dirichlet Processes based on Poisson Processes

Construction of Dependent Dirichlet Processes based on Poisson Processes. Dahua Lin, Eric Grimson , John Fisher Presented by Yingjian Wang Jun. 03, 2011. Outline. Measure space; Stochastic processes; Three operations on measure; Build Markov chain of Dirichlet processes;

edda
Download Presentation

Construction of Dependent Dirichlet Processes based on Poisson Processes

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Construction of Dependent Dirichlet Processesbased on Poisson Processes Dahua Lin, Eric Grimson, John Fisher Presented by Yingjian Wang Jun. 03, 2011

  2. Outline • Measure space; • Stochastic processes; • Three operations on measure; • Build Markov chain of Dirichlet processes; • The sampling algorithm; • Experiments;

  3. Measure space • The triple (X, Σ, μ) is called a measure space, with Σ is the σ-field of X; μ is a measure. • Σ is closed for complementation and countable unions of subsets of X (measurable). • If μ(X)=1, it is a probability space. • For a probability space (X, Σ, μ), X is the ‘sample space’; Σ is the ‘event space’. • Non-measurable set is a non-trivial result of the axiom of choice.

  4. Stochastic processes • Well, we are interested in stochastic processes (maybe for nonparametric Bayesian methods), why you talk the measure space? • Stochastic processes are defined/live in measure spaces. • Gamma process G on (X, Σ, μ): • Dirichlet process G on (X, Σ, μ):

  5. Operations on measure • Superposition (innovation): • Subsampling (removal): • Transition (move):

  6. Building Markov chain of DPs • Markov chain of base measures: • DPs with Markov base measures:

  7. The sampling algorithm • Previous phase DP: • Sample the next phase DP - D’:

  8. Experiments • Synthetic data: Gaussian mixtures with birth & death of components.

  9. Experiments • People flows at New York Grand Central Station: observation is location-velocity pair. • Infers a much smaller 20 flows with the average likelihood -3.34, compared with D-FMM’s -3.34 of 50 flows.

More Related