(Georgia Institute of Technology, 2006)
Oh, Sang Min; Rehg, James M.; Balch, Tucker; Dellaert, Frank
Switching Linear Dynamic System (SLDS) models are a popular technique for modeling complex nonlinear dynamic systems. An SLDS has significantly more descriptive power than an HMM by using continuous hidden states. However, the use of SLDS models in practical applications is challenging for several reasons. First, exact inference in SLDS models is computationally intractable. Second, the geometric duration model induced in standard SLDSs limits their representational power. Third, standard SLDSs do not provide a systematic way to robustly interpret systematic variations governed by higher order parameters.
The contributions in this paper address all three challenges above. First, we present a data-driven MCMC sampling method for SLDSs as a robust and efficient approximate inference method. Second, we present segmental switching linear dynamic systems (S-SLDS), where the geometric distributions are replaced with arbitrary duration models. Third, we extend the standard model with a parametric model that can capture systematic temporal and spatial variations. The resulting parametric SLDS model (P-SLDS) uses EM to robustly interpret parametrized motions by incorporating additional global parameters that underly systematic variations of the overall motion.
The overall development of the proposed inference methods and extensions for SLDSs provide a robust framework to interpret complex motions. The framework is applied to the honey bee dance interpretation task in the context of the ongoing BioTracking project at Georgia Institute of Technology. The experimental results suggest that the enhanced models provide an effective framework for a wide range of motion analysis applications.
(Georgia Institute of Technology, 2005)
Oh, Sang Min; Ranganathan, Ananth; Rehg, James M.; Dellaert, Frank
This paper aims to present a structured variational inference algorithm for switching linear dynamical systems (SLDSs) which was initially introduced by Pavlovic and Rehg. Starting with the need for the variational approach, we proceed to the derivation of the generic (model-independent) variational update formulas which are obtained under the mean field assumption. This leads us to the derivation of an approximate variational inference algorithm for an SLDS. The details of deriving the SLDS-specific variational update equations are presented.
(Georgia Institute of Technology, 2005)
Oh, Sang Min; Rehg, James M.; Dellaert, Frank
We introduce Segmental Switching Linear Dynamic Systems (S-SLDS), which improve on standard
SLDSs by explicitly incorporating duration modeling capabilities. We show that S-SLDSs can adopt
arbitrary finite-sized duration models that describe data more accurately than the geometric distributions
induced by standard SLDSs. We also show that we can convert an S-SLDS to an equivalent standard
SLDS with sparse structure in the resulting transition matrix. This insight makes it possible to adopt
existing inference and learning algorithms for the standard SLDS models to the S-SLDS framework. As
a consequence, the more powerful S-SLDS model can be adopted with only modest additional effort in
most cases where an SLDS model can be applied. The experimental results on honeybee dance decoding
tasks demonstrate the robust inference capabilities of the proposed S-SLDS model.