Manifold Learning for Multi-dimensional Auto-regressive Dynamical Models

Cuzzolin, Fabio

doi:10.1007/978-0-85729-057-1_3

Cited by 1 publication

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“…To compute geodesic distances, one can first reconstruct the underlying metric tensor field in the parameter space. Cuzzolin (2011) and Cuzzolin and Sapienza (2014) propose a general framework based on pullback metric to learn discriminative metric tensors in the space of Linear Dynamical Systems (LDS) and Hidden Markov Models (HMM), respectively. The manifold structure in the parameter space is induced by stability constraints on the LDS parameters, or by normalisation constraints on the HMM parameters.…”

Section: Introductionmentioning

confidence: 99%

Classification framework for partially observed dynamical systems

2017

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We present a general framework for classifying partially observed dynamical systems based on the idea of learning in the model space. In contrast to the existing approaches using model point estimates to represent individual data items, we employ posterior distributions over models, thus taking into account in a principled manner the uncertainty due to both the generative (observational and/or dynamic noise) and observation (sampling in time) processes. We evaluate the framework on two testbeds -a biological pathway model and a stochastic double-well system. Crucially, we show that the classifier performance is not impaired when the model class used for inferring posterior distributions is much more simple than the observation-generating model class, provided the reduced complexity inferential model class captures the essential characteristics needed for the given classification task.

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Section: Introductionmentioning

confidence: 99%