Abstract We describe a stochastic, dynamical system capable of inference and learning in a probabilistic latent variable model. The most challenging problem in such models—sampling the posterior distribution over latent variables—is proposed to be solved by harnessing natural sources of stochasticity inherent in electronic and neural systems. We demonstrate this idea for a sparse coding model by deriving a continuous-time equation for inferring its latent variables via Langevin dynamics. The model parameters are learned by simultaneously evolving according to another continuous-time equation, thus bypassing the need for digital accumulators or a global clock. Moreover, we show that Langevin dynamics lead to an efficient procedure for sampling from the posterior distribution in the L0 sparse regime, where latent variables are encouraged to be set to zero as opposed to having a small L1 norm. This allows the model to properly incorporate the notion of sparsity rather than having to resort to a relaxed version of sparsity to make optimization tractable. Simulations of the proposed dynamical system on both synthetic and natural image data sets demonstrate that the model is capable of probabilistically correct inference, enabling learning of the dictionary as well as parameters of the prior.
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Nonlinear Optimal Velocity Car Following Dynamics (II): Rate of Convergence In the Presence of Fast Perturbation
Traffic flow models have been the subject of extensive studies for decades. The interest in these models is both as the result of their important applications as well as their complex behavior which makes them theoretically challenging. In this paper, an optimal velocity dynamical model is considered and analyzed.We consider a dynamical model in the presence of perturbation and show that not only such a perturbed system
converges to an averaged problem, but also we can show its order of convergence. Such understanding is important from different aspects, and in particular, it shows how well we can approximate a perturbed system with its associated averaged problem.
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- Award ID(s):
- 1727785
- NSF-PAR ID:
- 10190501
- Date Published:
- Journal Name:
- Nonlinear Optimal Velocity Car Following Dynamics (II): Rate of Convergence In the Presence of Fast Perturbation
- Page Range / eLocation ID:
- 416 to 421
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.23919/ACC45564.2020.9147244
