Latent variable models have been widely applied for the analysis and visualization of large datasets. In the case of sequential data, closed-form inference is possible when the transition and observation functions are linear. However, approximate inference techniques are usually necessary when dealing with nonlinear dynamics and observation functions. Here, we propose a novel variational inference framework for the explicit modeling of time series, Variational Inference for Nonlinear Dynamics (VIND),  that is able to uncover nonlinear observation and transition functions from sequential data. The framework includes a structured approximate posterior , and an algorithm that relies on the fixed-point iteration method to find the best estimate for latent trajectories . We apply the method to several datasets and show that it is able to accurately infer the underlying dynamics of these systems , in some cases substantially outperforming state-of-the-art methods.
Latent variable models have been widely applied for the analysis of time series resulting from experimental neuroscience techniques. In these datasets, observations are relatively smooth and possibly nonlinear. We present Variational Inference for Nonlinear Dynamics (VIND), a variational inference framework that is able to uncover nonlinear , smooth latent dynamics from sequential data. The framework is a direct extension of PfLDS; including a structured approximate posterior describing spatially-dependent linear dynamics, as well as an algorithm that relies on the fixed-point iteration method to achieve convergence . We apply VIND to electrophysiology, single-cell voltage and widefield imaging datasets with state-of-the-art results in reconstruction error. In single-cell voltage data, VIND finds a 5D latent space, with variables akin to those of Hodgkin-Huxley-like models. VIND's learned dynamics are further quantified by predicting future neural activity. VIND excels in this task , in some cases substantially outperforming current methods.
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and visualization of large datasets. In the case of sequential data, closed-form inference is possible when the transition and observation functions are linear. However, approximate inference techniques are usually necessary when dealing with nonlinear dynamics and observation functions. Here, we propose a novel variational inference framework for the explicit modeling of time series,
of time series resulting from experimental neuroscience techniques. In these datasets, observations are relatively smooth and possibly nonlinear. We present
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a variational inference framework
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observation and transition functions
, smooth latent dynamics
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includes a
is a direct extension of PfLDS; including a
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, and
describing spatially-dependent linear dynamics, as well as
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find the best estimate for latent trajectories
achieve convergence
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the method to several datasets and show that it is able to accurately infer the underlying dynamics of these systems
VIND to electrophysiology, single-cell voltage and widefield imaging datasets with state-of-the-art results in reconstruction error. In single-cell voltage data, VIND finds a 5D latent space, with variables akin to those of Hodgkin-Huxley-like models. VIND's learned dynamics are further quantified by predicting future neural activity. VIND excels in this task
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state-of-the-art
current