Linear dynamical neural population models through nonlinear embeddings

By Yuanjun Gao, Evan Archer, Liam Paninski, John P. Cunningham. 2016

168 citations recorded by the source corpus.

A body of recent work in modeling neural activity focuses on recovering low-dimensional latent features that capture the statistical structure of large-scale neural populations. Most such approaches have focused on linear generative models, where inference is computationally tractable. Here, we propose fLDS, a general class of nonlinear generative models that permits the firing rate of each neuron to vary as an arbitrary smooth function of a latent, linear dynamical state. This extra flexibility allows the model to capture a richer set of neural variability than a purely linear model, but retains an easily visualizable low-dimensional latent space. To fit this class of non-conjugate models we propose a variational inference scheme, along with a novel approximate posterior capable of capturing rich temporal correlations across time. We show that our techniques permit inference in a wide class of generative models.We also show in application to two neural datasets that, compared to state-of-the-art neural population models, fLDS captures a much larger proportion of neural variability with a small number of latent dimensions, providing superior predictive performance and interpretability.

Subfields: Artificial Intelligence, Cognitive Neuroscience

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Citations in the corpus

A Disentangled Recognition and Nonlinear Dynamics Model for Unsupervised Learning (2017, neutral): “[10] models neural activity by finding a non-linear embedding of a neural time series into a LGSSM.”
Stochastic Variational Video Prediction (2017, background): “This would allow time-variant latent distributions which is more aligned with generative neural models for time-series(Johnson et al., 2016; Gao et al., 2016; Krishnan et al., 2017).”
SOLAR: Deep Structured Latent Representations for Model-Based Reinforcement Learning (2018, neutral): “This recognition model is identical to that used in other prior works [20, 34, 12], however, as with prior work in the LDS SVAE, we also have variational factors of the form q ( F t , Σ t ) , which represent our posterior belief about the system dynamics after observing the collected data.”
Inferring single-trial neural population dynamics using sequential auto-encoders (2017, methodology): “Recent examples include PLDS [23], switching LDS [27], GCLDS [10], and PfLDS [9].”
Towards the neural population doctrine. (2019, methodology): “Gao et al. [30] introduced ANNs as the nonlinear map from latent dynamics to observable neural population activity, a theme which has been elaborated both by including ANNs in the dynamics model, and otherwise [63–66].”
Variational Sequential Monte Carlo (2017, methodology): “We study a population of 105 motor cortex neurons simultaneously recorded in a macaque monkey as it performed reaching movements [c.f. Gao et al., 2016].”
SOLAR: Deep Structured Representations for Model-Based Reinforcement Learning (2018, unknown): “odel, parameterized by neural network weights ˚, that outputs the mean and diagonal covariance of a Gaussian distribution over z. This recognition model is identical to that used in other prior works [20, 34, 12], however, as with prior work in the LDS SVAE, we also have variational factors of the f”
Unsupervised Discovery of Demixed, Low-Dimensional Neural Dynamics across Multiple Timescales through Tensor Component Analysis (2017, methodology): “Simple linear models have a relatively constrained dynamical repertoire [12], while models with nonlinear 520 elements often have greater predictive abilities [17, 18], but at the expense of interpretability.”
Tree-Structured Recurrent Switching Linear Dynamical Systems for Multi-Scale Modeling (2018, methodology): “In recent years, this toolkit has been expanded to incorporate increasingly ﬂexible components like Gaussian processes (Frigola et al., 2014) and neural networks (Chung et al., 2015; Johnson et al., 2016; Gao et al., 2016; Krishnan et al., 2017) into probabilistic time series models.”
Contextual Explanation Networks (2017, background): “…networks [8, 9, 10], representing potential functions [11] and energy functions [12] with neural networks, encoding learnable structure into Gaussian process kernels with deep and recurrent networks [13, 14], or learning state-space models on top of nonlinear embeddings of observables [15, 16, 17].”
Scalable Bayesian GPFA with automatic relevance determination and discrete noise models (2021, methodology): “Importantly, the hyperparameters of bGPFA are efficiently optimized based on the ELBO on training data, which alleviates the need for cross-validation or complicated algorithms otherwise used for hyperparameter optimization in overparameterized models [16, 22, 27, 28, 58, 59].”
Learning Koopman Invariant Subspaces for Dynamic Mode Decomposition (2017, methodology): “[36] utilized VAE-based inference for neural population models, and Johnson et al.”