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Inferring neural population dynamics from multiple partial recordings of the same neural circuit,” NIPS
, 2013
"... Simultaneous recordings of the activity of large neural populations are extremely valuable as they can be used to infer the dynamics and interactions of neurons in a local circuit, shedding light on the computations performed. It is now possible to measure the activity of hundreds of neurons using 2 ..."
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Simultaneous recordings of the activity of large neural populations are extremely valuable as they can be used to infer the dynamics and interactions of neurons in a local circuit, shedding light on the computations performed. It is now possible to measure the activity of hundreds of neurons using 2photon calcium imaging. However, many computations are thought to involve circuits consisting of thousands of neurons, such as cortical barrels in rodent somatosensory cortex. Here we contribute a statistical method for “stitching ” together sequentially imaged sets of neurons into one model by phrasing the problem as fitting a latent dynamical system with missing observations. This method allows us to substantially expand the populationsizes for which population dynamics can be characterized—beyond the number of simultaneously imaged neurons. In particular, we demonstrate using recordings in mouse somatosensory cortex that this method makes it possible to predict noise correlations between nonsimultaneously recorded neuron pairs. 1
Clustered factor analysis of multineuronal spike data
"... Highdimensional, simultaneous recordings of neural spiking activity are often explored, analyzed and visualized with the help of latent variable or factor models. Such models are however illequipped to extract structure beyond shared, distributed aspects of firing activity across multiple cells. ..."
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Highdimensional, simultaneous recordings of neural spiking activity are often explored, analyzed and visualized with the help of latent variable or factor models. Such models are however illequipped to extract structure beyond shared, distributed aspects of firing activity across multiple cells. Here, we extend unstructured factor models by proposing a model that discovers subpopulations or groups of cells from the pool of recorded neurons. The model combines aspects of mixture of factor analyzer models for capturing clustering structure, and aspects of latent dynamical system models for capturing temporal dependencies. In the resulting model, we infer the subpopulations and the latent factors from data using variational inference and model parameters are estimated by Expectation Maximization (EM). We also address the crucial problem of initializing parameters for EM by extending a sparse subspace clustering algorithm to integervalued spike count observations. We illustrate the merits of the proposed model by applying it to calciumimaging data from spinal cord neurons, and we show that it uncovers meaningful clustering structure in the data. 1
Learning stable, regularised latent models of neural population dynamics
 Network
, 2012
"... Running title: Stable, regularised models of population dynamics Ongoing advances in experimental technique are making commonplace simultaneous recordings of the activity of tens to hundreds of cortical neurons at high temporal resolution. Latent population models, including Gaussianprocess factor ..."
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Running title: Stable, regularised models of population dynamics Ongoing advances in experimental technique are making commonplace simultaneous recordings of the activity of tens to hundreds of cortical neurons at high temporal resolution. Latent population models, including Gaussianprocess factor analysis and hidden linear dynamical system (LDS) models, have proven effective at capturing the statistical structure of such data sets. They can be estimated efficiently, yield useful visualisations of population activity, and are also integral buildingblocks of decoding algorithms for brainmachine interfaces (BMI). One practical challenge, particularly to LDS models, is that when parameters are learned using realistic volumes of data the resulting models often fail to reflect the true temporal continuity of the dynamics, and indeed may describe a biologicallyimplausible unstable population dynamic; that is, it may predict neural activity that grows without bound. We propose a method for learning LDS models based on expectation maximisation that constrains parameters to yield stable systems and at the same time promotes capture of temporal structure by appropriate regularisation. We show that when only little training data is available our method yields LDS parameter estimates which provide a substantially better statistical description of the data than alternatives, whilst guaranteeing stable dynamics. We demonstrate our methods using both synthetic data and extracellular multielectrode recordings from motor cortex. 1
Recurrent linear models of simultaneouslyrecorded neural populations
"... Population neural recordings with longrange temporal structure are often best understood in terms of a common underlying lowdimensional dynamical process. Advances in recording technology provide access to an everlarger fraction of the population, but the standard computational approaches availa ..."
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Population neural recordings with longrange temporal structure are often best understood in terms of a common underlying lowdimensional dynamical process. Advances in recording technology provide access to an everlarger fraction of the population, but the standard computational approaches available to identify the collective dynamics scale poorly with the size of the dataset. We describe a new, scalable approach to discovering lowdimensional dynamics that underlie simultaneously recorded spike trains from a neural population. We formulate the Recurrent Linear Model (RLM) by generalising the Kalmanfilterbased likelihood calculation for latent linear dynamical systems to incorporate a generalisedlinear observation process. We show that RLMs describe motorcortical population data better than either directlycoupled generalisedlinear models or latent linear dynamical system models with generalisedlinear observations. We also introduce the cascaded generalisedlinear model (CGLM) to capture lowdimensional instantaneous correlations in neural populations. The CGLM describes the cortical recordings better than either Ising or Gaussian models and, like the RLM, can be fit exactly and quickly. The CGLM can also be seen as a generalisation of a lowrank Gaussian model, in this case factor analysis. The computational tractability of the RLM and CGLM allow both to scale to very highdimensional neural data. 1
A Bayesian model for identifying hierarchically organised states in neural population activity
"... Neural population activity in cortical circuits is not solely driven by external inputs, but is also modulated by endogenous states which vary on multiple timescales. To understand information processing in cortical circuits, we need to understand the statistical structure of internal states and ..."
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Neural population activity in cortical circuits is not solely driven by external inputs, but is also modulated by endogenous states which vary on multiple timescales. To understand information processing in cortical circuits, we need to understand the statistical structure of internal states and their interaction with sensory inputs. Here, we present a statistical model for extracting hierarchically organised neural population states from multichannel recordings of neural spiking activity. Population states are modelled using a hidden Markov decision tree with statedependent tuning parameters and a generalised linear observation model. We present a variational Bayesian inference algorithm for estimating the posterior distribution over parameters from neural population recordings. On simulated data, we show that we can identify the underlying sequence of population states and reconstruct the ground truth parameters. Using population recordings from visual cortex, we find that a model with two levels of population states outperforms both a onestate and a twostate generalised linear model. Finally, we find that modelling of statedependence also improves the accuracy with which sensory stimuli can be decoded from the population response. 1
Extracting latent structure from multiple interacting neural populations,” in
 Proc. NIPS,
, 2014
"... Abstract Developments in neural recording technology are rapidly enabling the recording of populations of neurons in multiple brain areas simultaneously, as well as the identification of the types of neurons being recorded (e.g., excitatory vs. inhibitory). There is a growing need for statistical m ..."
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Abstract Developments in neural recording technology are rapidly enabling the recording of populations of neurons in multiple brain areas simultaneously, as well as the identification of the types of neurons being recorded (e.g., excitatory vs. inhibitory). There is a growing need for statistical methods to study the interaction among multiple, labeled populations of neurons. Rather than attempting to identify direct interactions between neurons (where the number of interactions grows with the number of neurons squared), we propose to extract a smaller number of latent variables from each population and study how these latent variables interact. Specifically, we propose extensions to probabilistic canonical correlation analysis (pCCA) to capture the temporal structure of the latent variables, as well as to distinguish withinpopulation dynamics from betweenpopulation interactions (termed Group Latent AutoRegressive Analysis, gLARA). We then applied these methods to populations of neurons recorded simultaneously in visual areas V1 and V2, and found that gLARA provides a better description of the recordings than pCCA. This work provides a foundation for studying how multiple populations of neurons interact and how this interaction supports brain function.
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"... Inferring neural population dynamics from multiple partial recordings of the same neural circuit 1 2 ..."
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Inferring neural population dynamics from multiple partial recordings of the same neural circuit 1 2
with application to neural population
"... Spectral learning of linear dynamics from generalisedlinear observations ..."
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Spectral learning of linear dynamics from generalisedlinear observations