scholarly journals Characterizing the nonlinear structure of shared variability in cortical neuron populations using latent variable models

2018 ◽  
Author(s):  
Matthew R Whiteway ◽  
Karolina Socha ◽  
Vincent Bonin ◽  
Daniel A Butts
Keyword(s):  
Neural Activity ◽  
Latent Variables ◽  
Latent Variable ◽  
Large Scale ◽  
Latent Variable Models ◽  
Neural Population ◽  
Variable Model ◽  
Experimental Conditions ◽  
Affine Model ◽  
Nonlinear Latent Variable Models

AbstractSensory neurons often have variable responses to repeated presentations of the same stimulus, which can significantly degrade the information contained in those responses. Such variability is often shared across many neurons, which in principle can allow a decoder to mitigate the effects of such noise, depending on the structure of the shared variability and its relationship to sensory encoding at the population level. Latent variable models offer an approach for characterizing the structure of this shared variability in neural population recordings, although they have thus far typically been used under restrictive mathematical assumptions, such as assuming linear transformations between the latent variables and neural activity. Here we leverage recent advances in machine learning to introduce two nonlinear latent variable models for analyzing large-scale neural recordings. We first present a general nonlinear latent variable model that is agnostic to the stimulus tuning properties of the individual neurons, and is hence well suited for exploring neural populations whose tuning properties are not well characterized. This motivates a second class of model, the Generalized Affine Model, which simultaneously determines each neuron’s stimulus selectivity and a set of latent variables that modulate these stimulus responses both additively and multiplicatively. While these approaches can detect general nonlinear relationships in shared neural variability, we find that neural activity recorded in anesthetized primary visual cortex (V1) is best described by a single additive and single multiplicative latent variable, i.e., an “affine model”. In contrast, application of the same models to recordings in awake macaque prefrontal cortex discover more general nonlinearities to compactly describe the population response variability. These results thus demonstrate how nonlinear latent variable models can be used to describe population variability, and suggest that a range of methods is necessary to study different brain regions under different experimental conditions.

scholarly journals Revealing unobserved factors underlying cortical activity using a rectified latent variable model applied to neural population recordings

2016 ◽  
Author(s):  
Matthew R. Whiteway ◽  
Daniel A. Butts
Keyword(s):  
Latent Variables ◽  
Latent Variable ◽  
Large Population ◽  
Component Analysis ◽  
Latent Variable Model ◽  
Neural Population ◽  
Model Parameters ◽  
Variable Model ◽  
Sensory Stimuli ◽  
External Stimuli

ABSTRACTThe activity of sensory cortical neurons is not only driven by external stimuli, but is also shaped by other sources of input to the cortex. Unlike external stimuli these other sources of input are challenging to experimentally control or even observe, and as a result contribute to variability of neuronal responses to sensory stimuli. However, such sources of input are likely not “noise”, and likely play an integral role in sensory cortex function. Here, we introduce the rectified latent variable model (RLVM) in order to identify these sources of input using simultaneously recorded cortical neuron populations. The RLVM is novel in that it employs non-negative (rectified) latent variables, and is able to be much less restrictive in the mathematical constraints on solutions due to the use an autoencoder neural network to initialize model parameters. We show the RLVM outperforms principal component analysis, factor analysis and independent component analysis across a variety of measures using simulated data. We then apply this model to the 2-photon imaging of hundreds of simultaneously recorded neurons in mouse primary somatosensory cortex during a tactile discrimination task. Across many experiments, the RLVM identifies latent variables related to both the tactile stimulation as well as non-stimulus aspects of the behavioral task, with a majority of activity explained by the latter. These results suggest that properly identifying such latent variables is necessary for a full understanding of sensory cortical function, and demonstrates novel methods for leveraging large population recordings to this end.

scholarly journals Identifying signal and noise structure in neural population activity with Gaussian process factor models

2020 ◽  
Author(s):  
Stephen L. Keeley ◽  
Mikio C. Aoi ◽  
Yiyi Yu ◽  
Spencer L. Smith ◽  
Jonathan W. Pillow
Keyword(s):  
Gaussian Process ◽  
Neural Activity ◽  
Latent Variable ◽  
Large Scale ◽  
Brain Regions ◽  
Factor Models ◽  
Latent Structure ◽  
Neural Population ◽  
Process Factor ◽  
Repeated Stimulus

AbstractNeural datasets often contain measurements of neural activity across multiple trials of a repeated stimulus or behavior. An important problem in the analysis of such datasets is to characterize systematic aspects of neural activity that carry information about the repeated stimulus or behavior of interest, which can be considered “signal”, and to separate them from the trial-to-trial fluctuations in activity that are not time-locked to the stimulus, which for purposes of such analyses can be considered “noise”. Gaussian Process factor models provide a powerful tool for identifying shared structure in high-dimensional neural data. However, they have not yet been adapted to the problem of characterizing signal and noise in multi-trial datasets. Here we address this shortcoming by proposing “signal-noise” Poisson-spiking Gaussian Process Factor Analysis (SNP-GPFA), a flexible latent variable model that resolves signal and noise latent structure in neural population spiking activity. To learn the parameters of our model, we introduce a Fourier-domain black box variational inference method that quickly identifies smooth latent structure. The resulting model reliably uncovers latent signal and trial-to-trial noise-related fluctuations in large-scale recordings. We use this model to show that predominantly, noise fluctuations perturb neural activity within a subspace orthogonal to signal activity, suggesting that trial-by-trial noise does not interfere with signal representations. Finally, we extend the model to capture statistical dependencies across brain regions in multi-region data. We show that in mouse visual cortex, models with shared noise across brain regions out-perform models with independent per-region noise.

scholarly journals Revealing unobserved factors underlying cortical activity with a rectified latent variable model applied to neural population recordings

2017 ◽  
Vol 117 (3) ◽  
pp. 919-936 ◽  
Author(s):  
Matthew R. Whiteway ◽  
Daniel A. Butts
Keyword(s):  
Latent Variables ◽  
Latent Variable ◽  
Large Population ◽  
Component Analysis ◽  
Latent Variable Model ◽  
Neural Population ◽  
Model Parameters ◽  
Variable Model ◽  
Sensory Stimuli ◽  
External Stimuli

The activity of sensory cortical neurons is not only driven by external stimuli but also shaped by other sources of input to the cortex. Unlike external stimuli, these other sources of input are challenging to experimentally control, or even observe, and as a result contribute to variability of neural responses to sensory stimuli. However, such sources of input are likely not “noise” and may play an integral role in sensory cortex function. Here we introduce the rectified latent variable model (RLVM) in order to identify these sources of input using simultaneously recorded cortical neuron populations. The RLVM is novel in that it employs nonnegative (rectified) latent variables and is much less restrictive in the mathematical constraints on solutions because of the use of an autoencoder neural network to initialize model parameters. We show that the RLVM outperforms principal component analysis, factor analysis, and independent component analysis, using simulated data across a range of conditions. We then apply this model to two-photon imaging of hundreds of simultaneously recorded neurons in mouse primary somatosensory cortex during a tactile discrimination task. Across many experiments, the RLVM identifies latent variables related to both the tactile stimulation as well as nonstimulus aspects of the behavioral task, with a majority of activity explained by the latter. These results suggest that properly identifying such latent variables is necessary for a full understanding of sensory cortical function and demonstrate novel methods for leveraging large population recordings to this end. NEW & NOTEWORTHY The rapid development of neural recording technologies presents new opportunities for understanding patterns of activity across neural populations. Here we show how a latent variable model with appropriate nonlinear form can be used to identify sources of input to a neural population and infer their time courses. Furthermore, we demonstrate how these sources are related to behavioral contexts outside of direct experimental control.

scholarly journals Gaussian Processes Proxy Model with Latent Variable Models and Variogram-Based Sensitivity Analysis for Assisted History Matching

Energies ◽  
2020 ◽  
Vol 13 (17) ◽  
pp. 4290
Author(s):  
Dongmei Zhang ◽  
Yuyang Zhang ◽  
Bohou Jiang ◽  
Xinwei Jiang ◽  
Zhijiang Kang
Keyword(s):  
Sensitivity Analysis ◽  
Gaussian Processes ◽  
Latent Variable ◽  
History Matching ◽  
Latent Variable Models ◽  
High Dimensional ◽  
Model Parameters ◽  
Variable Model ◽  
Assisted History Matching ◽  
Proxy Models

Reservoir history matching is a well-known inverse problem for production prediction where enormous uncertain reservoir parameters of a reservoir numerical model are optimized by minimizing the misfit between the simulated and history production data. Gaussian Process (GP) has shown promising performance for assisted history matching due to the efficient nonparametric and nonlinear model with few model parameters to be tuned automatically. Recently introduced Gaussian Processes proxy models and Variogram Analysis of Response Surface-based sensitivity analysis (GP-VARS) uses forward and inverse Gaussian Processes (GP) based proxy models with the VARS-based sensitivity analysis to optimize the high-dimensional reservoir parameters. However, the inverse GP solution (GPIS) in GP-VARS are unsatisfactory especially for enormous reservoir parameters where the mapping from low-dimensional misfits to high-dimensional uncertain reservoir parameters could be poorly modeled by GP. To improve the performance of GP-VARS, in this paper we propose the Gaussian Processes proxy models with Latent Variable Models and VARS-based sensitivity analysis (GPLVM-VARS) where Gaussian Processes Latent Variable Model (GPLVM)-based inverse solution (GPLVMIS) instead of GP-based GPIS is provided with the inputs and outputs of GPIS reversed. The experimental results demonstrate the effectiveness of the proposed GPLVM-VARS in terms of accuracy and complexity. The source code of the proposed GPLVM-VARS is available at https://github.com/XinweiJiang/GPLVM-VARS.

Information Matrices in Latent-Variable Models

1989 ◽  
Vol 14 (4) ◽  
pp. 335-350 ◽  
Author(s):  
Robert J. Mislevy ◽  
Kathleen M. Sheehan
Keyword(s):  
Latent Variables ◽  
Latent Variable ◽  
Information Matrix ◽  
Missing Information ◽  
Variable Model ◽  
Related Information ◽  
Expected Information ◽  
The Difference ◽  
Information Matrices ◽  
Practical Implications

The Fisher, or expected, information matrix for the parameters in a latent-variable model is bounded from above by the information that would be obtained if the values of the latent variables could also be observed. The difference between this upper bound and the information in the observed data is the “missing information.” This paper explicates the structure of the expected information matrix and related information matrices, and characterizes the degree to which missing information can be recovered by exploiting collateral variables for respondents. The results are illustrated in the context of item response theory models, and practical implications are discussed.

scholarly journals A Bayesian approach to nonlinear latent variable models using the Gibbs sampler and the metropolis-hastings algorithm

Psychometrika ◽  
1998 ◽  
Vol 63 (3) ◽  
pp. 271-300 ◽  
Author(s):  
Gerhard Arminger ◽  
Bengt O. Muthén
Keyword(s):  
Bayesian Approach ◽  
Gibbs Sampler ◽  
Latent Variable ◽  
Latent Variable Models ◽  
Nonlinear Latent Variable Models

Latent variable models are network models

2010 ◽  
Vol 33 (2-3) ◽  
pp. 166-166 ◽  
Author(s):  
Peter C. M. Molenaar
Keyword(s):  
Latent Variables ◽  
Latent Variable ◽  
Network Models ◽  
Latent Variable Models ◽  
Variable Theory ◽  
The Relationship

AbstractCramer et al. present an original and interesting network perspective on comorbidity and contrast this perspective with a more traditional interpretation of comorbidity in terms of latent variable theory. My commentary focuses on the relationship between the two perspectives; that is, it aims to qualify the presumed contrast between interpretations in terms of networks and latent variables.

scholarly journals A Flow-Based Deep Latent Variable Model for Speech Spectrogram Modeling and Enhancement

2020 ◽  
Author(s):  
Aditya Arie Nugraha ◽  
Kouhei Sekiguchi ◽  
Kazuyoshi Yoshii
Keyword(s):  
Speech Enhancement ◽  
Latent Variables ◽  
Latent Variable ◽  
Generative Models ◽  
Latent Variable Model ◽  
Variable Model ◽  
Variational Autoencoder ◽  
Latent Representations ◽  
Low Dimensional ◽  
Better Than

This paper describes a deep latent variable model of speech power spectrograms and its application to semi-supervised speech enhancement with a deep speech prior. By integrating two major deep generative models, a variational autoencoder (VAE) and a normalizing flow (NF), in a mutually-beneficial manner, we formulate a flexible latent variable model called the NF-VAE that can extract low-dimensional latent representations from high-dimensional observations, akin to the VAE, and does not need to explicitly represent the distribution of the observations, akin to the NF. In this paper, we consider a variant of NF called the generative flow (GF a.k.a. Glow) and formulate a latent variable model called the GF-VAE. We experimentally show that the proposed GF-VAE is better than the standard VAE at capturing fine-structured harmonics of speech spectrograms, especially in the high-frequency range. A similar finding is also obtained when the GF-VAE and the VAE are used to generate speech spectrograms from latent variables randomly sampled from the standard Gaussian distribution. Lastly, when these models are used as speech priors for statistical multichannel speech enhancement, the GF-VAE outperforms the VAE and the GF.

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