Parameter Estimation in Multiple Dynamic Synaptic Coupling Model Using Bayesian Point Process State-Space Modeling Framework

2021 ◽  
pp. 1-31
Author(s):  
Yalda Amidi ◽  
Behzad Nazari ◽  
Saeid Sadri ◽  
Ali Yousefi
Keyword(s):  
State Space ◽  
Point Process ◽  
Goodness Of Fit ◽  
Estimation Accuracy ◽  
Model Parameters ◽  
Synaptic Connections ◽  
Synaptic Coupling ◽  
Modeling Framework ◽  
Space Modeling ◽  
Spiking Activity

It is of great interest to characterize the spiking activity of individual neurons in a cell ensemble. Many different mechanisms, such as synaptic coupling and the spiking activity of itself and its neighbors, drive a cell's firing properties. Though this is a widely studied modeling problem, there is still room to develop modeling solutions by simplifications embedded in previous models. The first shortcut is that synaptic coupling mechanisms in previous models do not replicate the complex dynamics of the synaptic response. The second is that the number of synaptic connections in these models is an order of magnitude smaller than in an actual neuron. In this research, we push this barrier by incorporating a more accurate model of the synapse and propose a system identification solution that can scale to a network incorporating hundreds of synaptic connections. Although a neuron has hundreds of synaptic connections, only a subset of these connections significantly contributes to its spiking activity. As a result, we assume the synaptic connections are sparse, and to characterize these dynamics, we propose a Bayesian point-process state-space model that lets us incorporate the sparsity of synaptic connections within the regularization technique into our framework. We develop an extended expectation-maximization. algorithm to estimate the free parameters of the proposed model and demonstrate the application of this methodology to the problem of estimating the parameters of many dynamic synaptic connections. We then go through a simulation example consisting of the dynamic synapses across a range of parameter values and show that the model parameters can be estimated using our method. We also show the application of the proposed algorithm in the intracellular data that contains 96 presynaptic connections and assess the estimation accuracy of our method using a combination of goodness-of-fit measures.

Estimating a State-Space Model from Point Process Observations

2003 ◽  
Vol 15 (5) ◽  
pp. 965-991 ◽  
Author(s):  
Anne C. Smith ◽  
Emery N. Brown
Keyword(s):  
State Space ◽  
Point Process ◽  
State Space Model ◽  
The State ◽  
Conditional Intensity ◽  
Space Model ◽  
Neural Spiking ◽  
Latent Process ◽  
Conditional Intensity Function ◽  
Spiking Activity

A widely used signal processing paradigm is the state-space model. The state-space model is defined by two equations: an observation equation that describes how the hidden state or latent process is observed and a state equation that defines the evolution of the process through time. Inspired by neurophysiology experiments in which neural spiking activity is induced by an implicit (latent) stimulus, we develop an algorithm to estimate a state-space model observed through point process measurements. We represent the latent process modulating the neural spiking activity as a gaussian autoregressive model driven by an external stimulus. Given the latent process, neural spiking activity is characterized as a general point process defined by its conditional intensity function. We develop an approximate expectation-maximization (EM) algorithm to estimate the unobservable state-space process, its parameters, and the parameters of the point process. The EM algorithm combines a point process recursive nonlinear filter algorithm, the fixed interval smoothing algorithm, and the state-space covariance algorithm to compute the complete data log likelihood efficiently. We use a Kolmogorov-Smirnov test based on the time-rescaling theorem to evaluate agreement between the model and point process data. We illustrate the model with two simulated data examples: an ensemble of Poisson neurons driven by a common stimulus and a single neuron whose conditional intensity function is approximated as a local Bernoulli process.

scholarly journals State-space models reveal bursty movement behaviour of dance event visitors

2021 ◽  
Vol 10 (1) ◽  
Author(s):  
Philip Rutten ◽  
Michael H. Lees ◽  
Sander Klous ◽  
Peter M. A. Sloot
Keyword(s):  
State Space ◽  
Waiting Times ◽  
Movement Ecology ◽  
Joint Estimation ◽  
Movement Behaviour ◽  
Modeling Framework ◽  
Movement Data ◽  
Space Modeling ◽  
Crowd Behaviour ◽  
Heavy Tailed

AbstractPedestrian movements during large crowded events naturally consist of different modes of movement behaviour. Despite its importance for understanding crowd dynamics, intermittent movement behaviour is an aspect missing in the existing crowd behaviour literature. Here we analyse movement data generated from nearly 600 Wi-Fi sensors during large entertainment events in the Johan Cruijff ArenA football stadium in Amsterdam. We use the state-space modeling framework to investigate intermittent motion patterns. Movement models from the field of movement ecology are used to analyse individual pedestrian movement. Joint estimation of multiple movement tracks allows us to investigate statistical properties of measured movement metrics. We show that behavioural switching is not independent of external events, and the probability of being in one of the behavioural states changes over time. In addition, we show that the distribution of waiting times deviates from the exponential and is best fit by a heavy-tailed distribution. The heavy-tailed waiting times are indicative of bursty movement dynamics, which are here for the first time shown to characterise pedestrian movements in dense crowds. Bursty crowd behaviour has important implications for various diffusion-related processes, such as the spreading of infectious diseases.

scholarly journals Bayesian Decoder Models with a Discriminative Observation Process

2020 ◽  
Author(s):  
Mohammad R. Rezaei ◽  
Alex E. Hadjinicolaou ◽  
Sydney S. Cash ◽  
Uri T. Eden ◽  
Ali Yousefi
Keyword(s):  
State Space ◽  
Neural Activity ◽  
Model Development ◽  
High Dimensional ◽  
Modeling Framework ◽  
Movement Trajectories ◽  
State Process ◽  
Observation Process ◽  
Space Modeling ◽  
Low Dimensional

AbstractThe Bayesian state-space neural encoder-decoder modeling framework is an established solution to reveal how changes in brain dynamics encode physiological covariates like movement or cognition. Although the framework is increasingly being applied to progress the field of neuroscience, its application to modeling high-dimensional neural data continues to be a challenge. Here, we propose a novel solution that avoids the complexity of encoder models that characterize high-dimensional data as a function of the underlying state processes. We build a discriminative model to estimate state processes as a function of current and previous observations of neural activity. We then develop the filter and parameter estimation solutions for this new class of state-space modeling framework called the “direct decoder” model. We apply the model to decode movement trajectories of a rat in a W-shaped maze from the ensemble spiking activity of place cells and achieve comparable performance to modern decoding solutions, without needing an encoding step in the model development. We further demonstrate how a dynamical auto-encoder can be built using the direct decoder model; here, the underlying state process links the high-dimensional neural activity to the behavioral readout. The dynamical auto-encoder can optimally estimate the low-dimensional dynamical manifold which represents the relationship between brain and behavior.

Decoding Hidden Cognitive States From Behavior and Physiology Using a Bayesian Approach

2019 ◽  
Vol 31 (9) ◽  
pp. 1751-1788 ◽  
Author(s):  
Ali Yousefi ◽  
Ishita Basu ◽  
Angelique C. Paulk ◽  
Noam Peled ◽  
Emad N. Eskandar ◽  
...  
Keyword(s):  
Cognitive Processes ◽  
Goodness Of Fit ◽  
Spectral Power ◽  
Field Potential ◽  
High Dimensional ◽  
Cognitive State ◽  
Modeling Framework ◽  
Neural Data ◽  
Space Modeling ◽  
The Relationship

Cognitive processes, such as learning and cognitive flexibility, are both difficult to measure and to sample continuously using objective tools because cognitive processes arise from distributed, high-dimensional neural activity. For both research and clinical applications, that dimensionality must be reduced. To reduce dimensionality and measure underlying cognitive processes, we propose a modeling framework in which a cognitive process is defined as a low-dimensional dynamical latent variable—called a cognitive state, which links high-dimensional neural recordings and multidimensional behavioral readouts. This framework allows us to decompose the hard problem of modeling the relationship between neural and behavioral data into separable encoding-decoding approaches. We first use a state-space modeling framework, the behavioral decoder, to articulate the relationship between an objective behavioral readout (e.g., response times) and cognitive state. The second step, the neural encoder, involves using a generalized linear model (GLM) to identify the relationship between the cognitive state and neural signals, such as local field potential (LFP). We then use the neural encoder model and a Bayesian filter to estimate cognitive state using neural data (LFP power) to generate the neural decoder. We provide goodness-of-fit analysis and model selection criteria in support of the encoding-decoding result. We apply this framework to estimate an underlying cognitive state from neural data in human participants ([Formula: see text]) performing a cognitive conflict task. We successfully estimated the cognitive state within the 95% confidence intervals of that estimated using behavior readout for an average of 90% of task trials across participants. In contrast to previous encoder-decoder models, our proposed modeling framework incorporates LFP spectral power to encode and decode a cognitive state. The framework allowed us to capture the temporal evolution of the underlying cognitive processes, which could be key to the development of closed-loop experiments and treatments.

A Framework for Control Oriented Modeling of PEM Fuel Cells

2015 ◽  
Author(s):  
Benjamin L. Pence ◽  
Jixin Chen
Keyword(s):  
Fuel Cells ◽  
State Space ◽  
Polymer Electrolyte Membrane ◽  
Pem Fuel Cells ◽  
Algebraic Equations ◽  
Transient Effects ◽  
Modeling Framework ◽  
Two Phase ◽  
One Dimensional ◽  
Space Modeling

This paper develops a framework for along-the-channel and through-the-membrane control oriented modeling of polymer electrolyte membrane (PEM) fuel cells. The initial modeling framework is spatially one-dimensional by one-dimensional (1+1D) and is described by unsteady partial differential equations (PDEs). Numerical techniques convert the PDEs and boundary conditions to ordinary differential and algebraic equations that are convenient for state-space modeling. The modeling framework includes two-phase, thermal, and other transient effects. The generality of the modeling framework and its ability to be represented in state-space form facilitate complexity reduction and control-oriented application.

Time-varying process model for intelligent prediction of strain and temperature in micro-turning process

2017 ◽  
Vol 233 (5) ◽  
pp. 1626-1634 ◽  
Author(s):  
Soumen Mandal ◽  
Aniruddha Pal ◽  
Nagahanumaiah
Keyword(s):  
Kalman Filter ◽  
State Space ◽  
Process Model ◽  
Maximum Error ◽  
Cutting Edge ◽  
Model Parameters ◽  
Machining Parameters ◽  
Time Varying ◽  
Space Modeling ◽  
Micro Turning

Time-varying process models for micro-machining processes are important as they aid in control of machining parameters. In this research, a state-space-based process model for the temperature and strain generated near the cutting edge of the tool tip is identified using system identification approach. Fiber Bragg grating sensors were placed rigidly near the cutting edge of the tool tip in a micro-turning setup. Subsequently, micro-turning operations were carried out on aluminum and mild steel. The computer numerically controlled program was such that the machining parameters (feed velocity, depth of cut and RPM) change with machining time. The time-varying machining parameters act as inputs to the model, and the dynamic values of strain and temperature serve as model output. A state-space model was generated using the experimental data. Subsequently, a Kalman filter was used to intelligently predict the values of strain and temperature at the cutting edge of tool tip in advance using the model parameters identified by state-space modeling. Experimental results confirm that the time-varying model and the Kalman filter proposed in this research are effective in predicting the strain and temperature in advance with high accuracy. The maximum error in prediction of temperature was 0.4 °C, whereas for strain prediction, the maximum error was 0.3µ∈.

scholarly journals Computing Confidence Intervals for Point Process Models

2011 ◽  
Vol 23 (11) ◽  
pp. 2731-2745 ◽  
Author(s):  
Sridevi V. Sarma ◽  
David P. Nguyen ◽  
Gabriela Czanner ◽  
Sylvia Wirth ◽  
Matthew A. Wilson ◽  
...  
Keyword(s):  
Point Process ◽  
Process Model ◽  
Goodness Of Fit ◽  
Parametric Bootstrap ◽  
Process Models ◽  
Model Parameters ◽  
Bootstrap Sampling ◽  
Confidence Bounds ◽  
Extrinsic Factors ◽  
Point Process Models

Characterizing neural spiking activity as a function of intrinsic and extrinsic factors is important in neuroscience. Point process models are valuable for capturing such information; however, the process of fully applying these models is not always obvious. A complete model application has four broad steps: specification of the model, estimation of model parameters given observed data, verification of the model using goodness of fit, and characterization of the model using confidence bounds. Of these steps, only the first three have been applied widely in the literature, suggesting the need to dedicate a discussion to how the time-rescaling theorem, in combination with parametric bootstrap sampling, can be generally used to compute confidence bounds of point process models. In our first example, we use a generalized linear model of spiking propensity to demonstrate that confidence bounds derived from bootstrap simulations are consistent with those computed from closed-form analytic solutions. In our second example, we consider an adaptive point process model of hippocampal place field plasticity for which no analytical confidence bounds can be derived. We demonstrate how to simulate bootstrap samples from adaptive point process models, how to use these samples to generate confidence bounds, and how to statistically test the hypothesis that neural representations at two time points are significantly different. These examples have been designed as useful guides for performing scientific inference based on point process models.

scholarly journals Mapping of Visual Receptive Fields by Tomographic Reconstruction

2012 ◽  
Vol 24 (10) ◽  
pp. 2543-2578 ◽  
Author(s):  
Gordon Pipa ◽  
Zhe Chen ◽  
Sergio Neuenschwander ◽  
Bruss Lima ◽  
Emery N. Brown
Keyword(s):  
Point Process ◽  
Goodness Of Fit ◽  
Linear Models ◽  
Tomographic Reconstruction ◽  
Receptive Fields ◽  
Stimulus Presentation ◽  
Orientation Tuning ◽  
V1 Neurons ◽  
Baseline Activity ◽  
Spiking Activity

The moving bar experiment is a classic paradigm for characterizing the receptive field (RF) properties of neurons in primary visual cortex (V1). Current approaches for analyzing neural spiking activity recorded from these experiments do not take into account the point-process nature of these data and the circular geometry of the stimulus presentation. We present a novel analysis approach to mapping V1 receptive fields that combines point-process generalized linear models (PPGLM) with tomographic reconstruction computed by filtered-back projection. We use the method to map the RF sizes and orientations of 251 V1 neurons recorded from two macaque monkeys during a moving bar experiment. Our cross-validated goodness-of-fit analyses show that the PPGLM provides a more accurate characterization of spike train data than analyses based on rate functions computed by the methods of spike-triggered averages or first-order Wiener-Volterra kernel. Our analysis leads to a new definition of RF size as the spatial area over which the spiking activity is significantly greater than baseline activity. Our approach yields larger RF sizes and sharper orientation tuning estimates. The tomographic reconstruction paradigm further suggests an efficient approach to choosing the number of directions and the number of trials per direction in designing moving bar experiments. Our results demonstrate that standard tomographic principles for image reconstruction can be adapted to characterize V1 RFs and that two fundamental properties, size and orientation, may be substantially different from what is currently reported.

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