scholarly journals Modeling stimulus-dependent variability improves decoding of population neural responses

2017 ◽  
Author(s):  
Abed Ghanbari ◽  
Christopher M. Lee ◽  
Heather L. Read ◽  
Ian H. Stevenson
Keyword(s):  
Firing Rate ◽  
Poisson Model ◽  
Fano Factor ◽  
Response Variability ◽  
Additional Parameter ◽  
Neural Responses ◽  
Stimulus Movement ◽  
Tuning Curves ◽  
The Mean ◽  
Cmp Model

AbstractNeural responses to repeated presentations of an identical stimulus often show substantial trial-to-trial variability. How the mean firing rate varies in response to different stimuli or during different movements (tuning curves) has been extensively modeled in a wide variety of neural systems. However, the variability of neural responses can also have clear tuning independent of the tuning in the mean firing rate. This suggests that the variability could contain information regarding the stimulus/movement beyond what is encoded in the mean firing rate. Here we demonstrate how taking variability into account can improve neural decoding. In a typical neural coding model spike counts are assumed to be Poisson with the mean response depending on an external variable, such as a stimulus or movement. Bayesian decoding methods then use the probabilities under these Poisson tuning models (the likelihood) to estimate the probability of each stimulus given the spikes on a given trial (the posterior). However, under the Poisson model, spike count variability is always exactly equal to the mean (Fano factor = 1). Here we use two alternative models - the Conway-Maxwell-Poisson (CMP) model and Negative Binomial (NB) model - to more flexibly characterize how neural variability depends on external stimuli. These models both contain the Poisson distribution as a special case but have an additional parameter that allows the variance to be greater than the mean (Fano factor >1) or, for the CMP model, less than the mean (Fano factor <1). We find that neural responses in primary motor (M1), visual (V1), and auditory (A1) cortices have diverse tuning in both their mean firing rates and response variability. Across cortical areas, we find that Bayesian decoders using the CMP or NB models improve stimulus/movement estimation accuracy by 4-12% compared to the Poisson model. Moreover, the uncertainty of the non-Poisson decoders more accurately reflects the magnitude of estimation errors. In addition to tuning curves that reflect average neural responses, stimulus-dependent response variability may be an important aspect of the neural code. Modeling this structure could, potentially, lead to improvements in brain machine interfaces.

scholarly journals Changes in the Response Rate and Response Variability of Area V4 Neurons During the Preparation of Saccadic Eye Movements

2010 ◽  
Vol 103 (3) ◽  
pp. 1171-1178 ◽  
Author(s):  
Nicholas A. Steinmetz ◽  
Tirin Moore
Keyword(s):  
Eye Movements ◽  
Reaction Time ◽  
Firing Rate ◽  
Response Rate ◽  
Saccadic Eye Movements ◽  
Response Variability ◽  
Area V4 ◽  
The Mean ◽  
V4 Neurons ◽  
Saccade Preparation

The visually driven responses of macaque area V4 neurons are modulated during the preparation of saccadic eye movements, but the relationship between presaccadic modulation in area V4 and saccade preparation is poorly understood. Recent neurophysiological studies suggest that the variability across trials of spiking responses provides a more reliable signature of motor preparation than mean firing rate across trials. We compared the dynamics of the response rate and the variability in the rate across trials for area V4 neurons during the preparation of visually guided saccades. As in previous reports, we found that the mean firing rate of V4 neurons was enhanced when saccades were prepared to stimuli within a neuron's receptive field (RF) in comparison with saccades to a non-RF location. Further, we found robust decreases in response variability prior to saccades and found that these decreases predicted saccadic reaction times for saccades both to RF and non-RF stimuli. Importantly, response variability predicted reaction time whether or not there were any accompanying changes in mean firing rate. In addition to predicting saccade direction, the mean firing rate could also predict reaction time, but only for saccades directed to the RF stimuli. These results demonstrate that response variability of area V4 neurons, like mean response rate, provides a signature of saccade preparation. However, the two signatures reflect complementary aspects of that preparation.

scholarly journals Intrinsic Stabilization of Output Rates by Spike-Based Hebbian Learning

2001 ◽  
Vol 13 (12) ◽  
pp. 2709-2741 ◽  
Author(s):  
Richard Kempter ◽  
Wulfram Gerstner ◽  
J. Leo van Hemmen
Keyword(s):  
Firing Rate ◽  
Hebbian Learning ◽  
Piecewise Linear ◽  
Poisson Model ◽  
Intrinsic Rate ◽  
Postsynaptic Neuron ◽  
Temporal Correlations ◽  
Spiking Neuron Model ◽  
The Mean

We study analytically a model of long-term synaptic plasticity where synaptic changes are triggered by presynaptic spikes, postsynaptic spikes, and the time differences between presynaptic and postsynaptic spikes. The changes due to correlated input and output spikes are quantified by means of a learning window. We show that plasticity can lead to an intrinsic stabilization of the mean firing rate of the postsynaptic neuron. Subtractive normalization of the synaptic weights (summed over all presynaptic inputs converging on a postsynaptic neuron) follows if, in addition, the mean input rates and the mean input correlations are identical at all synapses. If the integral over the learning window is positive, firing-rate stabilization requires a non-Hebbian component, whereas such a component is not needed if the integral of the learning window is negative. A negative integral corresponds to anti-Hebbian learning in a model with slowly varying firing rates. For spike-based learning, a strict distinction between Hebbian and anti-Hebbian rules is questionable since learning is driven by correlations on the timescale of the learning window. The correlations between presynaptic and postsynaptic firing are evaluated for a piecewise-linear Poisson model and for a noisy spiking neuron model with refractoriness. While a negative integral over the learning window leads to intrinsic rate stabilization, the positive part of the learning window picks up spatial and temporal correlations in the input.

PARAMETER ESTIMATION ON HURDLE POISSON REGRESSION MODEL WITH CENSORED DATA

2012 ◽  
Vol 57 (1) ◽  
Author(s):  
SEYED EHSAN SAFFAR ◽  
ROBIAH ADNAN ◽  
WILLIAM GREENE
Keyword(s):  
Regression Model ◽  
Count Data ◽  
Poisson Regression ◽  
Goodness Of Fit ◽  
Poisson Model ◽  
Likelihood Method ◽  
Poisson Regression Model ◽  
Response Variable ◽  
The Mean ◽  
Over Dispersion

A Poisson model typically is assumed for count data. In many cases, there are many zeros in the dependent variable and because of these many zeros, the mean and the variance values of the dependent variable are not the same as before. In fact, the variance value of the dependent variable will be much more than the mean value of the dependent variable and this is called over–dispersion. Therefore, Poisson model is not suitable anymore for this kind of data because of too many zeros. Thus, it is suggested to use a hurdle Poisson regression model to overcome over–dispersion problem. Furthermore, the response variable in such cases is censored for some values. In this paper, a censored hurdle Poisson regression model is introduced on count data with many zeros. In this model, we consider a response variable and one or more than one explanatory variables. The estimation of regression parameters using the maximum likelihood method is discussed and the goodness–of–fit for the regression model is examined. We study the effects of right censoring on estimated parameters and their standard errors via an example.

scholarly journals Fano factor and the mean energy per ion pair in counting gases, at low x-ray energies

1997 ◽  
Vol 82 (2) ◽  
pp. 871-877 ◽  
Author(s):  
A. Pansky ◽  
A. Breskin ◽  
R. Chechik
Keyword(s):  
Fano Factor ◽  
Ion Pair ◽  
X Ray ◽  
The Mean ◽  
Low X

A Negative Binomial Regression Model for Accuracy Tests

2012 ◽  
Vol 36 (2) ◽  
pp. 88-103 ◽  
Author(s):  
Lai-Fa Hung
Keyword(s):  
Negative Binomial ◽  
Social Science Research ◽  
Poisson Model ◽  
Negative Binomial Regression ◽  
Science Research ◽  
Likelihood Method ◽  
Estimation Methods ◽  
Negative Binomial Regression Model ◽  
Marginal Maximum Likelihood ◽  
The Mean

Rasch used a Poisson model to analyze errors and speed in reading tests. An important property of the Poisson distribution is that the mean and variance are equal. However, in social science research, it is very common for the variance to be greater than the mean (i.e., the data are overdispersed). This study embeds the Rasch model within an overdispersion framework and proposes new estimation methods. The parameters in the proposed model can be estimated using the Markov chain Monte Carlo method implemented in WinBUGS and the marginal maximum likelihood method implemented in SAS. An empirical example based on models generated by the results of empirical data, which are fitted and discussed, is examined.

scholarly journals The unbiased estimation of r2 between two sets of noisy neural responses

2021 ◽  
Author(s):  
Dean Pospisil ◽  
Wyeth A Bair
Keyword(s):  
Correlation Coefficient ◽  
Pearson Correlation ◽  
Unbiased Estimation ◽  
Pearson Correlation Coefficient ◽  
Neural Responses ◽  
Neural Data ◽  
Tuning Curves ◽  
The Relationship

The Pearson correlation coefficient squared, r2, is often used in the analysis of neural data to estimate the relationship between neural tuning curves. Yet this metric is biased by trial-to-trial variability: as trial-to-trial variability increases, measured correlation decreases. Major lines of research are confounded by this bias, including the study of invariance of neural tuning across conditions and the similarity of tuning across neurons. To address this, we extend the estimator, r̂2ER, developed for estimating model-to-neuron correlation to the neuron-to-neuron case. We compare the estimator to a prior method developed by Spearman, commonly used in other fields but widely overlooked in neuroscience, and find that our method has less bias. We then apply our estimator to the study of two forms of invariance and demonstrate how it avoids drastic confounds introduced by trial-to-trial variability.

scholarly journals A modified fluctuation test for elucidating drug resistance in microbial and cancer cells

2020 ◽  
Author(s):  
Pavol Bokes ◽  
Abhyudai Singh
Keyword(s):  
Drug Resistance ◽  
Cancer Cells ◽  
Colony Size ◽  
Random Number ◽  
Initial Conditions ◽  
Fano Factor ◽  
Persister Cells ◽  
Efficient Treatment ◽  
Fluctuation Test ◽  
The Mean

AbstractClonal populations of microbial and cancer cells are often driven into a drug-tolerant persister state in response to drug therapy, and these persisters can subsequently adapt to the new drug environment via genetic and epigenetic mechanisms. Estimating the frequency with which drug-tolerance states arise, and its transition to drug-resistance, is critical for designing efficient treatment schedules. Here we study a stochastic model of cell proliferation where drug-tolerant persister cells transform into a drug-resistant state with a certain adaptation rate, and the resistant cells can then proliferate in the presence of the drug. Assuming a random number of persisters to begin with, we derive an exact analytical expression for the statistical moments and the distribution of the total cell count (i.e., colony size) over time. Interestingly, for Poisson initial conditions the noise in the colony size (as quantified by the Fano factor) becomes independent of the initial condition and only depends on the adaptation rate. Thus, experimentally quantifying the fluctuations in the colony sizes provides an estimate of the adaptation rate, which then can be used to infer the starting persister numbers from the mean colony size. Overall, our analysis introduces a modification of the classical Luria–Delbrück experiment, also called the “Fluctuation Test”, providing a valuable tool to quantify the emergence of drug resistance in cell populations.

Bayesian Estimation of Stimulus Responses in Poisson Spike Trains

2004 ◽  
Vol 16 (7) ◽  
pp. 1325-1343 ◽  
Author(s):  
Sidney R. Lehky
Keyword(s):  
Bayesian Method ◽  
Significant Degree ◽  
Spike Trains ◽  
Neural Responses ◽  
Interval Estimates ◽  
Poisson Statistics ◽  
Likelihood Functions ◽  
Bayesian Estimates ◽  
Mean And Variance ◽  
The Mean

A Bayesian method is developed for estimating neural responses to stimuli, using likelihood functions incorporating the assumption that spike trains follow either pure Poisson statistics or Poisson statistics with a refractory period. The Bayesian and standard estimates of the mean and variance of responses are similar and asymptotically converge as the size of the data sample increases. However, the Bayesian estimate of the variance of the variance is much lower. This allows the Bayesian method to provide more precise interval estimates of responses. Sensitivity of the Bayesian method to the Poisson assumption was tested by conducting simulations perturbing the Poisson spike trains with noise. This did not affect Bayesian estimates of mean and variance to a significant degree, indicating that the Bayesian method is robust. The Bayesian estimates were less affected by the presence of noise than estimates provided by the standard method.

Processing of form and motion in area 21a of cat visual cortex

1993 ◽  
Vol 10 (1) ◽  
pp. 93-115 ◽  
Author(s):  
B. Dreher ◽  
A. Michalski ◽  
R. H. T. Ho ◽  
C. W. F. Lee ◽  
W. Burke
Keyword(s):  
Spatial Organization ◽  
Receptive Fields ◽  
Direction Selectivity ◽  
Orientation Tuning ◽  
Area 17 ◽  
Horizontal Strip ◽  
Tuning Curves ◽  
Mean Width ◽  
Area 21A ◽  
The Mean

AbstractExtracellular recordings from single neurons have been made from presumed area 21a of the cerebral cortex of the cat, anesthetized with N2O/O2/sodium pentobarbitone mixture. Area 21a contains mainly a representation of a central horizontal strip of contralateral visual field about 5 deg above and below the horizontal meridian.Excitatory discharge fields of area 21a neurons were substantially (or slightly but significantly) larger than those of neurons at corresponding eccentricities in areas 17, 19, or 18, respectively. About 95% of area 21a neurons could be activated through either eye and the input from the ipsilateral eye was commonly dominant. Over 90% and less than 10% of neurons had, respectively, C-type and S-type receptive-field organization. Virtually all neurons were orientation-selective and the mean width at half-height of the orientation tuning curves at 52.9 deg was not significantly different from that of neurons in areas 17 and 18. About 30% of area 21a neurons had preferred orientations within 15 deg of the vertical.The mean direction-selectivity index (32.8%) of area 21a neurons was substantially lower than the indices for neurons in areas 17 or 18. Only a few neurons exhibited moderately strong end-zone inhibition. Area 21a neurons responded poorly to fast-moving stimuli and the mean preferred velocity at about 12.5 deg/s was not significantly different from that for area 17 neurons.Selective pressure block of Y fibers in contralateral optic nerve resulted in a small but significant reduction in the preferred velocities of neurons activated via the Y-blocked eye. By contrast, removal of the Y input did not produce significant changes in the spatial organization of receptive fields (S or C type), the size of the discharge fields, the width of orientation tuning curves, or direction-selectivity indices.Our results are consistent with the idea that area 21a receives its principal excitatory input from area 17 and is involved mainly in form rather than motion analysis.

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