507 research outputs found
The MVGC multivariate Granger causality toolbox: a new approach to Granger-causal inference
Background: Wiener-Granger causality (“G-causality”) is a statistical notion of causality applicable to time series data, whereby cause precedes, and helps predict, effect. It is defined in both time and frequency domains, and allows for the conditioning out of common causal influences. Originally developed in the context of econometric theory, it has since achieved broad application in the neurosciences and beyond. Prediction in the G-causality formalism is based on VAR (Vector AutoRegressive) modelling.
New Method: The MVGC Matlab c Toolbox approach to G-causal inference is based on multiple equivalent representations of a VAR model by (i) regression parameters, (ii) the autocovariance sequence and (iii) the cross-power spectral density of the underlying process. It features a variety of algorithms for moving between these representations, enabling selection of the most suitable algorithms with regard to computational efficiency and numerical accuracy.
Results: In this paper we explain the theoretical basis, computational strategy and application to empirical G-causal inference of the MVGC Toolbox. We also show via numerical simulations the advantages of our Toolbox over previous methods in terms of computational accuracy and statistical inference.
Comparison with Existing Method(s): The standard method of computing G-causality involves estimation of parameters for both a full and a nested (reduced) VAR model. The MVGC approach, by contrast, avoids explicit estimation of the reduced model, thus eliminating a source of estimation error and improving statistical power, and in addition facilitates fast and accurate estimation of the computationally awkward case of conditional G-causality in the frequency domain.
Conclusions: The MVGC Toolbox implements a flexible, powerful and efficient approach to G-causal inference.
Keywords: Granger causality, vector autoregressive modelling, time series analysi
FaDIn: Fast Discretized Inference for Hawkes Processes with General Parametric Kernels
Temporal point processes (TPP) are a natural tool for modeling event-based
data. Among all TPP models, Hawkes processes have proven to be the most widely
used, mainly due to their simplicity and computational ease when considering
exponential or non-parametric kernels. Although non-parametric kernels are an
option, such models require large datasets. While exponential kernels are more
data efficient and relevant for certain applications where events immediately
trigger more events, they are ill-suited for applications where latencies need
to be estimated, such as in neuroscience. This work aims to offer an efficient
solution to TPP inference using general parametric kernels with finite support.
The developed solution consists of a fast L2 gradient-based solver leveraging a
discretized version of the events. After supporting the use of discretization
theoretically, the statistical and computational efficiency of the novel
approach is demonstrated through various numerical experiments. Finally, the
effectiveness of the method is evaluated by modeling the occurrence of
stimuli-induced patterns from brain signals recorded with
magnetoencephalography (MEG). Given the use of general parametric kernels,
results show that the proposed approach leads to a more plausible estimation of
pattern latency compared to the state-of-the-art
A Semiparametric Bayesian Model for Detecting Synchrony Among Multiple Neurons
We propose a scalable semiparametric Bayesian model to capture dependencies
among multiple neurons by detecting their co-firing (possibly with some lag
time) patterns over time. After discretizing time so there is at most one spike
at each interval, the resulting sequence of 1's (spike) and 0's (silence) for
each neuron is modeled using the logistic function of a continuous latent
variable with a Gaussian process prior. For multiple neurons, the corresponding
marginal distributions are coupled to their joint probability distribution
using a parametric copula model. The advantages of our approach are as follows:
the nonparametric component (i.e., the Gaussian process model) provides a
flexible framework for modeling the underlying firing rates; the parametric
component (i.e., the copula model) allows us to make inference regarding both
contemporaneous and lagged relationships among neurons; using the copula model,
we construct multivariate probabilistic models by separating the modeling of
univariate marginal distributions from the modeling of dependence structure
among variables; our method is easy to implement using a computationally
efficient sampling algorithm that can be easily extended to high dimensional
problems. Using simulated data, we show that our approach could correctly
capture temporal dependencies in firing rates and identify synchronous neurons.
We also apply our model to spike train data obtained from prefrontal cortical
areas in rat's brain
Statistical Inference for Assessing Functional Connectivity of Neuronal Ensembles With Sparse Spiking Data
The ability to accurately infer functional connectivity between ensemble neurons using experimentally acquired spike train data is currently an important research objective in computational neuroscience. Point process generalized linear models and maximum likelihood estimation have been proposed as effective methods for the identification of spiking dependency between neurons. However, unfavorable experimental conditions occasionally results in insufficient data collection due to factors such as low neuronal firing rates or brief recording periods, and in these cases, the standard maximum likelihood estimate becomes unreliable. The present studies compares the performance of different statistical inference procedures when applied to the estimation of functional connectivity in neuronal assemblies with sparse spiking data. Four inference methods were compared: maximum likelihood estimation, penalized maximum likelihood estimation, using either l2 or l1 regularization, and hierarchical Bayesian estimation based on a variational Bayes algorithm. Algorithmic performances were compared using well-established goodness-of-fit measures in benchmark simulation studies, and the hierarchical Bayesian approach performed favorably when compared with the other algorithms, and this approach was then successfully applied to real spiking data recorded from the cat motor cortex. The identification of spiking dependencies in physiologically acquired data was encouraging, since their sparse nature would have previously precluded them from successful analysis using traditional methods.National Institutes of Health (U.S.) (Grant DP1-OD003646)National Institutes of Health (U.S.) (Grant Grant R01-DA015644)National Institutes of Health (U.S.) (Grant Grant R01-HL08450
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