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首页> 外文期刊>Journal of Computational Neuroscience >Integral equation methods for computing likelihoods and their derivatives in the stochastic integrate-and-fire model
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Integral equation methods for computing likelihoods and their derivatives in the stochastic integrate-and-fire model

机译：随机积分解雇模型中计算似然及其导数的积分方程方法

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We recently introduced likelihood-based methods for fitting stochastic integrate-and-fire models to spike train data. The key component of this method involves the likelihood that the model will emit a spike at a given time t. Computing this likelihood is equivalent to computing a Markov first passage time density (the probability that the model voltage crosses threshold for the first time at time t). Here we detail an improved method for computing this likelihood, based on solving a certain integral equation. This integral equation method has several advantages over the techniques discussed in our previous work: in particular, the new method has fewer free parameters and is easily differentiable (for gradient computations). The new method is also easily adaptable for the case in which the model conductance, not just the input current, is time-varying. Finally, we describe how to incorporate large deviations approximations to very small likelihoods.
机译：最近，我们引入了基于似然的方法来拟合随机积分和发射模型，以提高列车数据的利用率。该方法的关键部分涉及模型在给定时间t发出尖峰的可能性。计算该可能性等同于计算马尔可夫第一次通过时间密度（模型电压在时间t首次超过阈值的概率）。在此，我们基于求解某个积分方程，详细介绍了一种用于计算这种可能性的改进方法。与我们先前的工作中讨论的技术相比，该积分方程方法具有多个优点：特别是，新方法具有较少的自由参数，并且易于区分（用于梯度计算）。新方法还很容易适应模型电导（不仅是输入电流）随时间变化的情况。最后，我们描述了如何将大的偏差近似值合并到很小的可能性中。

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