Kavli Institute for Systems Neuroscience, Faculty of Medicine and Health Sciences, Norwegian University of Science and Technology, Trondheim, Norway.
Department of Mathematics, King's College London, London, United Kingdom.
PLoS Comput Biol. 2024 May 2;20(5):e1012074. doi: 10.1371/journal.pcbi.1012074. eCollection 2024 May.
We investigate the ability of the pairwise maximum entropy (PME) model to describe the spiking activity of large populations of neurons recorded from the visual, auditory, motor, and somatosensory cortices. To quantify this performance, we use (1) Kullback-Leibler (KL) divergences, (2) the extent to which the pairwise model predicts third-order correlations, and (3) its ability to predict the probability that multiple neurons are simultaneously active. We compare these with the performance of a model with independent neurons and study the relationship between the different performance measures, while varying the population size, mean firing rate of the chosen population, and the bin size used for binarizing the data. We confirm the previously reported excellent performance of the PME model for small population sizes N < 20. But we also find that larger mean firing rates and bin sizes generally decreases performance. The performance for larger populations were generally not as good. For large populations, pairwise models may be good in terms of predicting third-order correlations and the probability of multiple neurons being active, but still significantly worse than small populations in terms of their improvement over the independent model in KL-divergence. We show that these results are independent of the cortical area and of whether approximate methods or Boltzmann learning are used for inferring the pairwise couplings. We compared the scaling of the inferred couplings with N and find it to be well explained by the Sherrington-Kirkpatrick (SK) model, whose strong coupling regime shows a complex phase with many metastable states. We find that, up to the maximum population size studied here, the fitted PME model remains outside its complex phase. However, the standard deviation of the couplings compared to their mean increases, and the model gets closer to the boundary of the complex phase as the population size grows.
我们研究了成对最大熵（PME）模型描述从视觉、听觉、运动和躯体感觉皮层记录的大神经元群体的尖峰活动的能力。为了量化这种性能，我们使用（1）Kullback-Leibler（KL）散度，（2）对三阶相关进行预测的程度，以及（3）预测多个神经元同时活动的概率的能力。我们将这些与具有独立神经元的模型的性能进行了比较，并研究了不同性能指标之间的关系，同时改变了群体大小、所选群体的平均放电率以及用于将数据二值化的 bin 大小。我们证实了 PME 模型在小群体大小 N < 20 时的优异性能。但我们也发现，较大的平均放电率和 bin 大小通常会降低性能。较大的群体的性能通常不太好。对于大群体，成对模型可能在预测三阶相关和多个神经元活动的概率方面表现良好，但在 KL 散度方面，它们在改进独立模型方面的性能仍明显逊于小群体。我们表明，这些结果与皮质区域无关，也与推断成对耦合时使用近似方法还是 Boltzmann 学习无关。我们比较了推断出的耦合与 N 的缩放，并发现它与 Sherrington-Kirkpatrick（SK）模型很好地吻合，后者的强耦合状态显示出具有许多亚稳态的复杂相。我们发现，直到研究中最大的群体规模，拟合的 PME 模型仍然在其复杂相之外。然而，与平均值相比，耦合的标准差增加，并且随着群体规模的增长，模型越来越接近复杂相的边界。
