成对最大熵模型及其Glauber动力学：双峰、双稳、非遍历问题及其抑制消除
Pairwise maximum-entropy models and their Glauber dynamics: bimodality, bistability, non-ergodicity problems, and their elimination via inhibition
摘要：
在最近的神经科学文献中，已经使用成对最大熵模型来预测神经元群体的活动，仅给出神经元活动的时间平均相关性。本文提供的证据表明，成对模型，应用于实验记录，预测双峰分布的人口平均活动，并为一些人口规模的第二模式峰值在高活动，与90%的神经元人口活跃的时间窗口内的几毫秒。这种双峰性有几个不良后果：1。鉴于观察到的神经元活动，两种模式的存在是不现实的。2.从神经生物学的角度来看，对高活动模式的预测是不现实的。3.玻尔兹曼学习变得非遍历，因此通过这种方法找到的成对模型不是最大熵分布;类似地，通过平均场近似的常见变体解决逆问题也有同样的问题。4.与模型相关的Glauber动力学要么是不切实际的，要么不反映成对模型的分布。这种双峰性首先证明了一个实验数据集，包括159个神经元的活动记录从猕猴的运动皮层。使用一个减少的最大熵模型，然后提供证据表明，这种双峰影响典型的神经记录的人口规模的几百个或更多的神经元。作为一种方法来消除双峰及其随之而来的问题，提出了一种修改的成对模型，其中-最重要的-有一个相关的成对Glauber动力学。由于最小的不对称抑制，该模型避免了双峰性。它可以被解释为具有特定先验的最小相对熵模型，或具有附加约束的最大熵模型。
英文摘要：
Pairwise maximum-entropy models have been used in recent neuroscientific literature to predict the activity of neuronal populations, given only the time-averaged correlations of the neuron activities. This paper provides evidence that the pairwise model, applied to experimental recordings, predicts a bimodal distribution for the population-averaged activity, and for some population sizes the second mode peaks at high activities, with 90% of the neuron population active within time-windows of few milliseconds. This bimodality has several undesirable consequences: 1. The presence of two modes is unrealistic in view of observed neuronal activity. 2. The prediction of a high-activity mode is unrealistic on neurobiological grounds. 3. Boltzmann learning becomes non-ergodic, hence the pairwise model found by this method is not the maximum entropy distribution; similarly, solving the inverse problem by common variants of mean-field approximations has the same problem. 4. The Glauber dynamics associated with the model is either unrealistically bistable, or does not reflect the distribution of the pairwise model. This bimodality is first demonstrated for an experimental dataset comprising 159 neuron activities recorded from the motor cortex of macaque monkey. Using a reduced maximum-entropy model, evidence is then provided that this bimodality affects typical neural recordings of population sizes of a couple of hundreds or more neurons. As a way to eliminate the bimodality and its ensuing problems, a modified pairwise model is presented, which -- most important -- has an associated pairwise Glauber dynamics. This model avoids bimodality thanks to a minimal asymmetric inhibition. It can be interpreted as a minimum-relative-entropy model with a particular prior, or as a maximum-entropy model with an additional constraint.
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