最大信息维度：分析对自然信号的神经反应
Maximally informative dimensions: Analyzing neural responses to natural signals
摘要：
我们提出了一种方法，将允许对自然刺激，这是非高斯和表现出很强的相关性的神经反应进行严格的统计分析。我们想到了一个模型，在这个模型中，神经元对高维刺激空间中的少量刺激维度具有选择性，但在这个子空间内，响应可以是任意非线性的。现有的分析方法是基于刺激和响应之间的关联函数，但这些方法只能保证在高斯刺激集成的情况下工作。作为替代关联函数，我们最大限度地提高神经反应和低维子空间上的刺激的投影之间的互信息。该过程可以通过增加该子空间的维数来迭代地完成。那些允许恢复尖峰和完整的未投射刺激之间的所有信息的维度描述了相关的子空间。如果相关子空间的维数确实很小，即使在完全自然的刺激条件下，也可以映射出神经元的输入-输出函数。这些想法在模拟模型视觉神经元对自然场景的反应中得到了说明。
英文摘要：
We propose a method that would allow for a rigorous statistical analysis of neural responses to natural stimuli, which are non-Gaussian and exhibit strong correlations. We have in mind a model in which neurons are selective for a small number of stimulus dimensions out of the high dimensional stimulus space, but within this subspace the responses can be arbitrarily nonlinear. Existing analysis methods are based on correlation functions between stimuli and responses, but these methods are guaranteed to work only in the case of Gaussian stimulus ensembles. As an alternative to correlation functions, we maximize the mutual information between the neural responses and projections of the stimulus onto low dimensional subspaces. The procedure can be done iteratively by increasing the dimensionality of this subspace. Those dimensions that allow the recovery of all of the information between spikes and the full unprojected stimuli describe the relevant subspace. If the dimensionality of the relevant subspace indeed is small, it becomes feasible to map out the neuron's input-output function even under fully natural stimulus conditions. These ideas are illustrated in simulations on model visual neurons responding to natural scenes.
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