Schwartz Odelia, Sejnowski Terrence J, Dayan Peter
Howard Hughes Medical Institute, Computational Neurobiology Lab, Salk Institute for Biological Studies, La Jolla, CA 92037, USA.
Neural Comput. 2006 Nov;18(11):2680-718. doi: 10.1162/neco.2006.18.11.2680.
Gaussian scale mixture models offer a top-down description of signal generation that captures key bottom-up statistical characteristics of filter responses to images. However, the pattern of dependence among the filters for this class of models is prespecified. We propose a novel extension to the gaussian scale mixture model that learns the pattern of dependence from observed inputs and thereby induces a hierarchical representation of these inputs. Specifically, we propose that inputs are generated by gaussian variables (modeling local filter structure), multiplied by a mixer variable that is assigned probabilistically to each input from a set of possible mixers. We demonstrate inference of both components of the generative model, for synthesized data and for different classes of natural images, such as a generic ensemble and faces. For natural images, the mixer variable assignments show invariances resembling those of complex cells in visual cortex; the statistics of the gaussian components of the model are in accord with the outputs of divisive normalization models. We also show how our model helps interrelate a wide range of models of image statistics and cortical processing.
高斯尺度混合模型提供了一种自上而下的信号生成描述，它捕捉了滤波器对图像响应的关键自下而上的统计特征。然而，这类模型中滤波器之间的依赖模式是预先设定的。我们提出了一种对高斯尺度混合模型的新颖扩展，它从观察到的输入中学习依赖模式，从而诱导出这些输入的层次表示。具体来说，我们提出输入由高斯变量（对局部滤波器结构进行建模）生成，再乘以一个混合变量，该混合变量从一组可能的混合器中概率性地分配给每个输入。我们展示了生成模型的两个组件对于合成数据以及不同类别的自然图像（如通用集合和人脸）的推断。对于自然图像，混合变量分配显示出类似于视觉皮层中复杂细胞的不变性；模型高斯组件的统计数据与分离归一化模型的输出一致。我们还展示了我们的模型如何帮助将广泛的图像统计模型和皮层处理模型相互联系起来。
