Construction and evaluation of non-Gaussian spatio-temporal models through the use of gradient maps

对于时间和空间函数形式的数据，我们提出了一个统计模型来提取数据背后的复杂结构。我们使用梯度映射作为一个特殊的变换。特别地，我们应用了稀疏估计方法，这是最近在机器学习理论中开发的方法的类比。此外，我们将我们的模型推广到定向数据。我们还从估计损失的角度阐明了我们的模型的理论优点。

For data in the form of function of time and space, we proposed a statistical model to extract complex structures behind the data. We used the gradient map as a special transformation. In particular, we apply a sparse estimation method, which is an analogy of recently developed methodology in machine learning theory. Furthermore, we generalize our models to those of directional data. We also clarify a theoretical merit of our models from the viewpoint of loss of estimation.