Learning Non-linear Structures with Gaussian Markov Random Fields

Nowadays, one of the most changeling points in statistics is the analysis of high dimensional data. In such cases, it is commonly assumed that the dimensionality of the data is only artificially high: although each data point is described by thousands of features, it is assumed that it can be modeled as a function of only a few underlying parameters. Formally, it is assumed that the data points are samples from a low-dimensional manifold embedded in a high-dimensional space.