Nonlinear Statistical Learning with Truncated Gaussian Graphical Models
نویسندگان
چکیده
We introduce the truncated Gaussian graphical model (TGGM) as a novel framework for designing statistical models for nonlinear learning. A TGGM is a Gaussian graphical model (GGM) with a subset of variables truncated to be nonnegative. The truncated variables are assumed latent and integrated out to induce a marginal model. We show that the variables in the marginal model are non-Gaussian distributed and their expected relations are nonlinear. We use expectationmaximization to break the inference of the nonlinear model into a sequence of TGGM inference problems, each of which is efficiently solved by using the properties and numerical methods of multivariate Gaussian distributions. We use the TGGM to design models for nonlinear regression and classification, with the performances of these models demonstrated on extensive benchmark datasets and compared to state-of-the-art competing results.
منابع مشابه
Unsupervised Learning with Truncated Gaussian Graphical Models
Gaussian graphical models (GGMs) are widely used for statistical modeling, because of ease of inference and the ubiquitous use of the normal distribution in practical approximations. However, they are also known for their limited modeling abilities, due to the Gaussian assumption. In this paper, we introduce a novel variant of GGMs, which relaxes the Gaussian restriction and yet admits efficien...
متن کاملLearning Brain fMRI Structure Through Sparseness and Local Constancy
1 Objective We propose sparse and locally constant Gaussian graphical models as well as structural equation models for learning the functional connectivity in the whole-brain. fMRI datasets are typically under-sampled and high-dimensional, they often need to be represented with low-complexity statistical models, which are comprised of only the important probabilistic dependencies. Most methods ...
متن کاملLearning Directed Graphical Models from Nonlinear and Non-Gaussian Data Data Analysis Project for Master of Science in Machine Learning
Traditional constraint-based and score-based methods for learning directed graphical models from continuous data have two significant limitations: (i) they require (in practice) assuming dependencies are linear with Gaussian noise; (ii) they cannot distinguish between Markov equivalent structures. More recent structure learning methods avoid both limitations by directly exploiting characteristi...
متن کاملGraphical models via univariate exponential family distributions
Undirected graphical models, or Markov networks, are a popular class of statistical models, used in a wide variety of applications. Popular instances of this class include Gaussian graphical models and Ising models. In many settings, however, it might not be clear which subclass of graphical models to use, particularly for non-Gaussian and non-categorical data. In this paper, we consider a gene...
متن کاملGaussian graphical models and Ising models : modeling networks
There are two ways of exploring a network. The first is a global approach, in which a statistical model is fit on the whole graph. For instance, one can observe that the degree of each node follow a power law distribution, or explore how clusters or cliques form in the network. This approach is not really a graphical model approach, and is not useful in the actionable point of view. The graphic...
متن کامل