Exponential Families for Conditional Random Fields

Conditional Random Fields via Univariate Exponential Families

Conditional random fields, which model the distribution of a multivariate response conditioned on a set of covariates using undirected graphs, are widely used in a variety of multivariate prediction applications. Popular instances of this class of models, such as categorical-discrete CRFs, Ising CRFs, and conditional Gaussian based CRFs, are not well suited to the varied types of response varia...

Vector-Space Markov Random Fields via Exponential Families

We present Vector-Space Markov Random Fields (VS-MRFs), a novel class of undirected graphical models where each variable can belong to an arbitrary vector space. VS-MRFs generalize a recent line of work on scalar-valued, uni-parameter exponential family and mixed graphical models, thereby greatly broadening the class of exponential families available (e.g., allowing multinomial and Dirichlet di...

Conditional Random Fields for Airborne Lidar Point Cloud Classification in Urban Area

Over the past decades, urban growth has been known as a worldwide phenomenon that includes widening process and expanding pattern. While the cities are changing rapidly, their quantitative analysis as well as decision making in urban planning can benefit from two-dimensional (2D) and three-dimensional (3D) digital models. The recent developments in imaging and non-imaging sensor technologies, s...

Some New Characterization Results on Exponential and Related Distributions

Mixed Graphical Models via Exponential Families

Markov Random Fields, or undirected graphical models are widely used to model highdimensional multivariate data. Classical instances of these models, such as Gaussian Graphical and Ising Models, as well as recent extensions (Yang et al., 2012) to graphical models specified by univariate exponential families, assume all variables arise from the same distribution. Complex data from high-throughpu...