Exponential Families for Conditional Random Fields

By Yasemin Altun, Alex Smola, Thomas Hofmann. 2004

58 citations recorded by the source corpus.

In this paper we define conditional random fields in reproducing kernel Hilbert spaces and show connections to Gaussian Process classification. More specifically, we prove decomposition results for undirected graphical models and we give constructions for kernels. Finally we present efficient means of solving the optimization problem using reduced rank decompositions and we show how stationarity can be exploited efficiently in the optimization process.

Subfields: Artificial Intelligence

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Citations in the corpus

Generative and Latent Mean Map Kernels (2010, methodology): “embeds all probability distributions with the specified conditional independence relations using an exponential family model with kernel v [1].”
A Hilbert Space Embedding for Distributions (2007, background): “In this case [24] show that k(x, x) = ∑”
Hilbert space embeddings of conditional distributions with applications to dynamical systems (2009, methodology): “In the same spirit as the decomposition of sufficient statistics in exponential families (Altun et al., 2004; Zhang et al., 2009), we use the concatenation of the feature map φ(s) and ψ(o) as ω((s, o)); that is ω((s, o)) = (φ(st)>, ψ(ot+1)>)> whose kernel decomposes into the sum of two kernels: 〈ω((”
Cramer-Rao Lower Bound and Information Geometry (2013, background): “Exponential families provide a generic framework in Statistics, and are universal density approximators [2].”
Unifying Divergence Minimization and Statistical Inference Via Convex Duality (2006, methodology): “– For decomposing ψ(t), we obtain various graphical models and conditional random fields as described in [1].”
Kernel Measures of Independence for non-iid Data (2008, background): “In [2], it is shown that for this case the sufficient statistics decompose along the maximal cliques of the conditional independence graph.”
Nomograms for visualizing support vector machines (2005, background): “The kernel (2) is a special case of the kernels proposed by [5, 1, 16].”