Efficient Learning in Boltzmann Machines Using Linear Response Theory

By Hilbert J. Kappen, Francisco de Borja Rodríguez Ortiz. 1998

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Citations in the corpus

Protein 3D Structure Computed from Evolutionary Sequence Variation (2011, background): “A partial analogy can be drawn to the inverse Ising or Potts problem, in which heterogeneous local couplings between discrete state variables are derived from measurements of twopoint correlation functions [34,35,36,37,38].”
Bayesian reasoning and machine learning (2012, unknown): “The linearresponse method[153] may also be used, based on a perturbation expansion of the free energy.”
Consistency of Pseudolikelihood Estimation of Fully Visible Boltzmann Machines (2006, methodology): “Different kinds of approximation methods have therefore been developed, including pseudolikelihood (Besag, 1975), contrastive divergence (Hinton, 2002), and linear response theory (Kappen & Rodriguez, 1998).”
The Nonnegative Boltzmann Machine (1999, background): “Mean field approximations have previously been proposed as a deterministic alternative for learning in the binary Boltzmann machine, although there have been contrasting views on their validity [5, 6].”
A New Learning Algorithm for Mean Field Boltzmann Machines (2002, methodology): “Extensions of MFBM learning rules have been put forward, such as linear response corrections ( Kappen & Rodriquez, 1998 ) and TAP corrections (Galland, 1993).”
3D Protein Structure Predicted from Sequence (2011, unknown): “A partial analogy can be drawn to the inverse Ising or Potts problem, in which heterogeneous local couplings between discrete state variables are derived from measurements of two-‐point correlation func”
Linear Response Methods for Accurate Covariance Estimates from Mean Field Variational Bayes (2015, methodology): “These methods have been applied to find new learning algorithms for Boltzmann machines [13], covariance estimates for discrete factor graphs [14], and independent component analysis [15].”