Small-correlation expansions for the inverse Ising problem
By Vitor Sessak, Rémi Monasson. 2008
47 citations recorded by the source corpus.
We present a systematic small-correlation expansion to solve the inverse Ising problem and find a set of couplings and fields corresponding to a given set of correlations and magnetizations. Couplings are calculated up to the third order in the correlations for generic magnetizations and to the seventh order in the case of zero magnetizations; in addition, we show how to sum some useful classes of diagrams exactly. The resulting expansion outperforms existing algorithms on the Sherrington–Kirkpatrick spin-glass model.
Subfields: Condensed Matter Physics, Spectroscopy, Statistical and Nonlinear Physics
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Citations in the corpus
- Direct-coupling analysis of residue coevolution captures native contacts across many protein families (2011, neutral): “f iðAÞ f iðqÞ 1⁄4 exp hiðAÞ þ∑ A ∑ j≠i eijðA;BÞf jðBÞ ; [8]”
- Spin glass models for a network of real neurons (2009, unknown): “First, the simple relation between J ij and C ij predicted by the lowest order of perturbation theory [18, 53] is violated, as shown in Fig 4a, and the resulting errors in the predicted P ( { σ i } ) are significant, as shown in Fig 4b.”
- Fast pseudolikelihood maximization for direct-coupling analysis of protein structure from many homologous amino-acid sequences (2014, methodology): “ld method of [13] and the message-passing method of [14], both discussed below, are in this class, as well as other and more sophisticated methods which have so far not been tested on the PSP problem [15, 16, 17, 18]. The rst attempt to predict spatial proximity by inferred interaction parameters wa”
- Inverse statistical problems: from the inverse Ising problem to data science (2017, methodology): “es generated using the underlying model parameters (on the x-axis) and the same quantities generated using the inferred parameters (y-axis). The Sessak{Monasson expansion was computed as described in [201] with the series in the magnetic elds truncated at the third order excluding the loop terms. Th”