TY - JOUR
T1 - Adaptive Thouless-Anderson-Palmer equation for higher-order Markov random fields
AU - Takahashi, Chako
AU - Yasuda, Muneki
AU - Tanaka, Kazuyuki
N1 - Funding Information:
The authors would like to thank Shun Kataoka and Yuya Seki for their insightful comments and suggestions. The authors were supported by CREST, Japan Science and Technology Agency Grant (No. JPMJCR1402). One of the authors (C.T.) was partially supported by a Grant-in-Aid for JSPS Fellows from the Japan Society for the Promotion of Science Grant (No. JP17J03081). One of the authors (M.Y.) was partially supported by a Grant-in-Aid for Scientific Research from the Japan Society for the Promotion of Science Grant (Nos. 15K00330, 15H03699, 18K11459, and 18H03303). One of the authors (K.T.) was partially supported by a Grant-in-Aid for Scientific Research from the Japan Society for the Promotion of Science Grant (No. 18H03303).
Funding Information:
Acknowledgments The authors would like to thank Shun Kataoka and Yuya Seki for their insightful comments and suggestions. The authors were supported by CREST, Japan Science and Technology Agency Grant (No. JPMJCR1402). One of the authors (C.T.) was partially supported by a Grant-in-Aid for JSPS Fellows from the Japan Society for the Promotion of Science Grant (No. JP17J03081). One of the authors (M.Y.) was partially supported by a Grant-in-Aid for Scientific Research from the Japan Society for the Promotion of Science Grant (Nos. 15K00330, 15H03699, 18K11459, and 18H03303). One of the authors (K.T.) was partially supported by a Grant-in-Aid for Scientific Research from the Japan Society for the Promotion of Science Grant (No. 18H03303).
Publisher Copyright:
© 2020 The Author(s).
PY - 2020/6
Y1 - 2020/6
N2 - The adaptive Thouless-Anderson-Palmer (TAP) mean-field approximation is one of the advanced mean-field approaches, and it is known as a powerful accurate method for Markov random fields (MRFs) with quadratic interactions (pairwise MRFs). In this study, an extension of the adaptive TAP approximation for MRFs with many-body interactions (higher-order MRFs) is developed. We show that the adaptive TAP equation for pairwise MRFs is derived by naive mean-field approximation with diagonal consistency. Based on the equivalence of the approximate equation obtained from the naive mean-field approximation with diagonal consistency and the adaptive TAP equation in pairwise MRFs, we formulate approximate equations for higher-order Boltzmann machines, which is one of simplest higher-order MRFs, via the naive mean-field approximation with diagonal consistency.
AB - The adaptive Thouless-Anderson-Palmer (TAP) mean-field approximation is one of the advanced mean-field approaches, and it is known as a powerful accurate method for Markov random fields (MRFs) with quadratic interactions (pairwise MRFs). In this study, an extension of the adaptive TAP approximation for MRFs with many-body interactions (higher-order MRFs) is developed. We show that the adaptive TAP equation for pairwise MRFs is derived by naive mean-field approximation with diagonal consistency. Based on the equivalence of the approximate equation obtained from the naive mean-field approximation with diagonal consistency and the adaptive TAP equation in pairwise MRFs, we formulate approximate equations for higher-order Boltzmann machines, which is one of simplest higher-order MRFs, via the naive mean-field approximation with diagonal consistency.
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U2 - 10.7566/JPSJ.89.064007
DO - 10.7566/JPSJ.89.064007
M3 - Article
AN - SCOPUS:85090594952
VL - 89
JO - Journal of the Physical Society of Japan
JF - Journal of the Physical Society of Japan
SN - 0031-9015
IS - 6
M1 - 064007
ER -