{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:34:57Z","timestamp":1760243697871,"version":"build-2065373602"},"reference-count":70,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2022,9,19]],"date-time":"2022-09-19T00:00:00Z","timestamp":1663545600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"European Union\u2019s Horizon 2020 Research And Innovation Programme","award":["694630","1641\/21"],"award-info":[{"award-number":["694630","1641\/21"]}]},{"name":"ISF","award":["694630","1641\/21"],"award-info":[{"award-number":["694630","1641\/21"]}]},{"name":"WIN consortium via the Israel minister of economy and science","award":["694630","1641\/21"],"award-info":[{"award-number":["694630","1641\/21"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>A double-sided variant of the information bottleneck method is considered. Let (X,Y) be a bivariate source characterized by a joint pmf PXY. The problem is to find two independent channels PU|X and PV|Y (setting the Markovian structure U\u2192X\u2192Y\u2192V), that maximize I(U;V) subject to constraints on the relevant mutual information expressions: I(U;X) and I(V;Y). For jointly Gaussian X and Y, we show that Gaussian channels are optimal in the low-SNR regime but not for general SNR. Similarly, it is shown that for a doubly symmetric binary source, binary symmetric channels are optimal when the correlation is low and are suboptimal for high correlations. We conjecture that Z and S channels are optimal when the correlation is 1 (i.e., X=Y) and provide supporting numerical evidence. Furthermore, we present a Blahut\u2013Arimoto type alternating maximization algorithm and demonstrate its performance for a representative setting. This problem is closely related to the domain of biclustering.<\/jats:p>","DOI":"10.3390\/e24091321","type":"journal-article","created":{"date-parts":[[2022,9,19]],"date-time":"2022-09-19T21:47:27Z","timestamp":1663624047000},"page":"1321","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["The Double-Sided Information Bottleneck Function"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0498-273X","authenticated-orcid":false,"given":"Michael","family":"Dikshtein","sequence":"first","affiliation":[{"name":"Department of Electrical and Computer Engineering, Technion, Haifa 3200003, Israel"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5791-7923","authenticated-orcid":false,"given":"Or","family":"Ordentlich","sequence":"additional","affiliation":[{"name":"School of Computer Science and Engineering, The Hebrew University of Jerusalem, Jerusalem 9190401, Israel"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6594-3371","authenticated-orcid":false,"given":"Shlomo","family":"Shamai (Shitz)","sequence":"additional","affiliation":[{"name":"Department of Electrical and Computer Engineering, Technion, Haifa 3200003, Israel"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,9,19]]},"reference":[{"key":"ref_1","unstructured":"Tishby, N., Pereira, F.C.N., and Bialek, W. 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