The Double-Sided Information Bottleneck Function
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→X→Y→V), that maximize I(U;V) subject to constraints on the rel...
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| Published in | Entropy (Basel, Switzerland) Vol. 24; no. 9; p. 1321 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
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01.09.2022
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| Online Access | Get full text |
| ISSN | 1099-4300 1099-4300 |
| DOI | 10.3390/e24091321 |
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| Abstract | 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→X→Y→V), 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–Arimoto type alternating maximization algorithm and demonstrate its performance for a representative setting. This problem is closely related to the domain of biclustering. |
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| AbstractList | 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→X→Y→V), 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–Arimoto type alternating maximization algorithm and demonstrate its performance for a representative setting. This problem is closely related to the domain of biclustering. A double-sided variant of the information bottleneck method is considered. Let ( X , Y ) be a bivariate source characterized by a joint pmf P X Y . The problem is to find two independent channels P U | X and P V | Y (setting the Markovian structure U → X → Y → V ), 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–Arimoto type alternating maximization algorithm and demonstrate its performance for a representative setting. This problem is closely related to the domain of biclustering. A double-sided variant of the information bottleneck method is considered. Let (X,Y) be a bivariate source characterized by a joint pmf P[sub.XY]. The problem is to find two independent channels P[sub.U|X] and P[sub.V|Y] (setting the Markovian structure U→X→Y→V), 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–Arimoto type alternating maximization algorithm and demonstrate its performance for a representative setting. This problem is closely related to the domain of biclustering. 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→X→Y→V), 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-Arimoto type alternating maximization algorithm and demonstrate its performance for a representative setting. This problem is closely related to the domain of biclustering.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→X→Y→V), 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-Arimoto type alternating maximization algorithm and demonstrate its performance for a representative setting. This problem is closely related to the domain of biclustering. |
| Audience | Academic |
| Author | Ordentlich, Or Dikshtein, Michael Shamai (Shitz), Shlomo |
| AuthorAffiliation | 1 Department of Electrical and Computer Engineering, Technion, Haifa 3200003, Israel 2 School of Computer Science and Engineering, The Hebrew University of Jerusalem, Jerusalem 9190401, Israel |
| AuthorAffiliation_xml | – name: 1 Department of Electrical and Computer Engineering, Technion, Haifa 3200003, Israel – name: 2 School of Computer Science and Engineering, The Hebrew University of Jerusalem, Jerusalem 9190401, Israel |
| Author_xml | – sequence: 1 givenname: Michael orcidid: 0000-0002-0498-273X surname: Dikshtein fullname: Dikshtein, Michael – sequence: 2 givenname: Or orcidid: 0000-0002-5791-7923 surname: Ordentlich fullname: Ordentlich, Or – sequence: 3 givenname: Shlomo orcidid: 0000-0002-6594-3371 surname: Shamai (Shitz) fullname: Shamai (Shitz), Shlomo |
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| Snippet | 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... A double-sided variant of the information bottleneck method is considered. Let (X,Y) be a bivariate source characterized by a joint pmf P[sub.XY]. The problem... A double-sided variant of the information bottleneck method is considered. Let ( X , Y ) be a bivariate source characterized by a joint pmf P X Y . The problem... |
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| SubjectTerms | Algorithms biclustering Bivariate analysis Channels Clustering Codes Correlation Data compression Gene expression Hypothesis testing information bottleneck Information sources lossy compression Optimization Pattern recognition Random variables remote source coding |
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| Title | The Double-Sided Information Bottleneck Function |
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