Testing Against Independence and a R\'enyi Information Measure
The achievable error-exponent pairs for the type I and type II errors are characterized in a hypothesis testing setup where the observation consists of independent and identically distributed samples from either a known joint probability distribution or an unknown product distribution. The empirical...
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| creator | Lapidoth, Amos Pfister, Christoph |
| description | The achievable error-exponent pairs for the type I and type II errors are
characterized in a hypothesis testing setup where the observation consists of
independent and identically distributed samples from either a known joint
probability distribution or an unknown product distribution. The empirical
mutual information test, the Hoeffding test, and the generalized
likelihood-ratio test are all shown to be asymptotically optimal. An expression
based on a Renyi measure of dependence is shown to be the Fenchel biconjugate
of the error-exponent function obtained by fixing one error exponent and
optimizing the other. An example is provided where the error-exponent function
is not convex and thus not equal to its Fenchel biconjugate. |
| doi_str_mv | 10.48550/arxiv.1805.11059 |
| format | Article |
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characterized in a hypothesis testing setup where the observation consists of
independent and identically distributed samples from either a known joint
probability distribution or an unknown product distribution. The empirical
mutual information test, the Hoeffding test, and the generalized
likelihood-ratio test are all shown to be asymptotically optimal. An expression
based on a Renyi measure of dependence is shown to be the Fenchel biconjugate
of the error-exponent function obtained by fixing one error exponent and
optimizing the other. An example is provided where the error-exponent function
is not convex and thus not equal to its Fenchel biconjugate.</description><identifier>DOI: 10.48550/arxiv.1805.11059</identifier><language>eng</language><subject>Computer Science - Information Theory ; Mathematics - Information Theory</subject><creationdate>2018-05</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,776,881</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/1805.11059$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.1805.11059$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Lapidoth, Amos</creatorcontrib><creatorcontrib>Pfister, Christoph</creatorcontrib><title>Testing Against Independence and a R\'enyi Information Measure</title><description>The achievable error-exponent pairs for the type I and type II errors are
characterized in a hypothesis testing setup where the observation consists of
independent and identically distributed samples from either a known joint
probability distribution or an unknown product distribution. The empirical
mutual information test, the Hoeffding test, and the generalized
likelihood-ratio test are all shown to be asymptotically optimal. An expression
based on a Renyi measure of dependence is shown to be the Fenchel biconjugate
of the error-exponent function obtained by fixing one error exponent and
optimizing the other. An example is provided where the error-exponent function
is not convex and thus not equal to its Fenchel biconjugate.</description><subject>Computer Science - Information Theory</subject><subject>Mathematics - Information Theory</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNpjYJA0NNAzsTA1NdBPLKrILNMztDAw1TM0NDC15GSwC0ktLsnMS1dwTE_MzCsuUfDMS0ktSAUSecmpCol5KQqJCkEx6ql5lZlAqbT8otzEksz8PAXf1MTi0qJUHgbWtMSc4lReKM3NIO_mGuLsoQu2Kb6gKDM3sagyHmRjPNhGY8IqAEcsNYk</recordid><startdate>20180528</startdate><enddate>20180528</enddate><creator>Lapidoth, Amos</creator><creator>Pfister, Christoph</creator><scope>AKY</scope><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20180528</creationdate><title>Testing Against Independence and a R\'enyi Information Measure</title><author>Lapidoth, Amos ; Pfister, Christoph</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-arxiv_primary_1805_110593</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><topic>Computer Science - Information Theory</topic><topic>Mathematics - Information Theory</topic><toplevel>online_resources</toplevel><creatorcontrib>Lapidoth, Amos</creatorcontrib><creatorcontrib>Pfister, Christoph</creatorcontrib><collection>arXiv Computer Science</collection><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Lapidoth, Amos</au><au>Pfister, Christoph</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Testing Against Independence and a R\'enyi Information Measure</atitle><date>2018-05-28</date><risdate>2018</risdate><abstract>The achievable error-exponent pairs for the type I and type II errors are
characterized in a hypothesis testing setup where the observation consists of
independent and identically distributed samples from either a known joint
probability distribution or an unknown product distribution. The empirical
mutual information test, the Hoeffding test, and the generalized
likelihood-ratio test are all shown to be asymptotically optimal. An expression
based on a Renyi measure of dependence is shown to be the Fenchel biconjugate
of the error-exponent function obtained by fixing one error exponent and
optimizing the other. An example is provided where the error-exponent function
is not convex and thus not equal to its Fenchel biconjugate.</abstract><doi>10.48550/arxiv.1805.11059</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Computer Science - Information Theory Mathematics - Information Theory |
| title | Testing Against Independence and a R\'enyi Information Measure |
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