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  • Navrhujeme nový součtový rozklad pravděpodobnostních tabulek - rozklad na tenzory ranku jedna. Základní myšlenka je, rozložit pravděpodobnostní tabulku na posloupnost tabulek, jejichž součet je roven původní tabulce. Každá z tabulek v posloupnosti má stejný obor indexů jako původní tabulka, ale je vyjádřitelná jako součin jednorozměrných tabulek. Prvky tabulek mohou být libovolná reálná čísla, tedy i čísla záporná. Ukazujeme, že rozklad na tenzory ranku jedna může být použit pro zmenšení prostorové a časové složitosti pravděpodobnostní inference. Článek prezentuje explicitní vyjádření minimálního rozkladu některých speciálních tabulek a navrhuje numerickou metodu řešení v případě, že explicitní rozklad není znám. (cs)
  • We propose a new additive decomposition of probability tables - tensor rank-one decomposition. The basic idea is to decompose a probability table into a series of tables, such that the table that is the sum of the series is equal to the original table. Each table in the series has the same domain as the original table but can be expressed as a product of one-dimensional tables. Entries in tables are allowed to be any real number, i.e. they can be also negative numbers. The possibility of having negative numbers, in contrast to a multiplicative decomposition, opens new possibilities for a compact representation of probability tables. We show that tensor rank-one decomposition can be used to reduce the space and time requirements in probabilistic inference. We provide a closed form solution for minimal tensor rank-one decomposition for some special tables and propose a numerical algorithm that can be used in cases when the closed form solution is not known.
  • We propose a new additive decomposition of probability tables - tensor rank-one decomposition. The basic idea is to decompose a probability table into a series of tables, such that the table that is the sum of the series is equal to the original table. Each table in the series has the same domain as the original table but can be expressed as a product of one-dimensional tables. Entries in tables are allowed to be any real number, i.e. they can be also negative numbers. The possibility of having negative numbers, in contrast to a multiplicative decomposition, opens new possibilities for a compact representation of probability tables. We show that tensor rank-one decomposition can be used to reduce the space and time requirements in probabilistic inference. We provide a closed form solution for minimal tensor rank-one decomposition for some special tables and propose a numerical algorithm that can be used in cases when the closed form solution is not known. (en)
Title
  • Exploiting Tensor Rank-One Decomposition in Probabilistic Inference
  • Exploiting Tensor Rank-One Decomposition in Probabilistic Inference (en)
  • Využití rozkladu tenzoru na tenzory ranku jedna pro pravděpodobnostní inferenci (cs)
skos:prefLabel
  • Exploiting Tensor Rank-One Decomposition in Probabilistic Inference
  • Exploiting Tensor Rank-One Decomposition in Probabilistic Inference (en)
  • Využití rozkladu tenzoru na tenzory ranku jedna pro pravděpodobnostní inferenci (cs)
skos:notation
  • RIV/67985556:_____/07:00047082!RIV08-AV0-67985556
http://linked.open.../vavai/riv/strany
  • 747;764
http://linked.open...avai/riv/aktivita
http://linked.open...avai/riv/aktivity
  • P(1M0545), P(1M0572), P(GA201/04/0393), Z(AV0Z10300504), Z(AV0Z10750506)
http://linked.open...iv/cisloPeriodika
  • 5
http://linked.open...vai/riv/dodaniDat
http://linked.open...aciTvurceVysledku
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http://linked.open...iv/duvernostUdaju
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  • 421342
http://linked.open...ai/riv/idVysledku
  • RIV/67985556:_____/07:00047082
http://linked.open...riv/jazykVysledku
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  • graphical probabilistic models; probabilistic inference; tensor rank (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...odStatuVydavatele
  • CZ - Česká republika
http://linked.open...ontrolniKodProRIV
  • [34D64C2AFC11]
http://linked.open...i/riv/nazevZdroje
  • Kybernetika
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http://linked.open...UplatneniVysledku
http://linked.open...v/svazekPeriodika
  • 43
http://linked.open...iv/tvurceVysledku
  • Vomlel, Jiří
  • Savický, Petr
http://linked.open...n/vavai/riv/zamer
issn
  • 0023-5954
number of pages
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