Abstract
The paper presents algorithmical complexity estimates for local posteriori inference in algebraic Bayesian networks. We consider the ways of implementing the inference for three types of evidence (deterministic, stochastic, and imprecise). If we need to solve linear programming tasks for inference, the comlexity estimations are given in numbers of such tasks and numbers of variables and constraints in each task. In other cases, complexity estimates are given in numbers of arithmetic operations.
Highlights
A posteriori inference algorithms provide the way for decision making based on evidence upon uncertainty
that the matrix used in propagation can be represented as tensor product
 ñòàòüå ïðèâåä1⁄4í ïðèìåð, êîòîðûé äåìîíñòðèðóåò, ÷òî â îáùåì ñëó÷àå äëÿ ÔÇ ñ èíòåðâàëüíûìè îöåíêàìè íåâîçìîæíî ïîñòðîèòü òî÷íûå îöåíêè ïðîïàãàöèè ñòîõàñòè÷åñêîãî ñâèäåòåëüñòâà îñòàâàÿñü â ðàìêàõ ÇËÏ è íå íàêëàäûâàÿ äîïîëíèòåëüíûõ îãðàíè÷åíèé
Summary
Ïóñòü çàäàí ÔÇ ñ îöåíêàìè Pc− è Pc+, òîãäà ðåøåíèå ïåðâîé è âòîðîé çàäà÷ àïîñòåðèîðíîãî âûâîäà äëÿ äåòåðìèíèðîâàííîãî ñâèäåòåëüñòâà ìîæíî ïðåäñòàâèòü êàê ðåøåíèå ñåðèè çàäà÷ ëèíåéíîãî ïðîãðàììèðîâàíèÿ. ISSN 2078-9181 (print), ISSN 2078-9599 (online) ðåøåíèåì âòîðîé çàäà÷è àïîñòåðèîðíîãî âûâîäà â ñëó÷àå äåòåðìèíèðîâàííîãî ñâèäåòåëüñòâà è èíòåðâàëüíûõ îöåíîê âî ôðàãìåíòå çíàíèé. Òàê êàê (C , Pca) íåïðîòèâîðå÷èâûé, òî íà îñíîâå îöåíîê âåðîÿòíîñòåé äëÿ êîíúþíêòîâ Pca, ìîæíî ïîñòðîèòü îöåíêè âåðîÿòíîñòåé äëÿ êâàíòîâ QC : Pqa = I × Pca. Ýëåìåíòû ìíîæåñòâà QC ÿâëÿþòñÿ âçàèìîèñêëþ÷àþùèìè, òî åñòü ïðè ëþáîì çàôèêñèðîâàííîì îçíà÷èâàíèè âñåõ àòîìîâ èñòèííûì áóäåò îäèí è òîëüêî îäèí ýëåìåíò ìíîæåñòâà QC .
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