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Author:Beaver, Harriet
Title:Using Rule-based Constraint Programming to Find MAPs for Bayesian Networks
Bayes-verkon MAP-ongelman ratkaisu sääntöpohjaisella rajoiteohjelmoinnilla
Publication type:Master's thesis
Publication year:2004
Pages:49      Language:   eng
Department/School:Teknillisen fysiikan ja matematiikan osasto
Main subject:Tietojenkäsittelyteoria   (T-119)
Supervisor:Niemelä, Ilkka
Instructor:
OEVS:
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Location:P1 Ark Aalto     | Archive
Keywords:Bayesian networks
MAP problem
constraint programming
stable models
Smodels
Bayes-verkot
MAP-ongelma
rajoiteohjelmointi
stabiilit mallit
Abstract (eng): In recent years Bayesian belief networks have assumed increasing practical importance in many fields from medical diagnosis to pattern recognition, providing a formal mathematical framework for probabilistic reasoning.
In the maximum a posteriori (MAP) assignment problem on a given Bayesian belief network and some observed evidence, the objective is to find the network assignment with the highest conditional probability, given the evidence.

In this MSc thesis I investigate the possibility of solving MAP problems using Smodels, an efficient rule-based constraint programming system based on logic programs with stable model semantics.
I develop four different methods to translate MAP problems to logic programs so that the solutions to a particular MAP problem correspond to optimal stable models of its logic program translations.

For comparison with a more traditional method, I also translate the MAP problem to integer linear programming.
The comparison of the computational efficiency of these different methods suggests that for most problems integer linear programming performs better than any of the four logic program translations.

However, the optimal method depends on the type of the problem.
Smodels can be expected to perform better in a situation in which only some of the variables are of a probabilistic nature, and could offer an interesting framework for situations in which probabilistic knowledge is combined with symbolic constraints.
Abstract (fin): Bayes-verkot tarjoavat formaalin matemaattisen keinon probabilistiseen päättelyyn.
Jatkuvasti kasvavan kiinnostuksen myötä niiden käytännön merkitys on jo varsin laaja kattaen aloja lääketieteestä hahmontunnistukseen.
MAP-ongelmassa annettuna on Bayes-verkko sekä joitain verkon tilasta tehtyjä havaintoja.
Tarkoituksena on löytää todennäköisin mahdollinen verkon tila.
Tässä diplomityössä tutkin MAP-ongelman ratkaisua Smodels-järjestelmää käyttäen.
Smodels on sääntöpohjaisen rajoiteohjelmoinnin järjestelmä, joka perustuu stabiilien mallien semantiikkaa toteuttaviin logiikkaohjelmiin.

Kehitän neljä eri tapaa kääntää MAP-ongelmia logiikkaohjelmiksi siten, että logiikkaohjelmien optimaaliset stabiilit mallit vastaavat MAP-ongelman ratkaisuja.
Lisäksi teen vertailua varten käännöksen MAP-ongelmasta lineaariseen ohjelmointiin.
Käännösten suorituskyvyn vertailu antaa viitteitä siitä, että useimmille ongelmille lineaarinen ohjelmointi on vertailluista menetelmistä tehokkain, vaikkakin menetelmien suhteelliset tehokkuudet vaihtelevat kunkin ongelmatapauksen yksityiskohdista riippuen.

Smodels-ohjelman voidaan odottaa suoriutuvan tehokkaammin tilanteissa, joissa ainoastaan osa muuttujista on probabilistista laatua.
Satunnaismuuttujia ja symbolisia rajoitteita yhdistävissä tapauksissa Smodels saattaa osoittautua erittäin kiinnostavaksi menetelmäksi.
ED:2004-07-14
INSSI record number: 25439
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