5 research outputs found
Mixed Logical and Probabilistic Reasoning in the Game of Clue
Neller and Ziqian Luo ā18 presented a means of mixed logical and probabilistic reasoning with knowledge in the popular deductive mystery game Clue. Using at-least constraints, we more efficiently represented and reasoned about cardinality constraints on Clue card deal knowledge, and then employed a WalkSAT-based solution sampling algorithm with a tabu search metaheuristic in order to estimate the probabilities of unknown card places
The Faculty Notebook, September 2019
The Faculty Notebook is published periodically by the Office of the Provost at Gettysburg College to bring to the attention of the campus community accomplishments and activities of academic interest. Faculty are encouraged to submit materials for consideration for publication to the Associate Provost for Faculty Development. Copies of this publication are available at the Office of the Provost
Incremental inference on higher-order probabilistic graphical models applied to constraint satisfaction problems
Thesis (PhD)--Stellenbosch University, 2022.ENGLISH ABSTRACT: Probabilistic graphical models (PGMs) are used extensively in the probabilistic
reasoning domain. They are powerful tools for solving systems of complex relationships over a variety of probability distributions, such as medical and fault diagnosis, predictive modelling, object recognition, localisation and mapping, speech recognition, and language processing [5, 6, 7, 8, 9, 10, 11]. Furthermore, constraint
satisfaction problems (CSPs) can be formulated as PGMs and solved with PGM inference techniques. However, the prevalent literature on PGMs shows that suboptimal PGM structures are primarily used in practice and a suboptimal formulation
for constraint satisfaction PGMs.
This dissertation aimed to improve the PGM literature through accessible algorithms and tools for improved PGM structures and inference procedures, specifically focusing on constraint satisfaction. To this end, this dissertation presents three
published contributions to the current literature:
a comparative study to compare cluster graph topologies to the prevalent factor graphs [1],
an application of cluster graphs in land cover classification in the field of cartography [2], and
a comprehensive integration of various aspects required to formulate CSPs as
PGMs and an algorithm to solve this formulation for problems too complex
for traditional PGM tools [3].
First, we present a means of formulating and solving graph colouring problems with probabilistic graphical models. In contrast to the prevailing literature
that mostly uses factor graph configurations, we approach it from a cluster graph perspective, using the general-purpose cluster graph construction algorithm, LTRIP.
Our experiments indicate a significant advantage for preferring cluster graphs over factor graphs, both in terms of accuracy as well as computational efficiency.
Secondly, we use these tools to solve a practical problem: land cover classification. This process is complex due to measuring errors, inefficient algorithms, and
low-quality data. We proposed a PGM approach to boost geospatial classifications
from different sources and consider the effects of spatial distribution and inter-class dependencies (similarly to graph colouring). Our PGM tools were shown to be
robust and were able to produce a diverse, feasible, and spatially-consistent land cover classification even in areas of incomplete and conflicting evidence.
Lastly, in our third publication, we investigated and improved the PGM structures used for constraint satisfaction. It is known that tree-structured PGMs always result in an exact solution [12, p355], but is usually impractical for interesting
problems due to exponential blow-up. We, therefore, developed the āpurge-and mergeā algorithm to incrementally approximate a tree-structured PGM. This algorithm iteratively nudges a malleable graph structure towards a tree structure by selectively merging factors. The merging process is designed to avoid exponential
blow-up through sparse data structures from which redundancy is purged as the algorithm progresses. This algorithm is tested on constraint satisfaction puzzles such
as Sudoku, Fill-a-pix, and Kakuro and manages to outperform other PGM-based
approaches reported in the literature [13, 14, 15]. Overall, the research reported in
this dissertation contributed to developing a more optimised approach for higher order probabilistic graphical models. Further studies should concentrate on applying purge-and-merge on problems closer to probabilistic reasoning than constraint
satisfaction and report its effectiveness in that domain.AFRIKAANSE OPSOMMING: Grafiese waarskynlikheidsmodelle (PGM) word wyd gebruik vir komplekse
waarskynlikheidsprobleme. Dit is kragtige gereedskap om sisteme van komplekse
verhoudings oor ān versameling waarskynlikheidsverspreidings op te los, soos die
mediese en foutdiagnoses, voorspellingsmodelle, objekherkenning, lokalisering en
kartering, spraakherkenning en taalprosessering [5, 6, 7, 8, 9, 10, 11]. Voorts kan
beperkingvoldoeningsprobleme (CSP) as PGMās geformuleer word en met PGM
gevolgtrekkingtegnieke opgelos word. Die heersende literatuur oor PGMās toon
egter dat sub-optimale PGM-strukture hoofsaaklik in die praktyk gebruik word en
ān sub-optimale PGM-formulering vir CSPās.
Die doel met die verhandeling is om die PGM-literatuur deur toeganklike algoritmes en gereedskap vir verbeterde PGM-strukture en gevolgtrekking-prosedures
te verbeter deur op CSP toepassings te fokus. Na aanleiding hiervan voeg die verhandeling drie gepubliseerde bydraes by die huidige literatuur:
ān vergelykende studie om bundelgrafieke tot die heersende faktorgrafieke te
vergelyk [1],
ān praktiese toepassing vir die gebruik van bundelgrafieke in āland-coverā-
klassifikasie in die kartografieveld [2] en
ān omvattende integrasie van verskeie aspekte om CSPās as PGMās te formuleer en ān algoritme vir die formulering van probleme te kompleks vir tradisionele PGM-gereedskap [3]
Eerstens bied ons ān wyse van formulering en die oplos van grafiekkleurprobleme met PGMās. In teenstelling met die huidige literatuur wat meestal faktorgrafieke gebruik, benader ons dit van ān bundelgrafiek-perspektief deur die gebruik
van die automatiese bundelgrafiekkonstruksie-algoritme, LTRIP. Ons eksperimente
toon ān beduidende voorkeur vir bundelgrafieke teenoor faktorgrafieke, wat akku raatheid asook berekende doeltreffendheid betref.
Tweedens gebruik ons die gereedskap om ān praktiese probleem op te los: ālandcoverā-klassifikasie. Die proses is kompleks weens metingsfoute, ondoeltreffende
algoritmes en lae-gehalte data. Ons stel ān PGM-benadering voor om die georuimtelike klassifikasies van verskillende bronne te versterk, asook die uitwerking van ruimtelike verspreiding en interklas-afhanklikhede (soortgelyk aan grafiekkleurprobleme). Ons PGM-gereedskap is robuus en kon ān diverse, uitvoerbare en
ruimtelik-konsekwente āland-coverā-klassifikasie selfs in gebiede van onvoltooide
en konflikterende inligting bewys.
Ten slotte het ons in ons derde publikasie die PGM-strukture vir CSPās ondersoek en verbeter. Dit is bekend dat boomstrukture altyd tot ān eksakte oplossing
lei [12, p355], maar is weens eksponensiƫle uitbreiding gewoonlik onprakties vir interessante probleme. Ons het gevolglik die algoritme, purge-and-merge, ontwikkel
om inkrementeel ān boomstruktuur na te doen.
Die algoritme hervorm ān bundelgrafiek stapsgewys in ān boomstruktuur deur
faktore selektief te āmergeā. Die saamsmeltproses is ontwerp om eksponensiĆ«le
uitbreiding te vermy deur van yl datastrukture gebruik te maak waarvan die waarskeinlikheidsruimte ge-āpurgeā word namate die algoritme vorder. Die algoritme
is getoets op CSP-speletjies soos Sudoku, Fill-a-pix en Kakuro en oortref ander
PGM-gegronde benaderings waaroor in die literatuur verslag gedoen word [13,
14, 15]. In die geheel gesien, het die navorsing bygedra tot die ontwikkeling van
ān meer geoptimaliseerde benadering vir hoĆ«r-orde PGMās. Verdere studies behoort te fokus op die toepassing van purge-and-merge op probleme nader aan
waarskynlikheidsredenasie-probleme as aan CSPās en moet sy effektiwiteit in daar die domein rapporteer.Doctora
Mixed Logical and Probabilistic Reasoning in the Game of Clue
We describe a means of mixed logical and probabilistic reasoning with knowledge in the popular game Clue. Using pseudo-Boolean constraints we call at-least constraints, we more efficiently represent cardinality constraints on Clue card deal knowledge, perform more general constraint satisfaction in order to determine places where cards provably are or are not, and then employ a WalkSAT-based solution sampling algorithm with a tabu search metaheuristic in order to estimate the probabilities of unknown card places. Finding a tradeoff between WalkSAT-heuristic efficiency in finding solution samples and the sampling bias such a heuristic introduces, we empirically study algorithmic variations in order to learn how such sampling error may be reduced