13,745 research outputs found
SDDs are Exponentially More Succinct than OBDDs
Introduced by Darwiche (2011), sentential decision diagrams (SDDs) are
essentially as tractable as ordered binary decision diagrams (OBDDs), but tend
to be more succinct in practice. This makes SDDs a prominent representation
language, with many applications in artificial intelligence and knowledge
compilation. We prove that SDDs are more succinct than OBDDs also in theory, by
constructing a family of boolean functions where each member has polynomial SDD
size but exponential OBDD size. This exponential separation improves a
quasipolynomial separation recently established by Razgon (2013), and settles
an open problem in knowledge compilation
Decision diagrams in machine learning: an empirical study on real-life credit-risk data.
Decision trees are a widely used knowledge representation in machine learning. However, one of their main drawbacks is the inherent replication of isomorphic subtrees, as a result of which the produced classifiers might become too large to be comprehensible by the human experts that have to validate them. Alternatively, decision diagrams, a generalization of decision trees taking on the form of a rooted, acyclic digraph instead of a tree, have occasionally been suggested as a potentially more compact representation. Their application in machine learning has nonetheless been criticized, because the theoretical size advantages of subgraph sharing did not always directly materialize in the relatively scarce reported experiments on real-world data. Therefore, in this paper, starting from a series of rule sets extracted from three real-life credit-scoring data sets, we will empirically assess to what extent decision diagrams are able to provide a compact visual description. Furthermore, we will investigate the practical impact of finding a good attribute ordering on the achieved size savings.Advantages; Classifiers; Credit scoring; Data; Decision; Decision diagrams; Decision trees; Empirical study; Knowledge; Learning; Real life; Representation; Size; Studies;
New developments in the theory of Groebner bases and applications to formal verification
We present foundational work on standard bases over rings and on Boolean
Groebner bases in the framework of Boolean functions. The research was
motivated by our collaboration with electrical engineers and computer
scientists on problems arising from formal verification of digital circuits. In
fact, algebraic modelling of formal verification problems is developed on the
word-level as well as on the bit-level. The word-level model leads to Groebner
basis in the polynomial ring over Z/2n while the bit-level model leads to
Boolean Groebner bases. In addition to the theoretical foundations of both
approaches, the algorithms have been implemented. Using these implementations
we show that special data structures and the exploitation of symmetries make
Groebner bases competitive to state-of-the-art tools from formal verification
but having the advantage of being systematic and more flexible.Comment: 44 pages, 8 figures, submitted to the Special Issue of the Journal of
Pure and Applied Algebr
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Genetic algorithm approach to find the best input variable partitioning
Conference PaperThis paper presents a variable partition algorithm which combines the quasi-reduced ordered multiple-terminal multiple-valued decision diagrams and genetic algorithms (GAs). The algorithm is better than the previous techniques which find a good functional decomposition by non-exhaustive search and expands the range of searching for the best decomposition providing the optimal subtable multiplicity. The possible solutions are evaluated using the gain of decomposition for a multiple-output multiple-valued logic function. The distinct feature of GA is the possible solutions being coded by real numbers. Here the simplex-based crossover is proposed to use for the recombination stage of GA. It permits to increase the GA coverag
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