29,405 research outputs found
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;
EVMDD-based analysis and diagnosis methods of multi-state systems with multi-state components
A multi-state system with multi-state components is a model of systems, where performance,
capacity, or reliability levels of the systems are represented as states. It usually has more than
two states, and thus can be considered as a multi-valued function, called a structure function.
Since many structure functions are monotone increasing, their multi-state systems can be
represented compactly by edge-valued multi-valued decision diagrams (EVMDDs). This paper presents
an analysis method of multi-state systems with multi-state components using EVMDDs. Experimental
results show that, by using EVMDDs, structure functions can be represented more compactly than
existing methods using ordinary MDDs. Further, EVMDDs yield comparable computation time for
system analysis. This paper also proposes a new diagnosis method using EVMDDs, and shows that the
proposed method can infer the most probable causes for system failures more efficiently than conventional methods based on Bayesian networks.Japan Society for the Promotion of ScienceMinistry of Education, Culture, Sports, Science and Technology (MEXT)Hiroshima City UniversityGrant-in Aid No. 2500050 (MEXT)Grant no. 0206 (HCU)Grant in Aid for Scientific Research (JSPS
The Complexity of Reasoning with FODD and GFODD
Recent work introduced Generalized First Order Decision Diagrams (GFODD) as a
knowledge representation that is useful in mechanizing decision theoretic
planning in relational domains. GFODDs generalize function-free first order
logic and include numerical values and numerical generalizations of existential
and universal quantification. Previous work presented heuristic inference
algorithms for GFODDs and implemented these heuristics in systems for decision
theoretic planning. In this paper, we study the complexity of the computational
problems addressed by such implementations. In particular, we study the
evaluation problem, the satisfiability problem, and the equivalence problem for
GFODDs under the assumption that the size of the intended model is given with
the problem, a restriction that guarantees decidability. Our results provide a
complete characterization placing these problems within the polynomial
hierarchy. The same characterization applies to the corresponding restriction
of problems in first order logic, giving an interesting new avenue for
efficient inference when the number of objects is bounded. Our results show
that for formulas, and for corresponding GFODDs, evaluation and
satisfiability are complete, and equivalence is
complete. For formulas evaluation is complete, satisfiability
is one level higher and is complete, and equivalence is
complete.Comment: A short version of this paper appears in AAAI 2014. Version 2
includes a reorganization and some expanded proof
Advances in Functional Decomposition: Theory and Applications
Functional decomposition aims at finding efficient representations for Boolean functions. It is used in many applications, including multi-level logic synthesis, formal verification, and testing.
This dissertation presents novel heuristic algorithms for functional decomposition. These algorithms take advantage of suitable representations of the Boolean functions in order to be efficient.
The first two algorithms compute simple-disjoint and disjoint-support decompositions. They are based on representing the target function by a Reduced Ordered Binary Decision Diagram (BDD). Unlike other BDD-based algorithms, the presented ones can deal with larger target functions and produce more decompositions without requiring expensive manipulations of the representation, particularly BDD reordering.
The third algorithm also finds disjoint-support decompositions, but it is based on a technique which integrates circuit graph analysis and BDD-based decomposition. The combination of the two approaches results in an algorithm which is more robust than a purely BDD-based one, and that improves both the quality of the results and the running time.
The fourth algorithm uses circuit graph analysis to obtain non-disjoint decompositions. We show that the problem of computing non-disjoint decompositions can be reduced to the problem of computing multiple-vertex dominators. We also prove that multiple-vertex dominators can be found in polynomial time. This result is important because there is no known polynomial time algorithm for computing all non-disjoint decompositions of a Boolean function.
The fifth algorithm provides an efficient means to decompose a function at the circuit graph level, by using information derived from a BDD representation. This is done without the expensive circuit re-synthesis normally associated with BDD-based decomposition approaches.
Finally we present two publications that resulted from the many detours we have taken along the winding path of our research
On one-way cellular automata with a fixed number of cells
We investigate a restricted one-way cellular automaton (OCA) model where the number of cells is bounded by a constant number k, so-called kC-OCAs. In contrast to the general model, the generative capacity of the restricted model is reduced to the set of regular languages. A kC-OCA can be algorithmically converted to a deterministic finite automaton (DFA). The blow-up in the number of states is bounded by a polynomial of degree k. We can exhibit a family of unary languages which shows that this upper bound is tight in order of magnitude. We then study upper and lower bounds for the trade-off when converting DFAs to kC-OCAs. We show that there are regular languages where the use of kC-OCAs cannot reduce the number of states when compared to DFAs. We then investigate trade-offs between kC-OCAs with different numbers of cells and finally treat the problem of minimizing a given kC-OCA
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