Communications of the ACM
Information Processing Letters
Computational limitations on learning from examples
Journal of the ACM (JACM)
Cause-effect relationships and partially defined Boolean functions
Annals of Operations Research
Structure identification in relational data
Artificial Intelligence - Special volume on constraint-based reasoning
Learning with restricted focus of attention
COLT '93 Proceedings of the sixth annual conference on Computational learning theory
Mining association rules between sets of items in large databases
SIGMOD '93 Proceedings of the 1993 ACM SIGMOD international conference on Management of data
Predicting Cause-Effect Relationships from Incomplete Discrete Observations
SIAM Journal on Discrete Mathematics
The complexity and approximability of finding maximum feasible subsystems of linear relations
Theoretical Computer Science
Decomposability of partially defined Boolean functions
Discrete Applied Mathematics - Special volume on partitioning and decomposition in combinatorial optimization
COLT '95 Proceedings of the eighth annual conference on Computational learning theory
Learning to reason with a restricted view
COLT '95 Proceedings of the eighth annual conference on Computational learning theory
Positive and Horn decomposability of partially defined Boolean functions
Discrete Applied Mathematics
Learning from examples with unspecified attribute values (extended abstract)
COLT '97 Proceedings of the tenth annual conference on Computational learning theory
Logical settings for concept-learning
Artificial Intelligence
Knowing what doesn't matter: exploiting the omission of irrelevant data
Artificial Intelligence - Special issue on relevance
Error-free and best-fit extensions of partially defined Boolean functions
Information and Computation
Machine Learning
Machine Learning
Machine Learning
Boolean Analysis of Incomplete Examples
SWAT '96 Proceedings of the 5th Scandinavian Workshop on Algorithm Theory
On Horn Envelopes and Hypergraph Transversals
ISAAC '93 Proceedings of the 4th International Symposium on Algorithms and Computation
Monotone Extensions of Boolean Data Sets
ALT '97 Proceedings of the 8th International Conference on Algorithmic Learning Theory
Learning to reason the non monotonic case
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 2
Finding Essential Attributes in Binary Data
IDEAL '00 Proceedings of the Second International Conference on Intelligent Data Engineering and Automated Learning, Data Mining, Financial Engineering, and Intelligent Agents
Fully Consistent Extensions of Partially Defined Boolean Functions with Missing Bits
TCS '00 Proceedings of the International Conference IFIP on Theoretical Computer Science, Exploring New Frontiers of Theoretical Informatics
Logic based methods for SNPs tagging and reconstruction
Computers and Operations Research
Pareto-optimal patterns in logical analysis of data
Discrete Applied Mathematics
ISI'06 Proceedings of the 4th IEEE international conference on Intelligence and Security Informatics
Logic mining for financial data
ICCS'06 Proceedings of the 6th international conference on Computational Science - Volume Part IV
| Hi-index | 0.00 |
We model a given pair of sets of positive and negative examples, each of which may contain missing components, as a partially defined Boolean function with missing bits (pBmb) (T~,F~), where T~-@?{0,1*}^n and F~-@?{0,1*}^n, and ''*'' stands for a missing bit. Then we consider the problem of establishing a Boolean function (an extension) f : 0, 1^n - 0, 1 belonging to a given function class C, such that f is true (respectively, false) for every vector in T~ (respectively, in F~. This is a fundamental problem, encountered in many areas such as learning theory, pattern recognition, example-based knowledge bases, logical analysis of data, knowledge discovery and data mining. In this paper, depending upon how to deal with missing bits, we formulate three types of extensions called robust, consistent and most robust extensions, for various classes of Boolean functions such as general, positive, Horn, threshold, decomposable and k-DNF. The complexity of the associated problems are then clarified; some of them are solvable in polynomial time while the others are NP-hard.