Learning switch configurations

title: Monotone term decision lists
abstract: We introduce a new representation class of Boolean functions ? monotone term decision lists ? which combines compact representation size with tractability of essential operations. We present many properties of the class which make it an attractive alternative to traditional universal representation classes such as DNF formulas or decision trees. We study the learnability of monotone term decision lists in the exact model of equivalence and membership queries. We show that, for any constant k?0, k-term monotone decision lists are exactly and properly learnable with nO(k) membership queries in nO(k3) time. We also show that n?(k) membership queries are necessary for exact learning. In contrast, both k-term monotone decision lists (k?2) and general monotone term decision lists are not learnable with equivalence queries alone. We also show that a subclass of monotone term decision lists (disj-MDL) is learnable with equivalence and membership queries, while neither type of query alone suffices.

title: Read-Twice DNF Formulas are Properly Learnable
abstract: We show that read-twice DNF formulas-Boolean formulas in disjunctive normal form in which each variable appears at most twice-are exactly and properly learnable in polynomial time. Our algorithm uses membership queries and proper equivalence queries and is based on a simple, new characterization of minimal read-twice DNF formulas. The algorithm improves on earlier results of Hancock and Aizenstein and Pitt which showed that read-twice DNF formulas are learnable using more powerful equivalence queries, i.e., where the hypotheses could be arbitrary DNF formulas. We also improve on the time-complexity of these earlier algorithms. Other results which may be of independent interest outside of learning follow directly from this paper. Specifically, we show that read-twice DNF formulas can be tested for equivalence in polynomial time and that the smallest read-twice formula equivalent to a given one can be found in polynomial time.

title: How many queries are needed to learn?
abstract: We investigate the query complexity of exact learning in the membership and (proper) equivalence query model. We give a complete characterization of concept classes that are learnable with a polynomial number of polynomial sized queries in this model. We give applications of this characterization, including results on learning a natural subclass of DNF formulas, and on learning with membership queries alone. Query complexity has previously been used to prove lower bounds on the time complexity of exact learning. We show a new relationship between query complexity and time complexity in exact learning: If any “honest” class is exactly and properly learnable with polynomial query complexity, but not learnable in polynomial time, then P = NP. In particular, we show that an honest class is exactly polynomial-query learnable if and only if it is learnable using an oracle for Γp4.

title: Recognition Algorithms for Orders of Small Width and Graphs of Small Dilworth Number
abstract: Partially ordered sets of small width and graphs of small Dilworth number have many interesting properties and have been well studied. Here we show that recognition of such orders and graphs can be done more efficiently than by using the well-known algorithms based on bipartite matching and matrix multiplication. In particular, we show that deciding deciding if an order has width k can be done in O(kn2) time and whether a graph has Dilworth number k can be done in O(k2n2) time.For very small k we have even better results. We show that orders of width at most 3 can be recognized in O(n) time and of width at most 4 in O(nlog n).

title: Information Retrieval on the World Wide Web
abstract: Effective search and retrieval are enabling technologies for realizing the full potential of the Web. The authors examine relevant issues, including methods for representing document content. They also compare available search tools and suggest methods for improving retrieval effectiveness.

title: Concept Based Retrieval Using Generalized Retrieval Functions
abstract: One of the essential goals in information retrieval is to bridge the gap between the way users would prefer to specify their information needs and the way queries are required to be expressed. Rule Based Information Retrieval by Computer (RUBRIC) is one of the approaches proposed to achieve this goal. This approach involves the use of production rules to capture user-query concepts (or topics). In RUBRIC, a set of related production rules is represented as an AND/OR tree, or alternatively by a disjunction of Minimal Term Sets (MTSs). The retrieval output is determined by the evaluation of the weighted Boolean expressions of the AND/OR tree, and processing efficiency can be enhanced by employing MTSs. However, since the weighted Boolean expression ignores the term-term association unless it is explicitly represented in the tree, the terminological gap between users' queries and their information needs may still remain. To solve this problem, we adopt the generalized vector space model (GVSM) and the p-norm based extended Boolean model. Experiments are performed for two variations of the RUBRIC model, extended with GVSM, as well as for the integrated use of RUBRIC with the p-norm based extended Boolean model. The results are compared to the original RUBRIC model based on recall-precision.

title: Visualizing association mining results through hierarchical clusters
abstract: We propose a new methodology for visualizing association mining results. Inter-item distances are computed from combinations of itemset supports. The new distances retain a simple pairwise structure, and are consistent with important frequently occurring itemsets. Thus standard tools of visualization, e.g. hierarchical clustering dendrograms can still be applied, while the distance information upon which they are based is richer. Our approach is applicable to general association mining applications, as well as applications involving information spaces modeled by directed graphs, e.g. the Web. In the context of collections of hypertext documents, the inter-document distances capture the information inherent in a collection's link structure, a form of link mining. We demonstrate our methodology with document sets extracted from the Science Citation Index, applying a metric that measures consistency between clusters and frequent itemsets.