7133208
Statistical Learning Procedure in Loopy Belief Propagation for Probabilistic Image Processing
We give a fast and practical algorithm for statistical learning hyperparameters from observable data in probabilistic image processing, which is based on Gaussian graphical model and maximum likelihood estimation. Although hyperparameters in the probabilistic model are determined so as to maximize a marginal likelihood, a practical algorithm is described for the EM algorithm with the loopy belief propagation which is one of approximate inference algorithms in artificial intelligence
11983347
Linear Response Formula in Generalized Belief Propagation for Probabilistic Inference
Linear response formulas for the generalized belief propagation in approximate inference are derived by using generalized belief propagation. The linear response formulas can give us the marginal probability between every pair of nodes and we obtain good accuracy in some examples of practical probabilistic inferences
18193868
Interval Queries on Object Histories: Extended Abstract
This extended abstract introduces the notion of ’ interval queries ’ on historical data for objects (here, called ‘object histories’) and explores a certain closure property. As for describing historical data for objects, we use our mathematical model introduced in our earlier paper. The major construct in the model is a ‘computation-tuple sequence scheme’ (abbreviated CSS), which specifies the set of all possible ‘valid’ object histories for the same type of object. Interval queries are those queries which return an interval (history) from a given object history. We provide conditions under which an interval query applied to object histories described by one CSS yields, as its answers. the set of all object histories which can be described by another CSS.
3517036
Fixed Point Theory in Weak Second-Order Arithmetic
Abstract We develop a basic part of fixed point theory in the context of weak subsystems of second-order arithmetic. RCA0 is the system of recursive comprehension and Σ01 induction. WKL0 is RCA0 plus the weak Konig's lemma: every infinite tree of sequences of 0's and 1's has an infinite path. A topological space X is said to possess the fixed point property if every continuous function f:X→X has a point x ϵ X such that f(x) = x. Within WKL0 (indeed RCA0), we prove Brouwer's theorem asserting that every nonempty compact convex closed set C in R n has the fixed point property, provided that C is expressed as the completion of a countable subset of Q n. We then extend Brouwer's theorem to its infinite dimensional analogue (the Tychonoff-Schauder theorem for R N ) still within RCA0. As an application of this theorem, we prove the Cauchy-Peano theorem for ordinary differential equations within WKL0, which was first shown by Simpson without reference to the fixed point theorem. Within RCA0, we also prove the Markov-Kakutani theorem which asserts the existence of a common fixed point for certain families of affine mappings. Adapting Kakutani's ingenious proof for deducing the Hahn–Banach theorem from the Markov-Kakutani theorem, we also establish the Hahn-Banach theorem for seperable Banach spaces within WKL0, which was first shown by Brown and Simpson in a different way.
35660731
Some Properties of Fuzzy Sets of Type 2
The concept of fuzzy sets of type 2 has been defined by L. A. Zadeh as an extension of ordinary fuzzy sets. The fuzzy set of type 2 can be characterized by a fuzzy membership function the grade (or fuzzy grade) of which is a fuzzy set in the unit interval [0, 1] rather than a point in [0, 1]. This paper investigates the algebraic structures of fuzzy grades under the operations of join ⊔, meet ⊔, and negation ┐ which are defined by using the extension principle, and shows that convex fuzzy grades form a commutative semiring and normal convex fuzzy grades form a distributive lattice under ⊔ and ⊓. Moreover, the algebraic properties of fuzzy grades under the operations and which are slightly different from ⊔ and ⊓, respectively, are briefly discussed.
40817809
Query pairs as hypertext links
A new idea is proposed for constructing object-oriented hypertext database systems: query pairs as hypertext links, where each query is defined over a collection of document objects that are classified using a class hierarchy. With this idea, users need not modify their hypertext links against the insertions, deletions and updates of document objects. Also, when a database schema (here, a class hierarchy) evolves, a systematic method can be considered to modify user-defined query-pair links. The TextLink-III system that was developed based on this idea and that is currently running is described. The notable features of TextLink-III are the following: document objects are classified by class hierarchy and the notion of class expression is used for formulating a query for a class hierarchy; multiple viewpoint support; and less link maintenance against data updates.<<ETX>>
205099974
Organization of quasi-consecutive retrieval files
Abstract In 1972, Ghosh introduced the consecutive retrieval (CR) file organization. It is an efficient file organization in which all records pertinent to a query are consecutively stored on linear storage locations. In this paper, we introduce the quasi-consecutive retrieval (QCR) file organization. The QCR file organization is an extension of Ghosh's CR file organization and normally offers less redundancy. In the QCR file, all the records pertinent to each query are not necessarily stored consecutively, but rather they are stored within an area of the buffer size. In this paper, we discuss graph theoretic properties of CR files and QCR files by using the properties of interval graphs well known in graph theory. We provide a basic condition for the existence of a QCR file without redundancy for a given buffer size. By introducing redundant queries, such a condition is simplified. Furthermore, a heuristic computer algorithm is given to organize a QCR file with less redundancy for a given buffer size.