Support sets in exponential families and oriented matroid theory
نویسندگان
چکیده
We discuss how to obtain an implicit description of the closure of a discrete exponential family with a finite set of equations derived from an underlying oriented matroid. These equations are similar to the equations used in algebraic statistics, although they need not be polynomial in the general case. This framework allows us to study the possible support sets of an exponential families with the help of oriented matroid theory. In particular, if two exponential families induce the same oriented matroid, then they have the same support sets.
منابع مشابه
Degrees of M-fuzzy families of independent L-fuzzy sets
The present paper studies fuzzy matroids in view of degree. First wegeneralize the notion of $(L,M)$-fuzzy independent structure byintroducing the degree of $M$-fuzzy family of independent $L$-fuzzysets with respect to a mapping from $L^X$ to $M$. Such kind ofdegrees is proved to satisfy some axioms similar to those satisfiedby $(L,M)$-fuzzy independent structure. ...
متن کاملOriented matroid systems
The domination invariant has played an important part in reliability theory. While most of the work in this field has been restricted to various types of network system models, many of the results can be generalized to much wider families of systems associated with matroids. A matroid is an ordered pair (F,M), where F is a nonempty finite set and M is a collection of incomparable subsets of F ,...
متن کاملSome characteristics of matroids through rough sets
At present, practical application and theoretical discussion of rough sets are two hot problems in computer science. The core concepts of rough set theory are upper and lower approximation operators based on equivalence relations. Matroid, as a branch of mathematics, is a structure that generalizes linear independence in vector spaces. Further, matroid theory borrows extensively from the termin...
متن کاملHypergraphic Oriented Matroid Relational Dependency Flow Models of Chemical Reaction Networks
In this paper we derive and present an application of hypergraphic oriented matroids for the purpose of enumerating the variable interdependencies that define the chemical complexes associated with the kinetics of non-linear dynamical system representations of chemical kinetic reaction flow networks. The derivation of a hypergraphic oriented matroid is obtained by defining a closure operator on...
متن کاملThe lattice of convex sets of an oriented matroid
In this paper we further investigate the structure of the convex sets of an acyclic oriented matroid. This subject was first explored by Las Vergnas [6]. The main tool of our study is the theory of the anti-exchange closure [2]. We show that the convex closure of Las Vergnas satisfies the anti-exchange law in the case where the matroid is a geometry. From this we are able to detail the structur...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Int. J. Approx. Reasoning
دوره 52 شماره
صفحات -
تاریخ انتشار 2011