Related papers: Generalized Wick Decompositions
The notion of random self-decomposability is generalized here. Its relation to self-decomposability, Harris infinite divisibility and its connection with a stationary first order generalized autoregressive model are presented. The notion is…
We study several variants of decomposing a symmetric matrix into a sum of a low-rank positive semidefinite matrix and a diagonal matrix. Such decompositions have applications in factor analysis and they have been studied for many decades.…
In linear inverse problems, we have data derived from a noisy linear transformation of some unknown parameters, and we wish to estimate these unknowns from the data. Separable inverse problems are a powerful generalization in which the…
We introduce a novel framework for decomposing interventional causal effects into synergistic, redundant, and unique components, building on the intuition of Partial Information Decomposition (PID) and the principle of M\"obius inversion.…
Self-adjoint Dirac systems and subclasses of canonical systems, which generalize Dirac systems are studied. Explicit and global solutions of direct and inverse problems are obtained. A local Borg-Marchenko-type theorem, integral…
We construct an algorithm that reduces the complexity for computing generalized Dedekind sums from exponential to polynomial time. We do so by using an efficient word rewriting process in group theory.
The bias-variance decomposition is a central result in statistics and machine learning, but is typically presented only for the squared error. We present a generalization of the bias-variance decomposition where the prediction error is a…
This paper introduces a notion of decompositions of integral varifolds into countably many integral varifolds, and the existence of such decomposition of integral varifolds whose first variation is representable by integration is…
The structure of covariant instruments is studied and a general structure theorem is derived. A detailed characterization is given to covariant instruments in the case of an irreducible representation of a locally compact group.
Based on the definition of generalized partially bent functions, using the theory of linear transformation, the relationship among generalized partially bent functions over ring Z N, generalized bent functions over ring Z N and affine…
In this paper, it is shown that every polynomial function is mixed monotone globally with a polynomial decomposition function. For univariate polynomials, the decomposition functions can be constructed from the Gram matrix representation of…
Investigating relationships between variables in multi-dimensional data sets is a common task for data analysts and engineers. More specifically, it is often valuable to understand which ranges of which input variables lead to particular…
Prior proposals for cumulative statistics suggest making tiny random perturbations to the scores (independent variables in a regression) in order to ensure the scores' uniqueness. Uniqueness means that no score for any member of the…
We define a generalization of the Turing machine that computes on general sets. Our main theorem states that the class of generalized Turing machine computable functions and the class of Set Recursive functions coincide.
Cluster-Weighted Modeling (CWM) is a flexible mixture approach for modeling the joint probability of data coming from a heterogeneous population as a weighted sum of the products of marginal distributions and conditional distributions. In…
Dedekind sums are well-studied arithmetic sums, with values uniformly distributed on the unit interval. Based on their relation to certain modular forms, Dedekind sums may be defined as functions on the cusp set of $SL(2,\mathbb{Z})$. We…
Motivated by a connection with the factorization of multivariate polynomials, we study integral convex polytopes and their integral decompositions in the sense of the Minkowski sum. We first show that deciding decomposability of integral…
Let A be an arbitrary set. For any transformation T (self-map of A) let T(f)(x):=f(T(x)) (for all x in A) be the usual shift operator. A function g is called periodic, i.e., invariant mod T, if Tg=g (=Ig, where I is the identity operator).…
The article presents mathematical generalization of results which originated as solutions of practical problems, in particular, the modeling of transitional processes in electrical circuits and problems of resource allocation. However, the…
The paper introduces the concept of a cluster structure to define a joint distribution of the sample size and its exchangeable random partitions. The cluster structure allows the probability distribution of the random partitions of a subset…