Related papers: Multilinear function series in conditionally free …
In this paper, on the sublinear expectation space, we establish a comparison theorem between independent and convolutionary random vectors, which states that the partial sums of those two sequences of random vectors are identically…
In this paper, we observevd the amalgamated free probability of direct product of noncommutative probability spaces. We defined the amalgamated R-transforms, amalgamated moment series and the amalgamated boxed convolution. They maks us to…
The paper provides a necessary and sufficient condition for the composition of multivariable formal power series and present the Generalized Chain Rule for formal power series of multiple variables.
We define a new independence in non-commutative probability, called $\alpha$-freeness, with respect to a triplet of states. This concept unifies several independences in non-commutative probability, in particular, free, monotone,…
We introduce a finite version of free probability and show the link between recent results using polynomial convolutions and the traditional theory of free probability. One tool for accomplishing this is a seemingly new transformation that…
Conditional independence, and more generally conditional mutual independence, are central notions in probability theory. In their general forms, they include functional dependence as a special case. In this paper, we tackle two fundamental…
Functional data analysis in a mixed-effects model framework is done using operator calculus. In this approach the functional parameters are treated as serially correlated effects giving an alternative to the penalized likelihood approach,…
We give conditions on a finite set of series of rational numbers to ensure that they are algebraically independent. Specialising our results to polynomials of lower degree, we also obtain new results on irrationality and $mathbb{Q}$-linear…
The propositional logic is generalized on the real numbers field. the logical function with all properties of the classical probability function is obtained. The logical analog of the Bernoulli independent tests scheme is constructed. The…
A central limit theorem is established for a sum of random variables belonging to a sequence of random fields. The fields are assumed to have zero mean conditional on the past history and to satisfy certain conditional $\alpha$-mixing…
We extend Riemann's rearrangement theorem on conditionally convergent series of real numbers to multiple instead of simple sums.
This paper introduces the notion of pseudo-independence on the sublinear expectation space $(\Omega,\mathcal{F},\mathcal{P})$ via the classical conditional expectation, and the relations between pseudo-independence and Peng's independence…
In this paper, the maximal nonlinear conditional correlation of two random vectors $X$ and $Y$ given another random vector $Z$, denoted by $\rho_1(X,Y|Z)$, is defined as a measure of conditional association, which satisfies certain…
Many complex systems satisfy a set of constraints on their degrees of freedom, and at the same time, they are able to work and adapt to different conditions. Here, we describe the emergence of this ability in a simplified model in which the…
We consider a notion of bi-freeness for systems of non-commutative random variables with two faces, one of left variables and another of right variables. This includes bi-free convolution operations, bi-free cumulants and the bi-free…
We develop a constructive theory of finite multisets in Homotopy Type Theory, defining them as free commutative monoids. After recalling basic structural properties of the free commutative-monoid construction, we formalise and establish the…
We solve two longstanding major problems in Free Probability. This is achieved by generalising the theory to one with values in arbitrary commutative algebras. We prove the existence of the multi-variable $S$-transform, and show that it is…
We propose and study properties of maximum likelihood estimators in the class of conditional transformation models. Based on a suitable explicit parameterisation of the unconditional or conditional transformation function, we establish a…
Conditional independence testing is a key problem required by many machine learning and statistics tools. In particular, it is one way of evaluating the usefulness of some features on a supervised prediction problem. We propose a novel…
A combination of a finite number of linear independent states forms superposition in a way that cannot be conceived classically. Here, using the tools of resource theory of superposition, we give the conditions for a class of superposition…