Related papers: Algebraic Independence Relations in Randomizations

This paper shows that algebraic (in)dependence is encoded in Milnor K-theory of fields. As an application, we show that the isomorphism type of a field is determined by its Milnor K-theory, up to purely inseparable extensions, in most…

We extend the theory of d-separation to cases in which data instances are not independent and identically distributed. We show that applying the rules of d-separation directly to the structure of probabilistic models of relational data…

Subobject independence as morphism co-possibility has recently been defined in [2] and studied in the context of algebraic quantum field theory. This notion of independence is handy when it comes to systems coming from physics, but when…

This short expository paper outlines applications of computer algebra to the implication problem of conditional independence for Gaussian random variables. We touch on certificates for validity and invalidity of inference rules from the…

We study locally finite varieties (=primitive classes) of linear algebras over finite fields. We do not assume that our algebras are associative or Lie. We are interested in the basic properties of finite algebras in these varieties such…

For two independent, almost surely finite random variables, independence of their minimum (time) and the event that one of them is either greater, equal or less than the other (cause) is completely characterized. It is shown that, other…

We develope the framework of transitional conditional independence. For this we introduce transition probability spaces and transitional random variables. These constructions will generalize, strengthen and unify previous notions of…

For an $\omega$-categorical theory $T$ and model $\mathcal{M}$ of $T$ we define a hierarchy of ranks, the $n$-ranks for $n < \omega$ which only care about imaginary elements ``up to level $n$'', where level $n$ contains every element of $M$…

We consider the problem of bounding large deviations for non-i.i.d. random variables that are allowed to have arbitrary dependencies. Previous works typically assumed a specific dependence structure, namely the existence of independent…

Structural independence is the (conditional) independence that arises from the structure rather than the precise numerical values of a distribution. We develop this concept and relate it to $d$-separation and structural causal models.…

Let $X$ be a locally compact Abelian group, $Y$ be its character group. Following A. Kagan and G. Sz\'ekely we introduce a notion of $Q$-independence for random variables with values in $X$. We prove group analogues of the Cram\'er,…

Uniqueness and independence are two fundamental properties of data. Their enforcement in database systems can lead to higher quality data, faster data service response time, better data-driven decision making and knowledge discovery from…

A bounded Kolmogorov-Loveland selection rule is an adaptive strategy for recursively selecting a subsequence of an infinite binary sequence; such a subsequence may be interpreted as the query sequence of a time-bounded Turing machine. In…

We give a definition of some classes of boolean algebras generalizing free boolean algebras; they satisfy a universal property that certain functions extend to homomorphisms. We give a combinatorial property of generating sets of these…

Various limit-free formulas are given for the computation of the algebraic and the topological entropy, respectively in the settings of endomorphisms of locally finite discrete groups and of continuous endomorphisms of totally disconnected…

We generalize two main theorems of matching polynomials of undirected simple graphs, namely, real-rootedness and the Heilmann-Lieb root bound. Viewing the matching polynomial of a graph $G$ as the independence polynomial of the line graph…

We characterize thorn-independence in a variety of structures, focusing on the field of real numbers expanded by predicate defining a dense multiplicative subgroup, G, satisfying the Mann property and whose pth powers are of finite index in…

Two varieties $V, W$ of the same type are independent if there is a binary term $t(x,y)$ such that $V \models t(x,y) \approx x$ and $W \models t(x,y) \approx y$. In this note, we give necessary and sufficient conditions for two finite…

We present a Lagrangian approach to counting degrees of freedom in first-order field theories. The emphasis is on the systematic attainment of a complete set of constraints. In particular, we provide the first comprehensive procedure to…

We address the question of finding algebraic properties that are respectively equivalent, for a morphism between algebraic varieties over an algebraically closed field of characteristic zero, to be an homeomorphism for the Zariski topology…