Related papers: Conditional Independence in Possibility Theory
We propose a new nonparametric test for the supposition of independence between two continuous random variables. The test is based on the size of the longest increasing subsequence of a random permutation. We identified the independence…
We study notions of robustness of Markov kernels and probability distribution of a system that is described by $n$ input random variables and one output random variable. Markov kernels can be expanded in a series of potentials that allow to…
This paper analyzes independence concepts for sets of probability measures associated with directed acyclic graphs. The paper shows that epistemic independence and the standard Markov condition violate desirable separation properties. The…
A type theory is presented that combines (intuitionistic) linear types with type dependency, thus properly generalising both intuitionistic dependent type theory and full linear logic. A syntax and complete categorical semantics are…
This paper proposes new tests of conditional independence of two random variables given a single-index involving an unknown finite-dimensional parameter. The tests employ Rosenblatt transforms and are shown to be distribution-free while…
For a continuous random variable $Z$, testing conditional independence $X \perp\!\!\!\perp Y |Z$ is known to be a particularly hard problem. It constitutes a key ingredient of many constraint-based causal discovery algorithms. These…
We formulate and analyze a graphical model selection method for inferring the conditional independence graph of a high-dimensional nonstationary Gaussian random process (time series) from a finite-length observation. The observed process…
We congratulate Engelke and Hitz on a thought-provoking paper on graphical models for extremes. A key contribution of the paper is the introduction of a novel definition of conditional independence for a multivariate Pareto distribution.…
We propose a new conditional dependence measure and a statistical test for conditional independence. The measure is based on the difference between analytic kernel embeddings of two well-suited distributions evaluated at a finite set of…
Many forms of dependence manifest themselves over time, with behavior of variables in dynamical systems as a paradigmatic example. This paper studies temporal dependence in dynamical systems from a logical perspective, by enriching a…
A statistical language model assigns probability to strings of arbitrary length. Unfortunately, it is not possible to gather reliable statistics on strings of arbitrary length from a finite corpus. Therefore, a statistical language model…
Motivated by applications in biological science, we propose a novel test to assess the conditional mean dependence of a response variable on a large number of covariates. Our procedure is built on the martingale difference divergence…
We study the weak convergence of conditional empirical copula processes, when the conditioning event has a nonzero probability. The validity of several bootstrap schemes is stated, including the exchangeable bootstrap. We define general -…
Conditional independence in a multivariate normal (or Gaussian) distribution is characterized by the vanishing of subdeterminants of the distribution's covariance matrix. Gaussian conditional independence models thus correspond to algebraic…
So far, one-factor copulas induce conditional independence with respect to a latent factor. In this paper, we extend one-factor copulas to conditionally dependent models. This is achieved through new representations which allow to build new…
Recently P. Wocjan and M. Horodecki [quant-ph/0503129] gave a characterization of combinatorially independent permutation separability criteria. Combinatorial independence is a necessary condition for permutations to yield truly independent…
Testing the significance of a variable or group of variables $X$ for predicting a response $Y$, given additional covariates $Z$, is a ubiquitous task in statistics. A simple but common approach is to specify a linear model, and then test…
The Principle of Complementarity of Probabilities based on of noncommutative probability is introduced.
There are many kinds of exogeneity assumptions. How should researchers choose among them? When exogeneity is imposed on an unobservable like a potential outcome, we argue that the form of exogeneity should be chosen based on the kind of…
Many kinds of independence have been defined in non-commutative probability theory. Natural independence is an important class of independence; this class consists of five independences (tensor, free, Boolean, monotone and anti-monotone…