Related papers: Conditionally independent random variables
Causal inference methods based on conditional independence construct Markov equivalent graphs, and cannot be applied to bivariate cases. The approaches based on independence of cause and mechanism state, on the contrary, that causal…
In this paper we use e-values in the context of multiple hypothesis testing assuming that the base tests produce independent, or sequential, e-values. Our simulation and empirical studies and theoretical considerations suggest that, under…
It is a common saying that testing for conditional independence, i.e., testing whether whether two random vectors $X$ and $Y$ are independent, given $Z$, is a hard statistical problem if $Z$ is a continuous random variable (or vector). In…
We show that there can be no finite list of conditional independence relations which can be used to deduce all conditional independence implications among Gaussian random variables. To do this, we construct, for each $n> 3$ a family of $n$…
Most existing works on disentangled representation learning are solely built upon an marginal independence assumption: all factors in disentangled representations should be statistically independent. This assumption is necessary but…
It is shown that the ability of the interval probability representation to capture epistemological independence is severely limited. Two events are epistemologically independent if knowledge of the first event does not alter belief (i.e.,…
A {\em maximal inequality} seeks to estimate $\mathbb{E}\max_i X_i$ in terms of properties of the $X_i$. When the latter are independent, the union bound (in its various guises) can yield tight upper bounds. If, however, the $X_i$ are…
In this paper we introduce several natural definitions of asymptotic independence of two sequences of random elements. We discuss their basic properties, some simple connections between them and connections with properties of weak…
We consider the problem of constructing multiple independent conditional randomization tests using a single dataset. Because the tests are independent, the randomization p-values can be interpreted individually and combined using standard…
Conditional independence (CI) testing is frequently used in data analysis and machine learning for various scientific fields and it forms the basis of constraint-based causal discovery. Oftentimes, CI testing relies on strong, rather…
The object of observation in present paper is statistical independence of real sequences and its description as independence with re spect to certain class of densities.
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…
Statistical independence is a notion ubiquitous in various fields such as in statistics, probability, number theory and physics. We establish the stability of independence for any pair of random variables by their corresponding Brockwell…
In this paper, the notion of conditionally bi-free independence for pairs of algebras is introduced. The notion of conditional $(\ell, r)$-cumulants are introduced and it is demonstrated that conditionally bi-free independence is equivalent…
An ordinal view of independence is studied in the framework of possibility theory. We investigate three possible definitions of dependence, of increasing strength. One of them is the counterpart to the multiplication law in probability…
Independence testing plays a central role in statistical and causal inference from observational data. Standard independence tests assume that the data samples are independent and identically distributed (i.i.d.) but that assumption is…
A key challenge in causal inference from observational studies is the identification and estimation of causal effects in the presence of unmeasured confounding. In this paper, we introduce a novel approach for causal inference that…
In this paper, we focus on the problem of stable prediction across unknown test data, where the test distribution is agnostic and might be totally different from the training one. In such a case, previous machine learning methods might…
Contextual situations are those in which seemingly "the same" random variable changes its identity depending on the conditions under which it is recorded. Such a change of identity is observed whenever the assumption that the variable is…
In this paper we consider finite conditional random quantities and conditional previsions assessments in the setting of coherence. We use a suitable representation for conditional random quantities; in particular the indicator of a…