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We propose new concepts in order to analyze and model the dependence structure between two time series. Our methods rely exclusively on the order structure of the data points. Hence, the methods are stable under monotone transformations of…
Inferring a cause from its effect using observed time series data is a major challenge in natural and social sciences. Assuming the effect is generated by the cause trough a linear system, we propose a new approach based on the hypothesis…
We wish to test whether a real-valued variable $Z$ has explanatory power, in addition to a multivariate variable $X$, for a binary variable $Y$. Thus, we are interested in testing the hypothesis $\mathbb{P}(Y=1\, | \, X,Z)=\mathbb{P}(Y=1\,…
Let $\mathbf{X}(n) \in \mathbb{R}^d$ be a sequence of random vectors, where $n\in\mathbb{N}$ and $d = d(n)$. Under certain weakly dependence conditions, we prove that the distribution of the maximal component of $\mathbf{X}$ and the…
A Bayesian belief network is a model of a joint distribution over a finite set of variables, with a DAG structure representing immediate dependencies among the variables. For each node, a table of parameters (CPtable) represents local…
We consider situations where data have been collected such that the sampling depends on the outcome of interest and possibly further covariates, as for instance in case-control studies. Graphical models represent assumptions about the…
We show that there is a general, informative and reliable procedure for discovering causal relations when, for all the investigator knows, both latent variables and selection bias may be at work. Given information about conditional…
We develop a criterion to certify whether causal effects are identifiable in linear structural equation models with latent variables. Linear structural equation models correspond to directed graphs whose nodes represent the random variables…
Real-world problems, for example in climate applications, often require causal reasoning on spatially gridded time series data or data with comparable structure. While the underlying system is often believed to behave similarly at different…
We consider the case when decoherence is due to the fluctuations of some classical variable or parameter of a system and not to its entanglement with the environment. Under few and quite general assumptions, we derive a model-independent…
The general aim of this paper is to supply a method to decide whether a discrete system decoheres or not, and under what conditions decoherence occurs, with no need of appealing to computer simulations to obtain the time evolution of the…
The Contextuality-by-Default (CbD) theory allows one to separate contextuality from context-dependent errors and violations of selective influences (aka "no-signaling" or "no-disturbance" principles). This makes the theory especially…
The title refers to the Free Will Theorem by Conway and Kochen whose flashy formulation is: if experimenters possess free will, then so do particles. In more modest terms, the theorem says that individual pairs of spacelike separated…
Many frameworks exist to infer cause and effect relations in complex nonlinear systems but a complete theory is lacking. A new framework is presented that is fully nonlinear, provides a complete information theoretic disentanglement of…
Causal models with unobserved variables impose nontrivial constraints on the distributions over the observed variables. When a common cause of two variables is unobserved, it is impossible to uncover the causal relation between them without…
One of the common obstacles for learning causal models from data is that high-order conditional independence (CI) relationships between random variables are difficult to estimate. Since CI tests with conditioning sets of low order can be…
The necessary and sufficient conditions for a function to be totally or partially separable are derived. It is shown that a function is totally separable if and only if each component of the gradient vector of depends only on the…
The reduction criterion is a well known necessary condition for separable states, and states violating this condition are entangled and also 1-distillable. In this paper we introduce a new set of necessary conditions for separability of…
Discovery of causal relations is fundamental for understanding the dynamics of complex systems. While causal interactions are well defined for acyclic systems that can be separated into causally effective subsystems, a mathematical…
The estimator of a causal directed acyclic graph (DAG) with the PC algorithm is known to be consistent based on independent and identically distributed samples. In this paper, we consider the scenario when the multivariate samples are…