Related papers: Classifying Causal Structures: Ascertaining when C…
Causal models have proven extremely useful in offering formal representations of causal relationships between a set of variables. Yet in many situations, there are non-causal relationships among variables. For example, we may want variables…
An active area of research in the fields of machine learning and statistics is the development of causal discovery algorithms, the purpose of which is to infer the causal relations that hold among a set of variables from the correlations…
Explaining observations in terms of causes and effects is central to all of empirical science. Correlations between entangled quantum particles, however, seem to defy such an explanation. To recover a causal picture in this case, some of…
We present a class of inequality constraints on the set of distributions induced by local interventions on variables governed by a causal Bayesian network, in which some of the variables remain unmeasured. We derive bounds on causal effects…
The strength of classical correlations is subject to certain constraints, commonly known as Bell inequalities. Violation of these inequalities is the manifestation of nonlocality---displayed, in particular, by quantum mechanics, meaning…
We generalize the classical probability frame by adopting a wider family of random variables that includes nondeterministic ones. The frame that emerges is known to host a ''classical'' extension of quantum mechanics. We discuss the notion…
Causal inequalities are bounds on correlations obtained when operations take place in a causal sequence, i.e. in which the background time or definite causal structure pre-exists such that every operation is either in the future, in the…
In a Bell experiment, it is natural to seek a causal account of correlations wherein only a common cause acts on the outcomes. For this causal structure, Bell inequality violations can be explained only if causal dependencies are modelled…
We provide an interpretation of entanglement based on classical correlations between measurement outcomes of complementary properties: states that have correlations beyond a certain threshold are entangled. The reverse is not true, however.…
Bell's theorem shows that our intuitive understanding of causation must be overturned in light of quantum correlations. Nevertheless, quantum mechanics does not permit signalling and hence a notion of cause remains. Understanding this…
It is well-known that if one assumes quantum theory to hold locally, then processes with indefinite causal order and cyclic causal structures become feasible. Here, we study qualitative limitations on causal structures and correlations…
Instrumental variables allow for quantification of cause and effect relationships even in the absence of interventions. To achieve this, a number of causal assumptions must be met, the most important of which is the independence assumption,…
We investigate the possibility of distinguishing among different causal relations starting from a limited set of marginals. Our main tool is the notion of adhesivity, that is, the extension of probability or entropies defined only on…
Bell's inequalities can be understood in three different ways depending on whether the numbers featuring in the inequalities are interpreted as classical probabilities, classical conditional probabilities, or quantum probabilities. In the…
Prior work has shown that causal structure can be uniquely identified from observational data when these follow a structural equation model whose error terms have equal variances. We show that this fact is implied by an ordering among…
Causal Structure Learning (CSL), also referred to as causal discovery, amounts to extracting causal relations among variables in data. CSL enables the estimation of causal effects from observational data alone, avoiding the need to perform…
From behavioral sciences to biology to quantum mechanics, one encounters situations where (i) a system outputs several random variables in response to several inputs, (ii) for each of these responses only some of the inputs may "directly"…
Causal knowledge is vital for effective reasoning in science, as causal relations, unlike correlations, allow one to reason about the outcomes of interventions. Algorithms that can discover causal relations from observational data are based…
The presence of latent variables can greatly complicate inferences about causal relations between measured variables from statistical data. In many cases, the presence of latent variables makes it impossible to determine for two measured…
The frame of classical probability theory can be generalized by enlarging the usual family of random variables in order to encompass nondeterministic ones: this leads to a frame in which two kinds of correlations emerge: the classical…