The lecture will give a brief introduction to graphical models, their origins in Physics, Genetics, and Econometrics, their modern usages, and some future perspectives.
"Imsets, introduced by Studený (see Studený, 2005 for details), are an algebraic method for representing conditional independence models. They have many attractive properties when applied to such models, and they are particularly nice when applied to directed acyclic graph (DAG) models. In particular, the standard imset for a DAG is in one-to-one correspondence with the independence model it...
Quantum measurements have been a central topic of research in quantum theory for many years. In the context of causal structures and communication over networks, we are often particularly interested in local measurements of subsystems of a multi-partite system and classical processing of their inputs and outcomes. Formally, this processing can often be described by means of maps that are known...
"If one only performs experiments involving passive observations, in general there are multiple causal structures that can explain the same set of distributions over the observed variables. In this case, we say that these causal structures are observationally equivalent. In this work, we explore all the known techniques for proving observational equivalence or inequivalence, as well as some...
When some variables in a directed acyclic graph (DAG) are hidden, a notoriously complicated set of constraints on the distribution of observed variables is implied. In this talk, we present inequality constraints implied by graphical criteria in hidden variable DAGs. The constraints can intuitively be understood to follow from the fact that the capacity of variables along a causal pathway to...
"Quantum computing requires the ability to manipulate large nonclassical quantum systems. As we are far from any useful quantum computing advantage, certifying this ability is an important benchmark to assess progress toward this goal. This can be done using the nonlocal nature of quantum correlations, which allows to certify a non-trusted experimental apparatus from its input/output behaviour...
Quantum nonlocal correlations are generated by implementation of local quantum measurements on spatially separated quantum subsystems. Depending on the underlying mathematical model and the dimension of the underlying Hilbert spaces, various notions of sets of quantum correlations can be defined. This talk is devoted to the separations of some of these sets via simple ideas in quantum...
I will sketch the current state of play with classifying causal scenarios (aka DAGs with latent variables). Some are interesting: the classical correlations are constrained by non-trivial inequalities such as Bell’s. Some are boring: the classical correlations are constrained only by observable conditional independencies. Some we still don’t know. Along the way I will mention joint work with...
Distinguishing causation from correlation from observational data requires assumptions. We consider the setting where the unobserved confounder between two observed variables is simple in an information-theoretic sense, captured by its entropy. When the observed dependence is not due to causation, there exists a small-entropy variable that can make the observed variables conditionally...
Quantum causality is an emerging field of study which has the potential to greatly advance our understanding of quantum systems. In this paper, we put forth a theoretical framework for merging quantum information science and causal inference by exploiting entropic principles. For this purpose, we leverage the tradeoff between the entropy of hidden cause and the conditional mutual information...
According to recent new definitions, a multi-party behavior is genuinely multipartite nonlocal (GMNL) if it cannot be modeled by measurements on an underlying network of bipartite-only nonlocal resources, possibly supplemented with local (classical) resources shared by all parties. Three experimental results published in 2022 provide initial evidence, subject to postselection-related...
"Many relationships in causality, statistics or probability theory can be expressed as conditional independence relations between the occurring random variables. Since the invention of the notion of conditional independence one aim was to be able to also express such relationship between random and non-random variables, like the parameters of a stochastic model, the input variables of a...
Explaining the natural world through cause-and-effect relations is the fundamental principle of science. Although a classical theory of causality has been recently introduced, enabling us to model causation across diverse research fields, it is crucial to examine which aspects of it require modification or abandonment to also comprehend causality in the quantum world. To address this question,...
We investigate the problem of bounding counterfactual queries from an arbitrary collection of observational and experimental distributions and qualitative knowledge about the underlying data-generating model represented in the form of a causal diagram. We show that all counterfactual distributions in an arbitrary structural causal model (SCM) with finite discrete endogenous variables could be...
The class of problems in causal inference which seeks to isolate causal correlations solely from observational data even without interventions has come to the forefront of machine learning, neuroscience and social sciences. As new large scale quantum systems go online, it opens interesting questions of whether a quantum framework exists on isolating causal correlations without any...
For binary instrumental variable models, there seems to be a long-standing gap between two sets of bounds on the average treatment effect: the stronger Balke–Pearl ("sharp") bounds versus the weaker Robins–Manski ("natural") bounds. In the literature, the Balke–Pearl bounds are typically derived under stronger assumptions, i.e., either individual exclusion or joint exogeneity, which are...
"Is there a complete semi-definite programming hierarchy for quantum causal problems? We divide the question into two parts. First: Can quantum causal problems be expressed as polynomial optimization problems (this talk). Second: Can this class of polynomial optimizations be solved by means of SDPs (Laurens' talk). The optimizations we consider here are ""polynomial"" in two ways. They are...
"Many relevant tasks in Quantum Information processing can be expressed as polynomial optimization problems over states and operators. In the earlier talk by David, we saw that this is also the case for certain (quantum) causal compatibility and causal optimization problems.
This talk will focus on several closely related semidefinite programming (SDP) hierarchies that have recently been...
In a recent paper, Chaturvedi et al considered the interesting idea of routed Bell experiments. These are Bell experiments where Bob can measure his quantum particles at two distinct locations, one close to the source and another far away. This can be accomplished in the lab by using a switch that directs Bob's quantum particle either to the nearby measurement device or to the distant one,...
There has been recent interest in extending the concept of contextuality to cases of disturbance or inconsistent connectedness. This talk will describe an approach using probabilistic causal models, which generalize the hidden-variables models of Bell and Kochen & Specker, following recent work by Cavalcanti. I first prove an equivalence between three conditions on an arbitrary measurement...
"Linear structural equation models relate random variables of interest via a linear equation system that features stochastic noise. The models are naturally represented by directed graphs whose edges indicate non-zero coefficients in the linear equations. In this talk I will report on progress on combinatorial conditions for parameter identifiability in models with latent (i.e., unobserved)...
Causal reasoning is vital for effective reasoning in many domains, from healthcare to economics. In medical diagnosis, for example, a doctor aims to explain a patient’s symptoms by determining the diseases causing them. This is because causal relations, unlike correlations, allow one to reason about the consequences of possible treatments and to answer counterfactual queries. In this talk I...
