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Engineered infrastructure systems pose inverse problems in which hidden states, unknown parameters, and subsystem couplings must be inferred from sparse and noisy measurements. These problems are difficult because physical subsystems are…

The quantification of aleatoric and epistemic uncertainty in terms of conditional entropy and mutual information, respectively, has recently become quite common in machine learning. While the properties of these measures, which are rooted…

The description of the dynamics of complex systems, in particular the capture of the interaction structure and causal relationships between elements of the system, is one of the central questions of interdisciplinary research. While the…

We investigate the Peres-Horodecki positive partial transpose (PPT) criterion in the context of conserved quantities and derive a condition of in- separability for a composite bipartite system depending only on the dimen- sions of its…

We derive a collection of separability conditions for bipartite systems of dimensions d X d which is based on the entropic version of the uncertainty relations. A detailed analysis of the two-qubit case is given by comparing the new…

Entropic causal inference is a recent framework for learning the causal graph between two variables from observational data by finding the information-theoretically simplest structural explanation of the data, i.e., the model with smallest…

We provide a method for witnessing nonseparability of quantum processes on shared systems, which uses the channel-state duality. The method uses a maximally entangled state as a resource. We show that using the resource provides significant…

Nonseparability - multipartite states that cannot be factorized - is one of the most striking features of quantum mechanics, as it gives rise to entanglement and non-causal correlations. In quantum computing, it also contributes directly to…

We study bipartite entanglement in systems of N identical bosons distributed in M different modes. For such systems, a definition of separability not related to any a priori Hilbert space tensor product structure is needed and can be given…

Clustering evaluation measures are frequently used to evaluate the performance of algorithms. However, most measures are not properly normalized and ignore some information in the inherent structure of clusterings. We model the relation…

We study which outcomes are implementable by disclosing coarse statistics of a data-generating process rather than its full distribution. Players observe data whose joint distribution is only partially known: they know the expectations of…

Maximum entropy estimation is of broad interest for inferring properties of systems across many different disciplines. In this work, we significantly extend a technique we previously introduced for estimating the maximum entropy of a set of…

A special feature of the ground state in a topologically ordered phase is the existence of large scale correlations depending only on the topology of the regions. These correlations can be detected by the topological entanglement entropy or…

In statistical physics entropy is usually introduced as a global quantity which expresses the amount of information that would be needed to specify the microscopic configuration of a system. However, for lattice models with infinitely many…

Attempts to replicate probabilistic reasoning in expert systems have typically overlooked a critical ingredient of that process. Probabilistic analysis typically requires extensive judgments regarding interdependencies among hypotheses and…

Biochemistry, ecology, and neuroscience are examples of prominent fields aiming at describing interacting systems that exhibit non-trivial couplings to complex, ever-changing environments. We have recently shown that linear interactions and…

This paper examines networks of $n$ measuring parties sharing $m$ nonsignaling resources that can be locally wired together: that is, each party follows a scheme to measure the resources in a cascaded fashion with inputs to later resources…

Following on from the notion of (first-order) causality, which generalises the notion of being tracepreserving from CP-maps to abstract processes, we give a characterization for the most general kind of map which sends causal processes to…

Characterizing the entropy of a system is a crucial, and often computationally costly, step in understanding its thermodynamics. It plays a key role in the study of phase transitions, pattern formation, protein folding and more. Current…

We discuss a general Bayesian framework on modeling multidimensional function-valued processes by using a Gaussian process or a heavy-tailed process as a prior, enabling us to handle nonseparable and/or nonstationary covariance structure.…