Granger-causality meets causal inference in graphical models: Learning networks via non-invasive observations

Dimovska, Mihaela; Materassi, Donatello

doi:10.1109/cdc.2017.8264438

Cited by 11 publications

(12 citation statements)

References 29 publications

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“…Linear Dynamic Influence Models (LDIMs) are a class of networks representing input/output relations among stochastic processes Materassi and Salapaka (2012); Dimovska and Materassi (2017). Definition 7.…”

Section: Generative Class Of Network: Linear Dynamic Influence Modelsmentioning

confidence: 99%

“…Furthermore, even if the output is correct, these methods do not certify its correctness. On the other hand, there are methods, such as Runge et al (2015); Dimovska and Materassi (2017) that borrow tools from the theory of causal inference in graphical models Pearl (2009); Spirtes et al (2000). Even though these methods still cannot certify the correctness of their output, c IFAC 2020.…”

Section: Introductionmentioning

confidence: 99%

“…Even though these methods still cannot certify the correctness of their output, c IFAC 2020. Accepted for publication at the 21st International Federation of Automatic Control (IFAC) World Congress, Berlin, Germany, July 12-17, 2020. some of them have the attractive feature of guaranteeing no false positives Dimovska and Materassi (2017). Guaranteeing that there are also no false negatives in the recovered network topology is a more challenging task.…”

Section: Introductionmentioning

confidence: 99%

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An algorithm for reconstruction of triangle-free linear dynamic networks with verification of correctness

Dimovska,

Materassi

2020

Preprint

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Reconstructing a network of dynamic systems from observational data is an active area of research. Many approaches guarantee a consistent reconstruction under the relatively strong assumption that the network dynamics is governed by strictly causal transfer functions. However, in many practical scenarios, strictly causal models are not adequate to describe the system and it is necessary to consider models with dynamics that include direct feedthrough terms. In presence of direct feedthroughs, guaranteeing a consistent reconstruction is a more challenging task. Indeed, under no additional assumptions on the network, we prove that, even in the limit of infinite data, any reconstruction method is susceptible to inferring edges that do not exist in the true network (false positives) or not detecting edges that are present in the network (false negative). However, for a class of triangle-free networks introduced in this article, some consistency guarantees can be provided. We present a method that either exactly recovers the topology of a triangle-free network certifying its correctness or outputs a graph that is sparser than the topology of the actual network, specifying that such a graph has no false positives, but there are false negatives.

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Section: Generative Class Of Network: Linear Dynamic Influence Modelsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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An algorithm for reconstruction of triangle-free linear dynamic networks with verification of correctness

Dimovska,

Materassi

2020

Preprint

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“…In this work we develop our results for a class of dynamic stochastic networks called Linear Dynamic Influence Models (LDIMs), which have been extensively studied [17], [19], [20]. These networks can be considered as a special case of Dynamic Structure Function [9] with unknown (not measured) forcing signals that are modeled as mutually independent stochastic processes.…”

Section: Background and Problem Statementmentioning

confidence: 99%

“…Many network reconstruction methods that take into account the presence of direct feedthroughs are susceptible to inferring both false positive and false negative edges in the reconstructed network [13]- [15]. However, there are a few methods, designed for static [16] or dynamic systems [8], [17] that provide guarantees to obtain no false positives under the assumption that there are no algebraic loops in the networks. This article illustrates how the inference of false negatives is more delicate.…”

Section: Introductionmentioning

confidence: 99%

A brief explanation of the issue of faithfulness and link orientation in network reconstruction

Dimovska

Materassi

2019

2019 American Control Conference (ACC)

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Networked dynamic systems are often abstracted as directed graphs, where the observed system processes form the vertex set and directed edges are used to represent nonzero transfer functions. Recovering the exact underlying graph structure of such a networked dynamic system, given only observational data, is a challenging task. Under relatively mild well-posedness assumptions on the network dynamics, there are state-of-the-art methods which can guarantee the absence of false positives. However, in this article we prove that under the same well-posedness assumptions, there are instances of networks for which any method is susceptible to inferring false negative edges or false positive edges. Borrowing a terminology from the theory of graphical models, we say those systems are unfaithful to their networks. We formalize a variant of faithfulness for dynamic systems, called Granger-faithfulness, and for a large class of dynamic networks, we show that Granger-unfaithful systems constitute a Lebesgue zero-measure set. For the same class of networks, under the Granger-faithfulness assumption, we provide an algorithm that reconstructs the network topology with guarantees for no false positive and no false negative edges in its output. We augment the topology reconstruction algorithm with orientation rules for some of the inferred edges, and we prove the rules are consistent under the Granger-faithfulness assumption.

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Topology identification under spatially correlated noise

Veedu¹,

Salapaka²

2023

Automatica

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Granger-causality meets causal inference in graphical models: Learning networks via non-invasive observations

Cited by 11 publications

References 29 publications

An algorithm for reconstruction of triangle-free linear dynamic networks with verification of correctness

An algorithm for reconstruction of triangle-free linear dynamic networks with verification of correctness

A brief explanation of the issue of faithfulness and link orientation in network reconstruction

Topology identification under spatially correlated noise

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