Sparse randomized shortest paths routing with Tsallis divergence regularization

Leleux, Pierre; Courtain, Sylvain; Guex, Guillaume; Saerens, Marco

doi:10.1007/s10618-021-00742-y

Cited by 8 publications

(4 citation statements)

References 82 publications

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“…In addition, most of these different quantities derived from the RSP can easily be computed in closed form by using standard linear algebraic operations such as solving systems of linear equations or computing a matrix inverse. For a more thorough related work concerning the RSP framework, see for instance (Guex et al 2019, Leleux et al 2021.…”

Section: Related Workmentioning

confidence: 99%

Sensitivity to network perturbations in the randomized shortest paths framework: theory and applications in ecological connectivity

Kivimäki,

Van Moorter,

Saerens

2024

J. Phys. Complex.

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The Randomized Shortest Paths (RSP) framework, developed for network analysis, extends traditional proximity and distance measures between two nodes, such as shortest path distance and commute cost distance (related to resistance distance). Consequently, the RSP framework has gained popularity in studies on landscape connectivity within ecology and conservation, where the behavior of animals is neither random nor optimal.In this work, we study how local perturbations in a network affect proximity and distance measures derived from the RSP framework. For this sensitivity analysis, we develop computable expressions for derivatives with respect to weights on the edges or nodes of the network. Interestingly, the sensitivity of expected cost to edge or node features provides a new signed network centrality measure, the negative covariance between edge/node visits and path cost, that can be used for pinpointing strong and weak parts of a network. It is also shown that this quantity can be interpreted as minus the endured expected detour (in terms of cost) when constraining the walk to pass through the node or the edge.Our demonstration of this framework focuses on a migration corridor for wild reindeer (Rangifer rangifer) in Southern Norway. By examining the sensitivity of the expected cost of movement between winter and calving ranges to perturbations in local areas, we have identified priority areas crucial for the conservation of this migration corridor. This innovative approach not only holds great promise for conservation and restoration of migration corridors, but also more generally for connectivity corridors between important areas for biodiversity (e.g. protected areas) and climate adaptation. Furthermore, the derivations and computational methods introduced in this work present fundamental features of the RSP framework. These contributions are expected to be of interest to practitioners applying the framework across various disciplines, ranging from ecology, transport and communication networks to machine learning.

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Section: Related Workmentioning

confidence: 99%

Sensitivity to network perturbations in the randomized shortest paths framework: theory and applications in ecological connectivity

Kivimäki,

Van Moorter,

Saerens

2024

J. Phys. Complex.

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“…This formalism is based on full paths instead of standard "local" flows [1], and was initially inspired by a model developed in transportation science [2]. We start by providing a brief description (closely following [8,31]) of the RSP formalism before defining the problem and then deriving the algorithm for solving the constraints-based multi-inputs multi-outputs transport problem on the graph G ext .…”

Section: The Adjacency Matrix Of the Extended Graphmentioning

confidence: 99%

“…For the sake of completeness, this appendix introduces some important quantities that can be derived from the standard randomized shortest paths framework, and is largely inspired by [8,31]. These quantities of interest can be computed by taking the partial derivative of the optimal free energy (see [15,16,28,38,53] for details).…”

Section: B Computing Quantities Of Interest From the Rsp Modelmentioning

confidence: 99%

Relative Entropy-Regularized Optimal Transport on a Graph: a new algorithm and an experimental comparison

Courtain¹,

Guex²,

Kivimäki³

et al. 2021

Preprint

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Following [21,23], the present work investigates a new relative entropyregularized algorithm for solving the optimal transport on a graph problem 1 within the randomized shortest paths formalism. More precisely, a unit flow is injected into a set of input nodes and collected from a set of output nodes while minimizing the expected transportation cost together with a paths relative entropy regularization term, providing a randomized routing policy. The main advantage of this new formulation is the fact that it can easily accommodate edge flow capacity constraints which commonly occur in real-world problems. The resulting optimal routing policy, i.e., the probability distribution of following an edge in each node, is Markovian and is computed by constraining the input and output flows to the prescribed marginal probabilities thanks to a variant of the algorithm developed in [8]. Besides, experimental comparisons with other recently developed techniques show that the distance measure between nodes derived from the introduced model provides competitive results on semi-supervised classification tasks.

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“…The Tsallis formalism for risk assessment has become a popular approach owing to its greater flexibility than classical entropic approaches and its close relationship to physical phenomena and efficient machine learning schemes (Cao et al, 2019; Kumbhakar & Tsai, 2022; Leleux et al, 2021; Ma & Tian, 2021). In this paper, we use the Tsallis value‐at‐risk (TsVaR) (Zou et al, 2022) as a recently introduced generalization of the EVaR.…”

Section: Introductionmentioning

confidence: 99%

Statistical evaluation of a long‐memory process using the generalized entropic value‐at‐risk

Yoshioka,

Yoshioka

2023

Environmetrics

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The modeling and identification of time series data with a long memory are important in various fields. The streamflow discharge is one such example that can be reasonably described as an aggregated stochastic process of randomized affine processes where the probability measure, we call it reversion measure, for the randomization is not directly observable. Accurate identification of the reversion measure is critical because of its omnipresence in the aggregated stochastic process. However, the modeling accuracy is commonly limited by the available real‐world data. We resolve this issue by proposing the novel upper and lower bounds of a statistic of interest subject to ambiguity of the reversion measure. Here, we use the Tsallis value‐at‐risk (TsVaR) as a convex risk functional to generalize the widely used entropic value‐at‐risk (EVaR) as a sharp statistical indicator. We demonstrate that the EVaR cannot be used for evaluating key statistics, such as mean and variance, of the streamflow discharge due to the blowup of some exponential integrand. We theoretically show that the TsVaR can avoid this issue because it requires only the existence of some polynomial moment, not exponential moment. As a demonstration, we apply the semi‐implicit gradient descent method to calculate the TsVaR and corresponding Radon–Nikodym derivative for time series data of actual streamflow discharges in mountainous river environments.

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Sparse randomized shortest paths routing with Tsallis divergence regularization

Cited by 8 publications

References 82 publications

Sensitivity to network perturbations in the randomized shortest paths framework: theory and applications in ecological connectivity

Sensitivity to network perturbations in the randomized shortest paths framework: theory and applications in ecological connectivity

Relative Entropy-Regularized Optimal Transport on a Graph: a new algorithm and an experimental comparison

Statistical evaluation of a long‐memory process using the generalized entropic value‐at‐risk

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