A geometric characterisation of sensitivity analysis in monomial models

Leonelli, Manuele; Riccomagno, Eva

doi:10.48550/arxiv.1901.02058

Cited by 3 publications

(4 citation statements)

References 23 publications

(54 reference statements)

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“…Proportional covariation has been studied extensively and its choice is motivated by a wide array of theoretical properties (Chan and Darwiche, 2005;Leonelli et al, 2017;Leonelli and Riccomagno, 2018).…”

Section: Proportional Covariationmentioning

confidence: 99%

You Only Derive Once (YODO): Automatic Differentiation for Efficient Sensitivity Analysis in Bayesian Networks

Ballester-Ripoll¹,

Leonelli²

2022

Preprint

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Sensitivity analysis measures the influence of a Bayesian network's parameters on a quantity of interest defined by the network, such as the probability of a variable taking a specific value. In particular, the so-called sensitivity value measures the quantity of interest's partial derivative with respect to the network's conditional probabilities. However, finding such values in large networks with thousands of parameters can become computationally very expensive. We propose to use automatic differentiation combined with exact inference to obtain all sensitivity values in a single pass. Our method first marginalizes the whole network once using e.g. variable elimination and then backpropagates this operation to obtain the gradient with respect to all input parameters. We demonstrate our routines by ranking all parameters by importance on a Bayesian network modeling humanitarian crises and disasters, and then show the method's efficiency by scaling it to huge networks with up to 100'000 parameters. An implementation of the methods using the popular machine learning library PyTorch is freely available.

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Section: Proportional Covariationmentioning

confidence: 99%

You Only Derive Once (YODO): Automatic Differentiation for Efficient Sensitivity Analysis in Bayesian Networks

Ballester-Ripoll¹,

Leonelli²

2022

Preprint

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“…Both the LL and the QLL models are examples of so-called regular multiliear monomial models (cf. Leonelli & Riccomagno, 2018). A model closely related to the HAS independence on two features was considered in Leonelli & Riccomagno (2018), Example 1.…”

Section: Geometric Viewmentioning

confidence: 99%

“…Leonelli & Riccomagno, 2018). A model closely related to the HAS independence on two features was considered in Leonelli & Riccomagno (2018), Example 1. In their terminology, HAS models belong to the class of monomial discrete parametric models.…”

Section: Geometric Viewmentioning

confidence: 99%

Hierarchical Aitchison-Silvey models for incomplete binary sample spaces

Klimová¹,

Rudas²

2020

Preprint

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Multivariate sample spaces may be incomplete Cartesian products, when certain combinations of the categories of the variables are not possible. Traditional log-linear models, which generalize independence and conditional independence, do not apply in such cases, as they may associate positive probabilities with the non-existing cells. To describe the association structure in incomplete sample spaces, this paper develops a class of hierarchical multiplicative models which are defined by setting certain nonhomogeneous generalized odds ratios equal to one and are named after Aitchison and Silvey who were among the first to consider such ratios. These models are curved exponential families that do not contain an overall effect and, from an algebraic perspective, are non-homogeneous toric ideals. The relationship of this model class with log-linear models and quasi log-linear models is studied in detail in terms of both statistics and algebraic geometry. The existence of maximum likelihood estimates and their properties, as well as the relevant algorithms are also discussed.

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“…Multi-way sensitivity analyses, where more than one parameter is varied contemporaneously, have been proposed (e.g. Bolt andRenooij 2014, Chan andDarwiche 2004, Kjaerulff and van der Gaag 2000, Leonelli et al 2017, Leonelli andRiccomagno 2019). However, these quickly become computationally intractable.…”

Section: Introductionmentioning

confidence: 99%

Global sensitivity analysis in probabilistic graphical models

Ballester-Ripoll,

Leonelli

2021

Preprint

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We show how to apply Sobol's method of global sensitivity analysis to measure the influence exerted by a set of nodes' evidence on a quantity of interest expressed by a Bayesian network. Our method exploits the network structure so as to transform the problem of Sobol index estimation into that of marginalization inference. This way, we can efficiently compute indices for networks where brute-force or Monte Carlo based estimators for variance-based sensitivity analysis would require millions of costly samples. Moreover, our method gives exact results when exact inference is used, and also supports the case of correlated inputs.The proposed algorithm is inspired by the field of tensor networks, and generalizes earlier tensor sensitivity techniques from the acyclic to the cyclic case. We demonstrate the method on three medium to large Bayesian networks that cover the areas of project risk management and reliability engineering.

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A geometric characterisation of sensitivity analysis in monomial models

Cited by 3 publications

References 23 publications

You Only Derive Once (YODO): Automatic Differentiation for Efficient Sensitivity Analysis in Bayesian Networks

You Only Derive Once (YODO): Automatic Differentiation for Efficient Sensitivity Analysis in Bayesian Networks

Hierarchical Aitchison-Silvey models for incomplete binary sample spaces

Global sensitivity analysis in probabilistic graphical models

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