Uncertainty Propagation Using Probabilistic Affine Forms and Concentration of Measure Inequalities

  • Olivier Bouissou
  • Eric Goubault
  • Sylvie Putot
  • Aleksandar Chakarov
  • Sriram SankaranarayananEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9636)


We consider the problem of reasoning about the probability of assertion violations in straight-line, nonlinear computations involving uncertain quantities modeled as random variables. Such computations are quite common in many areas such as cyber-physical systems and numerical computation. Our approach extends probabilistic affine forms, an interval-based calculus for precisely tracking how the distribution of a given program variable depends on uncertain inputs modeled as noise symbols. We extend probabilistic affine forms using the precise tracking of dependencies between noise symbols combined with the expectations and higher order moments of the noise symbols. Next, we show how to prove bounds on the probabilities that program variables take on specific values by using concentration of measure inequalities. Thus, we enable a new approach to this problem that explicitly avoids subdividing the domain of inputs, as is commonly done in the related work. We illustrate the approach in this paper on a variety of challenging benchmark examples, and thus study its applicability to uncertainty propagation.


Chromatic Number Interval Arithmetic Measure Inequality High Order Moment Cumulative Density Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



This work was partially supported by the US NSF under award number 1320069, and the academic research chair “Complex Systems Engineering” of Ecole polytechnique, Thalès, FX, DGA, Dassault Aviation, DCNS Research, ENSTA ParisTech, Télécom ParisTech, Fondation ParisTech and FDO ENSTA. All opinions involved are those of the authors and not necessarily of our sponsors.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Olivier Bouissou
    • 2
  • Eric Goubault
    • 1
  • Sylvie Putot
    • 1
  • Aleksandar Chakarov
    • 3
  • Sriram Sankaranarayanan
    • 3
    Email author
  1. 1.LIX, Ecole Polytechnique, CNRSUniversité Paris-SaclayParis-SaclayFrance
  2. 2.CEA, LISTGif-sur-YvetteFrance
  3. 3.University of ColoradoBoulderUSA

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