7 research outputs found
Monotone Regression: A Simple and Fast O(n) PAVA Implementation
Efficient coding and improvements in the execution order of the up-and-down-blocks algorithm for monotone or isotonic regression leads to a significant increase in speed as well as a short and simple O(n) implementation. Algorithms that use monotone regression as a subroutine, e.g., unimodal or bivariate monotone regression, also benefit from the acceleration. A substantive comparison with and characterization of currently available implementations provides an extensive overview of up-and-down-blocks implementations for the pool-adjacent-violators algorithm for simple linear ordered monotone regression
How to Certify Machine Learning Based Safety-critical Systems? A Systematic Literature Review
Context: Machine Learning (ML) has been at the heart of many innovations over
the past years. However, including it in so-called 'safety-critical' systems
such as automotive or aeronautic has proven to be very challenging, since the
shift in paradigm that ML brings completely changes traditional certification
approaches.
Objective: This paper aims to elucidate challenges related to the
certification of ML-based safety-critical systems, as well as the solutions
that are proposed in the literature to tackle them, answering the question 'How
to Certify Machine Learning Based Safety-critical Systems?'.
Method: We conduct a Systematic Literature Review (SLR) of research papers
published between 2015 to 2020, covering topics related to the certification of
ML systems. In total, we identified 217 papers covering topics considered to be
the main pillars of ML certification: Robustness, Uncertainty, Explainability,
Verification, Safe Reinforcement Learning, and Direct Certification. We
analyzed the main trends and problems of each sub-field and provided summaries
of the papers extracted.
Results: The SLR results highlighted the enthusiasm of the community for this
subject, as well as the lack of diversity in terms of datasets and type of
models. It also emphasized the need to further develop connections between
academia and industries to deepen the domain study. Finally, it also
illustrated the necessity to build connections between the above mention main
pillars that are for now mainly studied separately.
Conclusion: We highlighted current efforts deployed to enable the
certification of ML based software systems, and discuss some future research
directions.Comment: 60 pages (92 pages with references and complements), submitted to a
journal (Automated Software Engineering). Changes: Emphasizing difference
traditional software engineering / ML approach. Adding Related Works, Threats
to Validity and Complementary Materials. Adding a table listing papers
reference for each section/subsection
Optimal Permutation Estimation in Crowd-Sourcing problems
Motivated by crowd-sourcing applications, we consider a model where we have
partial observations from a bivariate isotonic n x d matrix with an unknown
permutation * acting on its rows. Focusing on the twin problems of
recovering the permutation * and estimating the unknown matrix, we
introduce a polynomial-time procedure achieving the minimax risk for these two
problems, this for all possible values of n, d, and all possible sampling
efforts. Along the way, we establish that, in some regimes, recovering the
unknown permutation * is considerably simpler than estimating the matrix
MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications
Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described
Generalized averaged Gaussian quadrature and applications
A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal