1,250 research outputs found
Advances in Polynomial Optimization
Polynomial optimization has a wide range of practical applications in fields
such as optimal control, energy and water networks, facility location, management science, and finance. It also
generalizes relevant optimization problems thoroughly studied in the literature, such as mixed-binary linear
optimization, quadratic optimization, and complementarity problems. As finding globally optimal solutions is an
extremely challenging task, the development of efficient techniques for solving polynomial optimization problems is
of particular relevance. In this thesis we provide a detailed study of different techniques to solve this kind of
problems and we introduce some nobel approaches in this field, including the use of statistical learning techniques.
Furthermore, we also present a practical application of polynomial optimization to finance and more specifically,
portfolio design
Distributional Regression for Data Analysis
Flexible modeling of how an entire distribution changes with covariates is an
important yet challenging generalization of mean-based regression that has seen
growing interest over the past decades in both the statistics and machine
learning literature. This review outlines selected state-of-the-art statistical
approaches to distributional regression, complemented with alternatives from
machine learning. Topics covered include the similarities and differences
between these approaches, extensions, properties and limitations, estimation
procedures, and the availability of software. In view of the increasing
complexity and availability of large-scale data, this review also discusses the
scalability of traditional estimation methods, current trends, and open
challenges. Illustrations are provided using data on childhood malnutrition in
Nigeria and Australian electricity prices.Comment: Accepted for publication in Annual Review of Statistics and its
Applicatio
Bayesian subset simulation
We consider the problem of estimating a probability of failure ,
defined as the volume of the excursion set of a function above a given threshold, under a given
probability measure on . In this article, we combine the popular
subset simulation algorithm (Au and Beck, Probab. Eng. Mech. 2001) and our
sequential Bayesian approach for the estimation of a probability of failure
(Bect, Ginsbourger, Li, Picheny and Vazquez, Stat. Comput. 2012). This makes it
possible to estimate when the number of evaluations of is very
limited and is very small. The resulting algorithm is called Bayesian
subset simulation (BSS). A key idea, as in the subset simulation algorithm, is
to estimate the probabilities of a sequence of excursion sets of above
intermediate thresholds, using a sequential Monte Carlo (SMC) approach. A
Gaussian process prior on is used to define the sequence of densities
targeted by the SMC algorithm, and drive the selection of evaluation points of
to estimate the intermediate probabilities. Adaptive procedures are
proposed to determine the intermediate thresholds and the number of evaluations
to be carried out at each stage of the algorithm. Numerical experiments
illustrate that BSS achieves significant savings in the number of function
evaluations with respect to other Monte Carlo approaches
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