136 research outputs found
A generalized moment approach to sharp bounds for conditional expectations
In this paper, we address the problem of bounding conditional expectations
when moment information of the underlying distribution and the random event
conditioned upon are given. To this end, we propose an adapted version of the
generalized moment problem which deals with this conditional information
through a simple transformation. By exploiting conic duality, we obtain sharp
bounds that can be used for distribution-free decision-making under
uncertainty. Additionally, we derive computationally tractable mathematical
programs for distributionally robust optimization (DRO) with side information
by leveraging core ideas from ambiguity-averse uncertainty quantification and
robust optimization, establishing a moment-based DRO framework for prescriptive
stochastic programming.Comment: 43 pages, 5 figure
Polyhedral Predictive Regions For Power System Applications
Despite substantial improvement in the development of forecasting approaches,
conditional and dynamic uncertainty estimates ought to be accommodated in
decision-making in power system operation and market, in order to yield either
cost-optimal decisions in expectation, or decision with probabilistic
guarantees. The representation of uncertainty serves as an interface between
forecasting and decision-making problems, with different approaches handling
various objects and their parameterization as input. Following substantial
developments based on scenario-based stochastic methods, robust and
chance-constrained optimization approaches have gained increasing attention.
These often rely on polyhedra as a representation of the convex envelope of
uncertainty. In the work, we aim to bridge the gap between the probabilistic
forecasting literature and such optimization approaches by generating forecasts
in the form of polyhedra with probabilistic guarantees. For that, we see
polyhedra as parameterized objects under alternative definitions (under
and norms), the parameters of which may be modelled and predicted.
We additionally discuss assessing the predictive skill of such multivariate
probabilistic forecasts. An application and related empirical investigation
results allow us to verify probabilistic calibration and predictive skills of
our polyhedra.Comment: 8 page
Distributionally robust L1-estimation in multiple linear regression
Linear regression is one of the most important and widely used techniques in data analysis, for which a key step is the estimation of the unknown parameters. However, it is often carried out under the assumption that the full information of the error distribution is available. This is clearly unrealistic in practice. In this paper, we propose a distributionally robust formulation of L1-estimation (or the least absolute value estimation) problem, where the only knowledge on the error distribution is that it belongs to a well-defined ambiguity set. We then reformulate the estimation problem as a computationally tractable conic optimization problem by using duality theory. Finally, a numerical example is solved as a conic optimization problem to demonstrate the effectiveness of the proposed approach
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