Distributionally robust stochastic programs with side information based on trimmings
This is a research paper whose authors are Adrián Esteban-Pérez and Juan M. Morales.
Abstract:
- We look at stochastic programmes that are conditional on some covariate information, where the only knowledge of the possible relationship between the unknown parameters and the covariates is a limited data sample of their joint distribution. We build a data-driven Distributionally Robust Optimization (DRO) framework to hedge the decision against the inherent error in the process of inferring conditional information from limited joint data by leveraging the close relationship between the notion of trimmings of a probability measure and the partial mass transportation problem.
- We demonstrate that our technique is computationally as tractable as the usual (no side information) Wasserstein-metric-based DRO and provides performance guarantees. Furthermore, our DRO framework may be easily applied to data-driven decision-making issues involving tainted samples. Finally, using a single-item newsvendor problem and a portfolio allocation problem with side information, the theoretical findings are presented.
Conclusions:
- We used the relationship between probability reductions and partial mass transit in this study to give a straightforward, yet powerful and creative technique to expand the usual Wasserstein-metric-based DRO to the situation of conditional stochastic programming. In the process of inferring the conditional probability measure of the random parameters from a limited sample drawn from the genuine joint data-generating distribution, our technique generates judgments that are distributionally resilient to uncertainty. In a series of numerical tests based on the single-item newsvendor issue and a portfolio allocation problem, we proved that our strategy achieves much higher out-of-sample performance than several current options. We backed up these actual findings with theoretical analysis, demonstrating that our strategy had appealing performance guarantees.
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Answer:
62.273
Step-by-step explanation:
sorry it took me a little while to translate i speak only english
Answer:
See Down Here
Step-by-step explanation:
We want to get g(x) given that we know f(x) and the graphs for both functions. We will see that the correct option is D:
g(x) = (x/3)^2
By looking at the graph we can see that f(x) and g(x) are two quadratic functions, and g(x) is just a dilation of f(x).
This means that:
g(x) = A*f(x)
Where A is a real number.
We know that:
f(x) = x^2
And by looking at the graph, we also know that g(3) = 1.
Then we can write:
g(3) = A*f(3) = A*3^2 = 1
Now we can solve this for A:
A*3^2 = 1
A*9 = 1
A = 1/9
Then we have:
g(x) = (1/9)*f(x) = (1/9)*x^2 = (x/3)^2
So the correct option is D.
If you want to learn more about quadratic equations, you can read:
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Answer:
B 68
Step-by-step explanation:
I am pretty sure that if you are looking for perimeter there should only be two sets of numbers but if you are looking for area than the answer would be 212.0625