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:
194.
Step-by-step explanation:
x = (7+4√3)
x^2 = x = (7+4√3)^2
= 49 + 48 + 56√3
= 97 + 56√3
x^2 + 1/x^2 = 97 + 56√3 + 1/(97 + 56√3)
= 194.
Answer:
<em>q</em> = 12<em>x</em>
Step-by-step explanation:
<em>q</em> = 3<em>x</em> + 9<em>x</em>
Combine like terms
<em>q</em> = 12<em>x</em>
Answer:
Step-by-step explanation:
One is given the following expression:
In order to simplify and solve this problem, one must keep the following points in mind: the square root function (
) is a way of requesting one to find what number times itself equals the number underneath the radical sign. One must also remember the function of taking the square root of a negative number. Remember the following property: (
). Simplify the given equation. Factor each of the terms and rewrite the equation. Use the square root property to simplify the radicals and perform operations between them.
Take factors from out of under the radical:
Simplify,
The standard deviation is 4 games
A standard deviation (or σ) is a measure of how dispersed the facts are in relation to the mean. Low general deviation method statistics are clustered around the imply, and excessive trendy deviation indicates facts are more unfold.
Don't forget the statistics set: 2, 1, 3, 2, four. The mean and the sum of squares of deviations of the observations from the mean will be 2. 4 and 5.2, respectively. as a consequence, the same standard deviation could be √(5.2/5) = 1.01.
In data, the same old deviation is a degree of the quantity of variant or dispersion of a set of values. A low preferred deviation indicates that the values tend to be close to the mean of the set, while a high general deviation shows that the values unfold out over a much broader variety.
Given that,
mean = μ = 18
standard deviation = Σ = 6
n = 2
μ x = μ = 18 games
√ x = Σ / √ = 6
√2 = 4 games
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