Coverage probability

About: Coverage probability is a research topic. Over the lifetime, 2479 publications have been published within this topic receiving 53259 citations.

Assessing solution quality in stochastic programs

Abstract: Determining whether a solution is of high quality (optimal or near optimal) is fundamental in optimization theory and algorithms. In this paper, we develop Monte Carlo sampling-based procedures for assessing solution quality in stochastic programs. Quality is defined via the optimality gap and our procedures' output is a confidence interval on this gap. We review a multiple-replications procedure that requires solution of, say, 30 optimization problems and then, we present a result that justifies a computationally simplified single-replication procedure that only requires solving one optimization problem. Even though the single replication procedure is computationally significantly less demanding, the resulting confidence interval might have low coverage probability for small sample sizes for some problems. We provide variants of this procedure that require two replications instead of one and that perform better empirically. We present computational results for a newsvendor problem and for two-stage stochastic linear programs from the literature. We also discuss when the procedures perform well and when they fail, and we propose using ɛ-optimal solutions to strengthen the performance of our procedures.

A Stochastic Geometry Analysis of Inter-Cell Interference Coordination and Intra-Cell Diversity

Abstract: Inter-cell interference coordination (ICIC) and intra-cell diversity (ICD) play important roles in improving cellular downlink coverage. By modeling cellular base stations (BSs) as a homogeneous Poisson point process (PPP), this paper provides explicit finite-integral expressions for the coverage probability with ICIC and ICD, taking into account the temporal/spectral correlation of the signal and interference. In addition, we show that, in the high-reliability regime, where the user outage probability goes to zero, ICIC and ICD affect the network coverage in drastically different ways: ICD can provide order gain, whereas ICIC only offers linear gain. In the high-spectral efficiency regime where the SIR threshold goes to infinity, the order difference in the coverage probability does not exist; however, a linear difference makes ICIC a better scheme than ICD for realistic path loss exponents. Consequently, depending on the SIR requirements, different combinations of ICIC and ICD optimize the coverage probability.

Short-Term Wind Speed Interval Prediction Based on Ensemble GRU Model

Abstract: Wind speed interval prediction is playing an increasingly important role in wind power production. The intermittent and fluctuant characteristics of wind power make high-quality prediction interval challenging. In this paper, a novel hybrid model based on a gated recurrent unit neural network and variational mode decomposition is proposed for wind speed interval prediction. Initially, variational mode decomposition is employed to decompose the complex wind speed time series into simplified modes. Interval prediction model and a point prediction model based on a gated recurrent unit neural network are designed to conduct interval prediction in primary mode and point prediction in rest modes, respectively, before the composition and construction of the prediction interval. Then, an error prediction model based on a gated recurrent unit neural network is proposed to enhance the model performance by error correction. Eight cases from two wind fields are used to test and verify the proposed method. The results indicate that the proposed method is a highly qualified method that has a much higher prediction interval coverage probability and narrower prediction interval width.

Conditional validity of inductive conformal predictors

Abstract: Conformal predictors are set predictors that are automatically valid in the sense of having coverage probability equal to or exceeding a given confidence level. Inductive conformal predictors are a computationally efficient version of conformal predictors satisfying the same property of validity. However, inductive conformal predictors have only been known to control unconditional coverage probability. This paper explores various versions of conditional validity and various ways to achieve them using inductive conformal predictors and their modifications. In particular, it discusses a convenient expression of one of the modifications in terms of ROC curves.