Computing Simplicial Depth by Using Importance Sampling Algorithm and Its Application

Simplicial depth (SD) plays an important role in discriminant analysis, hypothesis testing, machine learning, and engineering computations. However, the computation of simplicial depth is hugely challenging because the exact algorithm is an NP problem with dimension d and sample size n as input arguments. The approximate algorithm for simplicial depth computation has extremely low efficiency, especially in high-dimensional cases. In this study, we design an importance sampling algorithm for the computation of simplicial depth. As an advanced Monte Carlo method, the proposed algorithm outperforms other approximate and exact algorithms in accuracy and efficiency, as shown by simulated and real data experiments. Furthermore, we illustrate the robustness of simplicial depth in regression analysis through a concrete physical data experiment.

Impact Assessment of Big Data on Higher Education Management Based on Time-Varying Clustering Sampling Algorithm

With the continuous development of social economy, education has received more and more attention. As an important part of higher education, it has been profoundly influenced by the era of data in recent years. In order to evaluate the impact of big data on higher education management, this paper introduced a time-varying lens algorithm (TLA) to analyze the business needs of teachers and education management by sorting out the business processes of education management, education thinking, and education practice. Through learning and mining the corresponding technology, improve the corresponding educational ability, and use big data to assist the management of higher education. The simulation results show that the time-varying clustering sampling algorithm is effective.

Cosmic Flow Measurement and Mock Sampling Algorithm of Cosmicflows-4 Tully−Fisher Catalog

Measurements of cosmic flows enable us to test whether cosmological models can accurately describe the evolution of the density field in the nearby universe. In this paper, we measure the low-order kinematic moments of the cosmic flow field, namely bulk flow and shear moments, using the Cosmicflows-4 Tully−Fisher catalog (CF4TF). To make accurate cosmological inferences with the CF4TF sample, it is important to make realistic mock catalogs. We present the mock sampling algorithm of CF4TF. These mocks can accurately realize the survey geometry and luminosity selection function, enabling researchers to explore how these systematics affect the measurements. These mocks can also be further used to estimate the covariance matrix and errors of the power spectrum and two-point correlation function in future work. In this paper, we use the mocks to test the cosmic flow estimator and find that the measurements are unbiased. The measured bulk flow in the local universe is 376 ± 23 (error) ± 183 (cosmic variance) km s−1 at depth d MLE = 35 Mpc h −1, to the Galactic direction of (l, b) = (298° ± 3°, −6° ± 3°). Both the measured bulk and shear moments are consistent with the concordance Λ Cold Dark Matter cosmological model predictions.