A Framework for Statistical Inference via Randomized Algorithms

Randomized algorithms, such as randomized sketching or projections, are a promising approach to ease the computational burden in analyzing large datasets. However, randomized algorithms also produce non-deterministic outputs, leading to the problem of evaluating their accuracy. In this paper, we develop a statistical inference framework for quantifying the uncertainty of the outputs of randomized algorithms. We develop appropriate statistical methods -- sub-randomization, multi-run plug-in and multi-run aggregation inference -- by using multiple runs of the same randomized algorithm, or by estimating the unknown parameters of the limiting distribution. As an example, we develop methods for statistical inference for least squares parameters via random sketching using matrices with i.i.d.entries, or uniform partial orthogonal matrices. For this, we characterize the limiting distribution of estimators obtained via sketch-and-solve as well as partial sketching methods. The analysis of i.i.d. sketches uses a trigonometric interpolation argument to establish a differential equation for the limiting expected characteristic function and find the dependence on the kurtosis of the entries of the sketching matrix. The results are supported via a broad range of simulations

Review: Karst springs in Shanxi, China

China is one of a few countries in the world where karst is intensively developed and karst water is heavily utilized as water supply sources. Shanxi is such a Province with the largest karst distribution in places in Northern China, where 19 large karst springs and their catchments are identified to provide important sources of the water supply and ecosystem functioning in Shanxi. Over the years, many problems associated with utilization of karst springs in Shanxi cropped out, including the decrease in spring flow, decline of groundwater level, groundwater contamination and pollution, etc., which severely restrict the sustainable utilization of karst water resources in Shanxi

Protection of Karst spring in Shanxi Region,China: A case study from Jinci Spring Catchment.

Philosophiae Doctor - PhDGroundwater is an important of water resources and plays a significant role in the water supply in most parts of the world. It is also an important ecological environment factor, and its variations often affect natural balance of the ecosystem. China is one of the few countries in the world where Karst is intensively developed Karst water is heavily utilized as water supply source. Shanxi is such a province with largest Karst distribution in places in North China, where 19 large Karst springs and their catchment are identified to provide an important source of the water supply and ecosystem functioning in Shanx

Decomposition-Based-Sorting and Angle-Based-Selection for Evolutionary Multiobjective and Many-Objective Optimization

Multiobjective evolutionary algorithm based on decomposition (MOEA/D) decomposes a multiobjective optimization problem (MOP) into a number of scalar optimization subproblems and then solves them in parallel. In many MOEA/D variants, each subproblem is associated with one and only one solution. An underlying assumption is that each subproblem has a different Pareto-optimal solution, which may not be held, for irregular Pareto fronts (PFs), e.g., disconnected and degenerate ones. In this paper, we propose a new variant of MOEA/D with sorting-and-selection (MOEA/D-SAS). Different from other selection schemes, the balance between convergence and diversity is achieved by two distinctive components, decomposition-based-sorting (DBS) and angle-based-selection (ABS). DBS only sorts ${L}$ closest solutions to each subproblem to control the convergence and reduce the computational cost. The parameter ${L}$ has been made adaptive based on the evolutionary process. ABS takes use of angle information between solutions in the objective space to maintain a more fine-grained diversity. In MOEA/D-SAS, different solutions can be associated with the same subproblems; and some subproblems are allowed to have no associated solution, more flexible to MOPs or many-objective optimization problems (MaOPs) with different shapes of PFs. Comprehensive experimental studies have shown that MOEA/D-SAS outperforms other approaches; and is especially effective on MOPs or MaOPs with irregular PFs. Moreover, the computational efficiency of DBS and the effects of ABS in MOEA/D-SAS are also investigated and discussed in detail

Asymptotic properties of spiked eigenvalues and eigenvectors of signal-plus-noise matrices with their applications

This paper is to consider a general low-rank signal plus noise model in high dimensional settings. Specifically, we consider the noise with a general covariance structure and the signal to be at the same magnitude as the noise. Our study focuses on exploring various asymptotic properties related to the spiked eigenvalues and eigenvectors. As applications, we propose a new criterion to estimate the number of clusters, and investigate the properties of spectral clustering

Specialized Courses Teaching Mode Innovation of the Independent College Based on MOOCS

Independent college is a new kind of school-running pattern, on the basis of independent college computer professional course teaching, based on the background of MOOCS, specialized course teaching mode principle, on the basis of design is given priority to, the class online course of classroom teaching mode. To a certain extent can motivate we will accelerate reform of the teaching mode of independent colleges, improve the teaching quality of education. Keywords: Moocs, Independent college, Specialized courses, Teaching mod

The disk reverberation mapping of X-ray weak quasars: a case study of SDSS J153913.47+395423.4

The widely adopted ``lamppost'' thermal reprocessing model, in which the variable UV/optical emission is a result of the accretion disk reprocessing of the highly fluctuating X-ray emission, can be tested by measuring inter-band time lags in quasars spanning a range of X-ray power. This work reports the inter-band time lag in an apparently X-ray weak quasar, SDSS J153913.47+395423.4. A significant cross-correlation with a time delay of $\sim 33$ days (observed-frame) is detected in the Zwicky Transient Facility (ZTF) $g$ and $r$ light curves of SDSS J153913.47+395423.4. The observed X-ray power seems to be too weak to account for the observed inter-band cross-correlation with time delay. Hence the X-ray weak quasar SDSS J153913.47+395423.4 is either intrinsically X-ray normal (but observationally X-ray weak), or the X-ray emission is not the only mechanism to drive UV/optical variability. In the former case, the required X-ray power is at least 19 times stronger than observed, which requires either an exceptionally anisotropic corona or Compton-thick obscuration. Alternatively, the Corona-heated Accretion disk Reprocessing (CHAR) or the EUV torus models may account for the observed time lags.Comment: 10 pages, 4 figures, accepted for publication in the Astrophysical Journa