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Xueqin Wang

Publications and source records attributed to Xueqin Wang.

34 records · Page 2Linked to original sources
arXiv2023

Nonparametric Statistical Inference via Metric Distribution Function in Metric Spaces

Distribution function is essential in statistical inference, and connected with samples to form a directed closed loop by the correspondence theorem in measure theory and the Glivenko-Cantelli and Donsker properties. This connection creates a paradigm for statistical inference. However, existing distribution functions are defined in Euclidean spaces and no longer convenient to use in rapidly evolving data objects of complex nature. It is imperative to develop the concept of distribution function in a more general space to meet emerging needs. Note that the linearity allows us to use hypercubes to define the distribution function in a Euclidean space, but without the linearity in a metric space, we must work with the metric to investigate the probability measure. We introduce a class of metric distribution functions through the metric between random objects and a fixed location in metric spaces. We overcome this challenging step by proving the correspondence theorem and the Glivenko-Cantelli theorem for metric distribution functions in metric spaces that lie the foundation for conducting rational statistical inference for metric space-valued data. Then, we develop homogeneity test and mutual independence test for non-Euclidean random objects, and present comprehensive empirical evidence to support the performance of our proposed methods.

stat.ME↗
arXiv2023

Best-Subset Selection in Generalized Linear Models: A Fast and Consistent Algorithm via Splicing Technique

In high-dimensional generalized linear models, it is crucial to identify a sparse model that adequately accounts for response variation. Although the best subset section has been widely regarded as the Holy Grail of problems of this type, achieving either computational efficiency or statistical guarantees is challenging. In this article, we intend to surmount this obstacle by utilizing a fast algorithm to select the best subset with high certainty. We proposed and illustrated an algorithm for best subset recovery in regularity conditions. Under mild conditions, the computational complexity of our algorithm scales polynomially with sample size and dimension. In addition to demonstrating the statistical properties of our method, extensive numerical experiments reveal that it outperforms existing methods for variable selection and coefficient estimation. The runtime analysis shows that our implementation achieves approximately a fourfold speedup compared to popular variable selection toolkits like glmnet and ncvreg.

stat.ML↗
arXiv2023

Batch mode active learning for efficient parameter estimation

For many tasks of data analysis, we may only have the information of the explanatory variable and the evaluation of the response values are quite expensive. While it is impractical or too costly to obtain the responses of all units, a natural remedy is to judiciously select a good sample of units, for which the responses are to be evaluated. In this paper, we adopt the classical criteria in design of experiments to quantify the information of a given sample regarding parameter estimation. Then, we provide a theoretical justification for approximating the optimal sample problem by a continuous problem, for which fast algorithms can be further developed with the guarantee of global convergence. Our results have the following novelties: (i) The statistical efficiency of any candidate sample can be evaluated without knowing the exact optimal sample; (ii) It can be applied to a very wide class of statistical models; (iii) It can be integrated with a broad class of information criteria; (iv) It is much faster than existing algorithms. $(v)$ A geometric interpretation is adopted to theoretically justify the relaxation of the original combinatorial problem to continuous optimization problem.

stat.CO↗
arXiv2022

Simultaneous Best Subset Selection and Dimension Reduction via Primal-Dual Iterations

Sparse reduced rank regression is an essential statistical learning method. In the contemporary literature, estimation is typically formulated as a nonconvex optimization that often yields to a local optimum in numerical computation. Yet, their theoretical analysis is always centered on the global optimum, resulting in a discrepancy between the statistical guarantee and the numerical computation. In this research, we offer a new algorithm to address the problem and establish an almost optimal rate for the algorithmic solution. We also demonstrate that the algorithm achieves the estimation with a polynomial number of iterations. In addition, we present a generalized information criterion to simultaneously ensure the consistency of support set recovery and rank estimation. Under the proposed criterion, we show that our algorithm can achieve the oracle reduced rank estimation with a significant probability. The numerical studies and an application in the ovarian cancer genetic data demonstrate the effectiveness and scalability of our approach.

stat.ME↗
arXiv2022

High Dimensional Portfolio Selection with Cardinality Constraints

The expanding number of assets offers more opportunities for investors but poses new challenges for modern portfolio management (PM). As a central plank of PM, portfolio selection by expected utility maximization (EUM) faces uncontrollable estimation and optimization errors in ultrahigh-dimensional scenarios. Past strategies for high-dimensional PM mainly concern only large-cap companies and select many stocks, making PM impractical. We propose a sample-average approximation-based portfolio strategy to tackle the difficulties above with cardinality constraints. Our strategy bypasses the estimation of mean and covariance, the Chinese walls in high-dimensional scenarios. Empirical results on S&P 500 and Russell 2000 show that an appropriate number of carefully chosen assets leads to better out-of-sample mean-variance efficiency. On Russell 2000, our best portfolio profits as much as the equally-weighted portfolio but reduces the maximum drawdown and the average number of assets by 10% and 90%, respectively. The flexibility and the stability of incorporating factor signals for augmenting out-of-sample performances are also demonstrated. Our strategy balances the trade-off among the return, the risk, and the number of assets with cardinality constraints. Therefore, we provide a theoretically sound and computationally efficient strategy to make PM practical in the growing global financial market.

stat.AP↗
arXiv2022

A Splicing Approach to Best Subset of Groups Selection

Best subset of groups selection (BSGS) is the process of selecting a small part of non-overlapping groups to achieve the best interpretability on the response variable. It has attracted increasing attention and has far-reaching applications in practice. However, due to the computational intractability of BSGS in high-dimensional settings, developing efficient algorithms for solving BSGS remains a research hotspot. In this paper,we propose a group-splicing algorithm that iteratively detects the relevant groups and excludes the irrelevant ones. Moreover, coupled with a novel group information criterion, we develop an adaptive algorithm to determine the optimal model size. Under mild conditions, it is certifiable that our algorithm can identify the optimal subset of groups in polynomial time with high probability. Finally, we demonstrate the efficiency and accuracy of our methods by comparing them with several state-of-the-art algorithms on both synthetic and real-world datasets.

cs.LG↗
arXiv2022

Interpreting and predicting the economy flows: A time-varying parameter global vector autoregressive integrated the machine learning model

The paper proposes a time-varying parameter global vector autoregressive (TVP-GVAR) framework for predicting and analysing developed region economic variables. We want to provide an easily accessible approach for the economy application settings, where a variety of machine learning models can be incorporated for out-of-sample prediction. The LASSO-type technique for numerically efficient model selection of mean squared errors (MSEs) is selected. We show the convincing in-sample performance of our proposed model in all economic variables and relatively high precision out-of-sample predictions with different-frequency economic inputs. Furthermore, the time-varying orthogonal impulse responses provide novel insights into the connectedness of economic variables at critical time points across developed regions. We also derive the corresponding asymptotic bands (the confidence intervals) for orthogonal impulse responses function under standard assumptions.

econ.EM↗
arXiv2022

abess: A Fast Best Subset Selection Library in Python and R

We introduce a new library named abess that implements a unified framework of best-subset selection for solving diverse machine learning problems, e.g., linear regression, classification, and principal component analysis. Particularly, the abess certifiably gets the optimal solution within polynomial times with high probability under the linear model. Our efficient implementation allows abess to attain the solution of best-subset selection problems as fast as or even 20x faster than existing competing variable (model) selection toolboxes. Furthermore, it supports common variants like best group subset selection and $\ell_2$ regularized best-subset selection. The core of the library is programmed in C++. For ease of use, a Python library is designed for conveniently integrating with scikit-learn, and it can be installed from the Python library Index. In addition, a user-friendly R library is available at the Comprehensive R Archive Network. The source code is available at: https://github.com/abess-team/abess.

stat.ML↗
arXiv2020

A Fast and Effective Method of Macula Automatic Detection for Retina Images

Retina image processing is one of the crucial and popular topics of medical image processing. The macula fovea is responsible for sharp central vision, which is necessary for human behaviors where visual detail is of primary importance, such as reading, writing, driving, etc. This paper proposes a novel method to locate the macula through a series of morphological processing. On the premise of maintaining high accuracy, our approach is simpler and faster than others. Furthermore, for the hospital's real images, our method is also able to detect the macula robustly.

eess.IV↗
arXiv2020

Computational analysis of pathological image enables interpretable prediction for microsatellite instability

Microsatellite instability (MSI) is associated with several tumor types and its status has become increasingly vital in guiding patient treatment decisions. However, in clinical practice, distinguishing MSI from its counterpart is challenging since the diagnosis of MSI requires additional genetic or immunohistochemical tests. In this study, interpretable pathological image analysis strategies are established to help medical experts to automatically identify MSI. The strategies only require ubiquitous Haematoxylin and eosin-stained whole-slide images and can achieve decent performance in the three cohorts collected from The Cancer Genome Atlas. The strategies provide interpretability in two aspects. On the one hand, the image-level interpretability is achieved by generating localization heat maps of important regions based on the deep learning network; on the other hand, the feature-level interpretability is attained through feature importance and pathological feature interaction analysis. More interestingly, both from the image-level and feature-level interpretability, color features and texture characteristics are shown to contribute the most to the MSI predictions. Therefore, the classification models under the proposed strategies can not only serve as an efficient tool for predicting the MSI status of patients, but also provide more insights to pathologists with clinical understanding.

stat.ML↗
arXiv2020

The Effects of Stringent Interventions for Coronavirus Pandemic

The pandemic of COVID-19 has caused severe public health consequences around the world. Many interventions of COVID-19 have been implemented. It is of great public health and societal importance to evaluate the effects of interventions in the pandemic of COVID-19. In this paper, with help of synthetic control method, regression discontinuity and a Susceptible-Infected and infectious without isolation-Hospitalized in isolation-Removed (SIHR) model, we evaluate the horizontal and longitudinal effects of stringent interventions implemented in Wenzhou, a representative urban city of China, where stringent interventions were enforced to curb its own epidemic situation with rapidly increasing newly confirmed cases. We found that there were statistically significant treatment effects of those stringent interventions which reduced the cumulative confirmed cases of COVID-19. Those reduction effects would increase over time. Also, if the stringent interventions were delayed by 2 days or mild interventions were implemented instead, the expected number of cumulative confirmed cases would have been nearly 2 times or 5 times of the actual number. The effects of stringent interventions are significant in mitigating the epidemic situation of COVID-19. The slower the interventions were implemented, the more severe the epidemic would have been, and the stronger the interventions would have been required.

physics.soc-ph↗
arXiv2020

BeSS: An R Package for Best Subset Selection in Linear, Logistic and CoxPH Models

We introduce a new R package, BeSS, for solving the best subset selection problem in linear, logistic and Cox's proportional hazard (CoxPH) models. It utilizes a highly efficient active set algorithm based on primal and dual variables, and supports sequential and golden search strategies for best subset selection. We provide a C++ implementation of the algorithm using Rcpp interface. We demonstrate through numerical experiments based on enormous simulation and real datasets that the new BeSS package has competitive performance compared to other R packages for best subset selection purpose.

stat.CO↗
arXiv2019

Ball: An R package for detecting distribution difference and association in metric spaces

The rapid development of modern technology facilitates the appearance of numerous unprecedented complex data which do not satisfy the axioms of Euclidean geometry, while most of the statistical hypothesis tests are available in Euclidean or Hilbert spaces. To properly analyze the data of more complicated structures, efforts have been made to solve the fundamental test problems in more general spaces. In this paper, a publicly available R package Ball is provided to implement Ball statistical test procedures for K-sample distribution comparison and test of mutual independence in metric spaces, which extend the test procedures for two sample distribution comparison and test of independence. The tailormade algorithms as well as engineering techniques are employed on the Ball package to speed up computation to the best of our ability. Two real data analyses and several numerical studies have been performed and the results certify the powerfulness of Ball package in analyzing complex data, e.g., spherical data and symmetric positive matrix data.

stat.CO↗
arXiv2019

Hierarchical Change-Point Detection for Multivariate Time Series via a Ball Detection Function

Sequences of random objects arise from many real applications, including high throughput omic data and functional imaging data. Those sequences are usually dependent, non-linear, or even Non-Euclidean, and an important problem is change-point detection in such dependent sequences in Banach spaces or metric spaces. The problem usually requires the accurate inference for not only whether changes might have occurred but also the locations of the changes when they did occur. To this end, we first introduce a Ball detection function and show that it reaches its maximum at the change-point if a sequence has only one change point. Furthermore, we propose a consistent estimator of Ball detection function based on which we develop a hierarchical algorithm to detect all possible change points. We prove that the estimated change-point locations are consistent. Our procedure can estimate the number of change-points and detect their locations without assuming any particular types of change-points as a change can occur in a sequence in different ways. Extensive simulation studies and analyses of two interesting real datasets wind direction and Bitcoin price demonstrate that our method has considerable advantages over existing competitors, especially when data are non-Euclidean or when there are distributional changes in the variance.

math.ST↗
arXiv2001

A unifying generalization of Sperner's theorem

Sperner's bound on the size of an antichain in the lattice P(S) of subsets of a finite set S has been generalized in three different directions: by Erdos to subsets of P(S) in which chains contain at most r elements; by Meshalkin to certain classes of compositions of S; by Griggs, Stahl, and Trotter through replacing the antichains by certain sets of pairs of disjoint elements of P(S). We unify Erdos's, Meshalkin's, and Griggs-Stahl-Trotter's inequalities with a common generalization. We similarly unify their accompanying LYM inequalities. Our bounds do not in general appear to be the best possible.

math.CO↗