arXiv subjects

Wang Zhou

Publications and source records attributed to Wang Zhou.

At least 55 records · Page 3Linked to original sources

arXiv2020

PAIRS AutoGeo: an Automated Machine Learning Framework for Massive Geospatial Data

An automated machine learning framework for geospatial data named PAIRS AutoGeo is introduced on IBM PAIRS Geoscope big data and analytics platform. The framework simplifies the development of industrial machine learning solutions leveraging geospatial data to the extent that the user inputs are minimized to merely a text file containing labeled GPS coordinates. PAIRS AutoGeo automatically gathers required data at the location coordinates, assembles the training data, performs quality check, and trains multiple machine learning models for subsequent deployment. The framework is validated using a realistic industrial use case of tree species classification. Open-source tree species data are used as the input to train a random forest classifier and a modified ResNet model for 10-way tree species classification based on aerial imagery, which leads to an accuracy of $59.8\%$ and $81.4\%$, respectively. This use case exemplifies how PAIRS AutoGeo enables users to leverage machine learning without extensive geospatial expertise.

cs.CV↗

arXiv2020

Monitoring the Impact of Wildfires on Tree Species with Deep Learning

One of the impacts of climate change is the difficulty of tree regrowth after wildfires over areas that traditionally were covered by certain tree species. Here a deep learning model is customized to classify land covers from four-band aerial imagery before and after wildfires to study the prolonged consequences of wildfires on tree species. The tree species labels are generated from manually delineated maps for five land cover classes: Conifer, Hardwood, Shrub, ReforestedTree and Barren land. With an accuracy of $92\%$ on the test split, the model is applied to three wildfires on data from 2009 to 2018. The model accurately delineates areas damaged by wildfires, changes in tree species and rebound of burned areas. The result shows clear evidence of wildfires impacting the local ecosystem and the outlined approach can help monitor reforested areas, observe changes in forest composition and track wildfire impact on tree species.

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arXiv2020

Lifelong Object Detection

Recent advances in object detection have benefited significantly from rapid developments in deep neural networks. However, neural networks suffer from the well-known issue of catastrophic forgetting, which makes continual or lifelong learning problematic. In this paper, we leverage the fact that new training classes arrive in a sequential manner and incrementally refine the model so that it additionally detects new object classes in the absence of previous training data. Specifically, we consider the representative object detector, Faster R-CNN, for both accurate and efficient prediction. To prevent abrupt performance degradation due to catastrophic forgetting, we propose to apply knowledge distillation on both the region proposal network and the region classification network, to retain the detection of previously trained classes. A pseudo-positive-aware sampling strategy is also introduced for distillation sample selection. We evaluate the proposed method on PASCAL VOC 2007 and MS COCO benchmarks and show competitive mAP and 6x inference speed improvement, which makes the approach more suitable for real-time applications. Our implementation will be publicly available.

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arXiv2020

Robust Covariance Estimation for High-dimensional Compositional Data with Application to Microbial Communities Analysis

Microbial communities analysis is drawing growing attention due to the rapid development of high-throughput sequencing techniques nowadays. The observed data has the following typical characteristics: it is high-dimensional, compositional (lying in a simplex) and even would be leptokurtic and highly skewed due to the existence of overly abundant taxa, which makes the conventional correlation analysis infeasible to study the co-occurrence and co-exclusion relationship between microbial taxa. In this article, we address the challenges of covariance estimation for this kind of data. Assuming the basis covariance matrix lying in a well-recognized class of sparse covariance matrices, we adopt a proxy matrix known as centered log-ratio covariance matrix in the literature, which is approximately indistinguishable from the real basis covariance matrix as the dimensionality tends to infinity. We construct a Median-of-Means (MOM) estimator for the centered log-ratio covariance matrix and propose a thresholding procedure that is adaptive to the variability of individual entries. By imposing a much weaker finite fourth moment condition compared with the sub-Gaussianity condition in the literature, we derive the optimal rate of convergence under the spectral norm. In addition, we also provide theoretical guarantee on support recovery. The adaptive thresholding procedure of the MOM estimator is easy to implement and gains robustness when outliers or heavy-tailedness exist. Thorough simulation studies are conducted to show the advantages of the proposed procedure over some state-of-the-arts methods. At last, we apply the proposed method to analyze a microbiome dataset in human gut. The R script for implementing the method is available at https://github.com/heyongstat/RCEC.

stat.ME↗

arXiv2020

Statistical inference in massive datasets by empirical likelihood

In this paper, we propose a new statistical inference method for massive data sets, which is very simple and efficient by combining divide-and-conquer method and empirical likelihood. Compared with two popular methods (the bag of little bootstrap and the subsampled double bootstrap), we make full use of data sets, and reduce the computation burden. Extensive numerical studies and real data analysis demonstrate the effectiveness and flexibility of our proposed method. Furthermore, the asymptotic property of our method is derived.

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arXiv2020

The rate of convergence of harmonic explorer to SLE4

Using the estimate of the difference between the discrete harmonic function and its corresponding continuous version we derive a rate of convergence of the Loewner driving function for the harmonic explorer to the Brownian motion with speed 4 on the real line. Based on this convergence rate, the derivative estimate for chordal $\mbox{SLE}_4$, and the estimate of tip structure modulus for harmonic explorer paths, we obtain an explicit power-law rate of convergence of the harmonic explorer paths to the trace of chordal $\mbox{SLE}_4$ in the supremum distance.

math.PR↗

arXiv2019

Generalizable Resource Allocation in Stream Processing via Deep Reinforcement Learning

This paper considers the problem of resource allocation in stream processing, where continuous data flows must be processed in real time in a large distributed system. To maximize system throughput, the resource allocation strategy that partitions the computation tasks of a stream processing graph onto computing devices must simultaneously balance workload distribution and minimize communication. Since this problem of graph partitioning is known to be NP-complete yet crucial to practical streaming systems, many heuristic-based algorithms have been developed to find reasonably good solutions. In this paper, we present a graph-aware encoder-decoder framework to learn a generalizable resource allocation strategy that can properly distribute computation tasks of stream processing graphs unobserved from training data. We, for the first time, propose to leverage graph embedding to learn the structural information of the stream processing graphs. Jointly trained with the graph-aware decoder using deep reinforcement learning, our approach can effectively find optimized solutions for unseen graphs. Our experiments show that the proposed model outperforms both METIS, a state-of-the-art graph partitioning algorithm, and an LSTM-based encoder-decoder model, in about 70% of the test cases.

cs.LG↗

arXiv2018

Performance Estimation of Synthesis Flows cross Technologies using LSTMs and Transfer Learning

Due to the increasing complexity of Integrated Circuits (ICs) and System-on-Chip (SoC), developing high-quality synthesis flows within a short market time becomes more challenging. We propose a general approach that precisely estimates the Quality-of-Result (QoR), such as delay and area, of unseen synthesis flows for specific designs. The main idea is training a Recurrent Neural Network (RNN) regressor, where the flows are inputs and QoRs are ground truth. The RNN regressor is constructed with Long Short-Term Memory (LSTM) and fully-connected layers. This approach is demonstrated with 1.2 million data points collected using 14nm, 7nm regular-voltage (RVT), and 7nm low-voltage (LVT) FinFET technologies with twelve IC designs. The accuracy of predicting the QoRs (delay and area) within one technology is $\boldsymbol{\geq}$\textbf{98.0}\% over $\sim$240,000 test points. To enable accurate predictions cross different technologies and different IC designs, we propose a transfer-learning approach that utilizes the model pre-trained with 14nm datasets. Our transfer learning approach obtains estimation accuracy $\geq$96.3\% over $\sim$960,000 test points, using only 100 data points for training.

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arXiv2018

High-dimensional covariance matrices in elliptical distributions with application to spherical test

This paper discusses fluctuations of linear spectral statistics of high-dimensional sample covariance matrices when the underlying population follows an elliptical distribution. Such population often possesses high order correlations among their coordinates, which have great impact on the asymptotic behaviors of linear spectral statistics. Taking such kind of dependency into consideration, we establish a new central limit theorem for the linear spectral statistics in this paper for a class of elliptical populations. This general theoretical result has wide applications and, as an example, it is then applied to test the sphericity of elliptical populations.

math.ST↗

arXiv2018

High Dimensional Elliptical Sliced Inverse Regression in non-Gaussian Distributions

Sliced inverse regression (SIR) is the most widely-used sufficient dimension reduction method due to its simplicity, generality and computational efficiency. However, when the distribution of the covariates deviates from the multivariate normal distribution, the estimation efficiency of SIR is rather low. In this paper, we propose a robust alternative to SIR - called elliptical sliced inverse regression (ESIR) for analysing high dimensional, elliptically distributed data. There are wide range of applications of the elliptically distributed data, especially in finance and economics where the distribution of the data is often heavy-tailed. To tackle the heavy-tailed elliptically distributed covariates, we novelly utilize the multivariate Kendall's tau matrix in a framework of so-called generalized eigenvector problem for sufficient dimension reduction. Methodologically, we present a practical algorithm for our method. Theoretically, we investigate the asymptotic behavior of the ESIR estimator and obtain the corresponding convergence rate under high dimensional setting. Quantities of simulation results show that ESIR significantly improves the estimation efficiency in heavy-tailed scenarios. A stock exchange data analysis also demonstrates the effectiveness of our method. Moreover, ESIR can be easily extended to most other sufficient dimension reduction methods.

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arXiv2017

Distribution Regression

Linear regression is a fundamental and popular statistical method. There are various kinds of linear regression, such as mean regression and quantile regression. In this paper, we propose a new one called distribution regression, which allows broad-spectrum of the error distribution in the linear regression. Our method uses nonparametric technique to estimate regression parameters. Our studies indicate that our method provides a better alternative than mean regression and quantile regression under many settings, particularly for asymmetrical heavy-tailed distribution or multimodal distribution of the error term. Under some regular conditions, our estimator is $\sqrt n$-consistent and possesses the asymptotically normal distribution. The proof of the asymptotic normality of our estimator is very challenging because our nonparametric likelihood function cannot be transformed into sum of independent and identically distributed random variables. Furthermore, penalized likelihood estimator is proposed and enjoys the so-called oracle property with diverging number of parameters. Numerical studies also demonstrate the effectiveness and the flexibility of the proposed method.

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arXiv2017

Canonical correlation coefficients of high-dimensional Gaussian vectors: finite rank case

Consider a Gaussian vector $\mathbf{z}=(\mathbf{x}',\mathbf{y}')'$, consisting of two sub-vectors $\mathbf{x}$ and $\mathbf{y}$ with dimensions $p$ and $q$ respectively, where both $p$ and $q$ are proportional to the sample size $n$. Denote by $Σ_{\mathbf{u}\mathbf{v}}$ the population cross-covariance matrix of random vectors $\mathbf{u}$ and $\mathbf{v}$, and denote by $S_{\mathbf{u}\mathbf{v}}$ the sample counterpart. The canonical correlation coefficients between $\mathbf{x}$ and $\mathbf{y}$ are known as the square roots of the nonzero eigenvalues of the canonical correlation matrix $Σ_{\mathbf{x}\mathbf{x}}^{-1}Σ_{\mathbf{x}\mathbf{y}}Σ_{\mathbf{y}\mathbf{y}}^{-1}Σ_{\mathbf{y}\mathbf{x}}$. In this paper, we focus on the case that $Σ_{\mathbf{x}\mathbf{y}}$ is of finite rank $k$, i.e. there are $k$ nonzero canonical correlation coefficients, whose squares are denoted by $r_1\geq\cdots\geq r_k>0$. We study the sample counterparts of $r_i,i=1,\ldots,k$, i.e. the largest $k$ eigenvalues of the sample canonical correlation matrix $§_{\mathbf{x}\mathbf{x}}^{-1}§_{\mathbf{x}\mathbf{y}}§_{\mathbf{y}\mathbf{y}}^{-1}§_{\mathbf{y}\mathbf{x}}$, denoted by $λ_1\geq\cdots\geq λ_k$. We show that there exists a threshold $r_c\in(0,1)$, such that for each $i\in\{1,\ldots,k\}$, when $r_i\leq r_c$, $λ_i$ converges almost surely to the right edge of the limiting spectral distribution of the sample canonical correlation matrix, denoted by $d_{+}$. When $r_i>r_c$, $λ_i$ possesses an almost sure limit in $(d_{+},1]$. We also obtain the limiting distribution of $λ_i$'s under appropriate normalization. Specifically, $λ_i$ possesses Gaussian type fluctuation if $r_i>r_c$, and follows Tracy-Widom distribution if $r_i<r_c$. Some applications of our results are also discussed.

math.ST↗

arXiv2017

On spectral properties of high-dimensional spatial-sign covariance matrices in elliptical distributions with applications

Spatial-sign covariance matrix (SSCM) is an important substitute of sample covariance matrix (SCM) in robust statistics. This paper investigates the SSCM on its asymptotic spectral behaviors under high-dimensional elliptical populations, where both the dimension $p$ of observations and the sample size $n$ tend to infinity with their ratio $p/n\to c\in (0, \infty)$. The empirical spectral distribution of this nonparametric scatter matrix is shown to converge in distribution to a generalized Marčenko-Pastur law. Beyond this, a new central limit theorem (CLT) for general linear spectral statistics of the SSCM is also established. For polynomial spectral statistics, explicit formulae of the limiting mean and covarance functions in the CLT are provided. The derived results are then applied to an estimation procedure and a test procedure for the spectrum of the shape component of population covariance matrices.

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arXiv2015

Spectral statistics of large dimensional Spearman's rank correlation matrix and its application

Let $\mathbf{Q}=(Q_1,\ldots,Q_n)$ be a random vector drawn from the uniform distribution on the set of all $n!$ permutations of $\{1,2,\ldots,n\}$. Let $\mathbf{Z}=(Z_1,\ldots,Z_n)$, where $Z_j$ is the mean zero variance one random variable obtained by centralizing and normalizing $Q_j$, $j=1,\ldots,n$. Assume that $\mathbf {X}_i,i=1,\ldots ,p$ are i.i.d. copies of $\frac{1}{\sqrt{p}}\mathbf{Z}$ and $X=X_{p,n}$ is the $p\times n$ random matrix with $\mathbf{X}_i$ as its $i$th row. Then $S_n=XX^*$ is called the $p\times n$ Spearman's rank correlation matrix which can be regarded as a high dimensional extension of the classical nonparametric statistic Spearman's rank correlation coefficient between two independent random variables. In this paper, we establish a CLT for the linear spectral statistics of this nonparametric random matrix model in the scenario of high dimension, namely, $p=p(n)$ and $p/n\to c\in(0,\infty)$ as $n\to\infty$. We propose a novel evaluation scheme to estimate the core quantity in Anderson and Zeitouni's cumulant method in [Ann. Statist. 36 (2008) 2553-2576] to bypass the so-called joint cumulant summability. In addition, we raise a two-step comparison approach to obtain the explicit formulae for the mean and covariance functions in the CLT. Relying on this CLT, we then construct a distribution-free statistic to test complete independence for components of random vectors. Owing to the nonparametric property, we can use this test on generally distributed random variables including the heavy-tailed ones.

math.ST↗

arXiv2015

Convergence of the empirical spectral distribution function of Beta matrices

Let $\mathbf{B}_n=\mathbf {S}_n(\mathbf {S}_n+α_n\mathbf {T}_N)^{-1}$, where $\mathbf {S}_n$ and $\mathbf {T}_N$ are two independent sample covariance matrices with dimension $p$ and sample sizes $n$ and $N$, respectively. This is the so-called Beta matrix. In this paper, we focus on the limiting spectral distribution function and the central limit theorem of linear spectral statistics of $\mathbf {B}_n$. Especially, we do not require $\mathbf {S}_n$ or $\mathbf {T}_N$ to be invertible. Namely, we can deal with the case where $p>\max\{n,N\}$ and $p<n+N$. Therefore, our results cover many important applications which cannot be simply deduced from the corresponding results for multivariate $F$ matrices.

math.PR↗

arXiv2015

The logarithmic law of random determinant

Consider the square random matrix $A_n=(a_{ij})_{n,n}$, where $\{a_{ij}:=a_{ij}^{(n)},i,j=1,\ldots,n\}$ is a collection of independent real random variables with means zero and variances one. Under the additional moment condition \[\sup_n\max_{1\leq i,j\leq n}\mathbb{E}a_{ij}^4<\infty,\] we prove Girko's logarithmic law of $\det A_n$ in the sense that as $n\rightarrow\infty$ \begin{eqnarray*}\frac{\log|\det A_n|-(1/2)\log(n-1)!}{\sqrt{(1/2)\log n}}\stackrel{d}{ \longrightarrow}N(0,1).\end{eqnarray*}

math.PR↗

arXiv2015

Universality for the largest eigenvalue of sample covariance matrices with general population

This paper is aimed at deriving the universality of the largest eigenvalue of a class of high-dimensional real or complex sample covariance matrices of the form $\mathcal{W}_N=Σ^{1/2}XX^*Σ^{1/2}$. Here, $X=(x_{ij})_{M,N}$ is an $M\times N$ random matrix with independent entries $x_{ij},1\leq i\leq M,1\leq j\leq N$ such that $\mathbb{E}x_{ij}=0$, $\mathbb{E}|x_{ij}|^2=1/N$. On dimensionality, we assume that $M=M(N)$ and $N/M\rightarrow d\in(0,\infty)$ as $N\rightarrow\infty$. For a class of general deterministic positive-definite $M\times M$ matrices $Σ$, under some additional assumptions on the distribution of $x_{ij}$'s, we show that the limiting behavior of the largest eigenvalue of $\mathcal{W}_N$ is universal, via pursuing a Green function comparison strategy raised in [Probab. Theory Related Fields 154 (2012) 341-407, Adv. Math. 229 (2012) 1435-1515] by Erdős, Yau and Yin for Wigner matrices and extended by Pillai and Yin [Ann. Appl. Probab. 24 (2014) 935-1001] to sample covariance matrices in the null case ($Σ=I$). Consequently, in the standard complex case ($\mathbb{E}x_{ij}^2=0$), combing this universality property and the results known for Gaussian matrices obtained by El Karoui in [Ann. Probab. 35 (2007) 663-714] (nonsingular case) and Onatski in [Ann. Appl. Probab. 18 (2008) 470-490] (singular case), we show that after an appropriate normalization the largest eigenvalue of $\mathcal{W}_N$ converges weakly to the type 2 Tracy-Widom distribution $\mathrm{TW}_2$. Moreover, in the real case, we show that when $Σ$ is spiked with a fixed number of subcritical spikes, the type 1 Tracy-Widom limit $\mathrm{TW}_1$ holds for the normalized largest eigenvalue of $\mathcal {W}_N$, which extends a result of Féral and Péché in [J. Math. Phys. 50 (2009) 073302] to the scenario of nondiagonal $Σ$ and more generally distributed $X$.

math.PR↗

arXiv2014

Random conformal welding for finitely connected regions

Given a finitely connected region $Ω$ of the Riemann sphere whose complement consists of $m$ mutually disjoint closed disks $\bar{U}_j$, the random homeomorphism $h_j$ on the boundary component $\partial U_j$ is constructed using the exponential Gaussian free field. The existence and uniqueness of random conformal welding of $Ω$ with $h_j$ is established by investigating a non-uniformly elliptic Betrami equation with a random complex dilatation. This generalizes the result of Astala, Jones, Kupiainen and Saksman to multiply connected domains.

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