arXiv subjects

Yihong Wu

Publications and source records attributed to Yihong Wu.

At least 91 records · Page 5Linked to original sources

arXiv2022

VisImages: A Fine-Grained Expert-Annotated Visualization Dataset

Images in visualization publications contain rich information, e.g., novel visualization designs and implicit design patterns of visualizations. A systematic collection of these images can contribute to the community in many aspects, such as literature analysis and automated tasks for visualization. In this paper, we build and make public a dataset, VisImages, which collects 12,267 images with captions from 1,397 papers in IEEE InfoVis and VAST. Built upon a comprehensive visualization taxonomy, the dataset includes 35,096 visualizations and their bounding boxes in the images.We demonstrate the usefulness of VisImages through three use cases: 1) investigating the use of visualizations in the publications with VisImages Explorer, 2) training and benchmarking models for visualization classification, and 3) localizing visualizations in the visual analytics systems automatically.

cs.CV↗

arXiv2022

Learning Mixtures of Permutations: Groups of Pairwise Comparisons and Combinatorial Method of Moments

In applications such as rank aggregation, mixture models for permutations are frequently used when the population exhibits heterogeneity. In this work, we study the widely used Mallows mixture model. In the high-dimensional setting, we propose a polynomial-time algorithm that learns a Mallows mixture of permutations on $n$ elements with the optimal sample complexity that is proportional to $\log n$, improving upon previous results that scale polynomially with $n$. In the high-noise regime, we characterize the optimal dependency of the sample complexity on the noise parameter. Both objectives are accomplished by first studying demixing permutations under a noiseless query model using groups of pairwise comparisons, which can be viewed as moments of the mixing distribution, and then extending these results to the noisy Mallows model by simulating the noiseless oracle.

math.ST↗

arXiv2022

Random Graph Matching in Geometric Models: the Case of Complete Graphs

This paper studies the problem of matching two complete graphs with edge weights correlated through latent geometries, extending a recent line of research on random graph matching with independent edge weights to geometric models. Specifically, given a random permutation $π^*$ on $[n]$ and $n$ iid pairs of correlated Gaussian vectors $\{X_{π^*(i)}, Y_i\}$ in $\mathbb{R}^d$ with noise parameter $σ$, the edge weights are given by $A_{ij}=κ(X_i,X_j)$ and $B_{ij}=κ(Y_i,Y_j)$ for some link function $κ$. The goal is to recover the hidden vertex correspondence $π^*$ based on the observation of $A$ and $B$. We focus on the dot-product model with $κ(x,y)=\langle x, y \rangle$ and Euclidean distance model with $κ(x,y)=\|x-y\|^2$, in the low-dimensional regime of $d=o(\log n)$ wherein the underlying geometric structures are most evident. We derive an approximate maximum likelihood estimator, which provably achieves, with high probability, perfect recovery of $π^*$ when $σ=o(n^{-2/d})$ and almost perfect recovery with a vanishing fraction of errors when $σ=o(n^{-1/d})$. Furthermore, these conditions are shown to be information-theoretically optimal even when the latent coordinates $\{X_i\}$ and $\{Y_i\}$ are observed, complementing the recent results of [DCK19] and [KNW22] in geometric models of the planted bipartite matching problem. As a side discovery, we show that the celebrated spectral algorithm of [Ume88] emerges as a further approximation to the maximum likelihood in the geometric model.

math.ST↗

arXiv2022

Settling the Sharp Reconstruction Thresholds of Random Graph Matching

This paper studies the problem of recovering the hidden vertex correspondence between two edge-correlated random graphs. We focus on the Gaussian model where the two graphs are complete graphs with correlated Gaussian weights and the Erdős-Rényi model where the two graphs are subsampled from a common parent Erdős-Rényi graph $\mathcal{G}(n,p)$. For dense graphs with $p=n^{-o(1)}$, we prove that there exists a sharp threshold, above which one can correctly match all but a vanishing fraction of vertices and below which correctly matching any positive fraction is impossible, a phenomenon known as the "all-or-nothing" phase transition. Even more strikingly, in the Gaussian setting, above the threshold all vertices can be exactly matched with high probability. In contrast, for sparse Erdős-Rényi graphs with $p=n^{-Θ(1)}$, we show that the all-or-nothing phenomenon no longer holds and we determine the thresholds up to a constant factor. Along the way, we also derive the sharp threshold for exact recovery, sharpening the existing results in Erdős-Rényi graphs. The proof of the negative results builds upon a tight characterization of the mutual information based on the truncated second-moment computation and an "area theorem" that relates the mutual information to the integral of the reconstruction error. The positive results follows from a tight analysis of the maximum likelihood estimator that takes into account the cycle structure of the induced permutation on the edges.

math.ST↗

arXiv2022

Lightweight Object-level Topological Semantic Mapping and Long-term Global Localization based on Graph Matching

Mapping and localization are two essential tasks for mobile robots in real-world applications. However, largescale and dynamic scenes challenge the accuracy and robustness of most current mature solutions. This situation becomes even worse when computational resources are limited. In this paper, we present a novel lightweight object-level mapping and localization method with high accuracy and robustness. Different from previous methods, our method does not need a prior constructed precise geometric map, which greatly releases the storage burden, especially for large-scale navigation. We use object-level features with both semantic and geometric information to model landmarks in the environment. Particularly, a learning topological primitive is first proposed to efficiently obtain and organize the object-level landmarks. On the basis of this, we use a robot-centric mapping framework to represent the environment as a semantic topology graph and relax the burden of maintaining global consistency at the same time. Besides, a hierarchical memory management mechanism is introduced to improve the efficiency of online mapping with limited computational resources. Based on the proposed map, the robust localization is achieved by constructing a novel local semantic scene graph descriptor, and performing multi-constraint graph matching to compare scene similarity. Finally, we test our method on a low-cost embedded platform to demonstrate its advantages. Experimental results on a large scale and multi-session real-world environment show that the proposed method outperforms the state of arts in terms of lightweight and robustness.

cs.RO↗

arXiv2021

Scale-Net: Learning to Reduce Scale Differences for Large-Scale Invariant Image Matching

Most image matching methods perform poorly when encountering large scale changes in images. To solve this problem, firstly, we propose a scale-difference-aware image matching method (SDAIM) that reduces image scale differences before local feature extraction, via resizing both images of an image pair according to an estimated scale ratio. Secondly, in order to accurately estimate the scale ratio, we propose a covisibility-attention-reinforced matching module (CVARM) and then design a novel neural network, termed as Scale-Net, based on CVARM. The proposed CVARM can lay more stress on covisible areas within the image pair and suppress the distraction from those areas visible in only one image. Quantitative and qualitative experiments confirm that the proposed Scale-Net has higher scale ratio estimation accuracy and much better generalization ability compared with all the existing scale ratio estimation methods. Further experiments on image matching and relative pose estimation tasks demonstrate that our SDAIM and Scale-Net are able to greatly boost the performance of representative local features and state-of-the-art local feature matching methods.

cs.CV↗

arXiv2021

Sharp regret bounds for empirical Bayes and compound decision problems

We consider the classical problems of estimating the mean of an $n$-dimensional normally (with identity covariance matrix) or Poisson distributed vector under the squared loss. In a Bayesian setting the optimal estimator is given by the prior-dependent conditional mean. In a frequentist setting various shrinkage methods were developed over the last century. The framework of empirical Bayes, put forth by Robbins (1956), combines Bayesian and frequentist mindsets by postulating that the parameters are independent but with an unknown prior and aims to use a fully data-driven estimator to compete with the Bayesian oracle that knows the true prior. The central figure of merit is the regret, namely, the total excess risk over the Bayes risk in the worst case (over the priors). Although this paradigm was introduced more than 60 years ago, little is known about the asymptotic scaling of the optimal regret in the nonparametric setting. We show that for the Poisson model with compactly supported and subexponential priors, the optimal regret scales as $Θ((\frac{\log n}{\log\log n})^2)$ and $Θ(\log^3 n)$, respectively, both attained by the original estimator of Robbins. For the normal mean model, the regret is shown to be at least $Ω((\frac{\log n}{\log\log n})^2)$ and $Ω(\log^2 n)$ for compactly supported and subgaussian priors, respectively, the former of which resolves the conjecture of Singh (1979) on the impossibility of achieving bounded regret; before this work, the best regret lower bound was $Ω(1)$. In addition to the empirical Bayes setting, these results are shown to hold in the compound setting where the parameters are deterministic. As a side application, the construction in this paper also leads to improved or new lower bounds for density estimation of Gaussian and Poisson mixtures.

math.ST↗

arXiv2021

Optimal estimation of high-dimensional location Gaussian mixtures

This paper studies the optimal rate of estimation in a finite Gaussian location mixture model in high dimensions without separation conditions. We assume that the number of components $k$ is bounded and that the centers lie in a ball of bounded radius, while allowing the dimension $d$ to be as large as the sample size $n$. Extending the one-dimensional result of Heinrich and Kahn \cite{HK2015}, we show that the minimax rate of estimating the mixing distribution in Wasserstein distance is $Θ((d/n)^{1/4} + n^{-1/(4k-2)})$, achieved by an estimator computable in time $O(nd^2+n^{5/4})$. Furthermore, we show that the mixture density can be estimated at the optimal parametric rate $Θ(\sqrt{d/n})$ in Hellinger distance and provide a computationally efficient algorithm to achieve this rate in the special case of $k=2$. Both the theoretical and methodological development rely on a careful application of the method of moments. Central to our results is the observation that the information geometry of finite Gaussian mixtures is characterized by the moment tensors of the mixing distribution, whose low-rank structure can be exploited to obtain a sharp local entropy bound.

math.ST↗

arXiv2021

Giant enhancement of anomalous Hall effect in Cr modulation-doped non-collinear antiferromagnetic Mn3Sn thin films

We report on Cr doping effect in Mn3Sn polycrystalline films with both uniform and modulation doping. It is found that Cr doping with low concentration does not cause notable changes to the structural and magnetic properties of Mn3Sn, but it significantly enhances the anomalous Hall conductivity, particularly for modulation-doped samples at low temperature. A Hall conductivity as high as 184.8 Ω-1 cm-1 is obtained for modulation-doped samples at 50 K, in a sharp contrast to vanishingly small values for undoped samples at the same temperature. We attribute the enhancement to the change of Fermi level induced by Cr doping

cond-mat.mtrl-sci↗

arXiv2021

Polynomial methods in statistical inference: theory and practice

This survey provides an exposition of a suite of techniques based on the theory of polynomials, collectively referred to as polynomial methods, which have recently been applied to address several challenging problems in statistical inference successfully. Topics including polynomial approximation, polynomial interpolation and majorization, moment space and positive polynomials, orthogonal polynomials and Gaussian quadrature are discussed, with their major probabilistic and statistical applications in property estimation on large domains and learning mixture models. These techniques provide useful tools not only for the design of highly practical algorithms with provable optimality, but also for establishing the fundamental limits of the inference problems through the method of moment matching. The effectiveness of the polynomial method is demonstrated in concrete problems such as entropy and support size estimation, distinct elements problem, and learning Gaussian mixture models.

math.ST↗

arXiv2021

Heteroskedastic PCA: Algorithm, Optimality, and Applications

A general framework for principal component analysis (PCA) in the presence of heteroskedastic noise is introduced. We propose an algorithm called HeteroPCA, which involves iteratively imputing the diagonal entries of the sample covariance matrix to remove estimation bias due to heteroskedasticity. This procedure is computationally efficient and provably optimal under the generalized spiked covariance model. A key technical step is a deterministic robust perturbation analysis on singular subspaces, which can be of independent interest. The effectiveness of the proposed algorithm is demonstrated in a suite of problems in high-dimensional statistics, including singular value decomposition (SVD) under heteroskedastic noise, Poisson PCA, and SVD for heteroskedastic and incomplete data.

math.ST↗

arXiv2021

Origin and Large Enhancement of Large Spin Hall Angle in Weyl Semimetals LaAl$X$ ($X$=Si, Ge)

We study the origin of the strong spin Hall effect (SHE) in a recently discovered family of Weyl semimetals, LaAl$X$ ($X$=Si, Ge) via a first-principles approach with maximally localized Wannier functions. We show that the strong intrinsic SHE in LaAl$X$ originates from the multiple slight anticrossings of nodal lines and points near $E_F$ due to their high mirror symmetry and large spin-orbit interaction. It is further found that both electrical and thermal means can enhance the spin Hall conductivity ($σ_{SH}$). However, the former also increases the electrical conductivity ($σ_{c}$), while the latter decreases it. As a result, the independent tuning of $σ_{SH}$ and $σ_{c}$ by thermal means can enhance the spin Hall angle (proportional to $\frac{σ_{SH}}{σ_{c}}$), a figure of merit of charge-to-spin current interconversion of spin-orbit torque devices. The underlying physics of such independent changes of the spin Hall and electrical conductivity by thermal means is revealed through the band-resolved and $k$-resolved spin Berry curvature. Our finding offers a new way in the search of high SHA materials for room-temperature spin-orbitronics applications.

cond-mat.mes-hall↗

arXiv2021

The planted matching problem: Sharp threshold and infinite-order phase transition

We study the problem of reconstructing a perfect matching $M^*$ hidden in a randomly weighted $n\times n$ bipartite graph. The edge set includes every node pair in $M^*$ and each of the $n(n-1)$ node pairs not in $M^*$ independently with probability $d/n$. The weight of each edge $e$ is independently drawn from the distribution $\mathcal{P}$ if $e \in M^*$ and from $\mathcal{Q}$ if $e \notin M^*$. We show that if $\sqrt{d} B(\mathcal{P},\mathcal{Q}) \le 1$, where $B(\mathcal{P},\mathcal{Q})$ stands for the Bhattacharyya coefficient, the reconstruction error (average fraction of misclassified edges) of the maximum likelihood estimator of $M^*$ converges to $0$ as $n\to \infty$. Conversely, if $\sqrt{d} B(\mathcal{P},\mathcal{Q}) \ge 1+ε$ for an arbitrarily small constant $ε>0$, the reconstruction error for any estimator is shown to be bounded away from $0$ under both the sparse and dense model, resolving the conjecture in [Moharrami et al. 2019, Semerjian et al. 2020]. Furthermore, in the special case of complete exponentially weighted graph with $d=n$, $\mathcal{P}=\exp(λ)$, and $\mathcal{Q}=\exp(1/n)$, for which the sharp threshold simplifies to $λ=4$, we prove that when $λ\le 4-ε$, the optimal reconstruction error is $\exp\left( - Θ(1/\sqrtε) \right)$, confirming the conjectured infinite-order phase transition in [Semerjian et al. 2020].

math.ST↗

arXiv2021

Likelihood landscape and maximum likelihood estimation for the discrete orbit recovery model

We study the non-convex optimization landscape for maximum likelihood estimation in the discrete orbit recovery model with Gaussian noise. This model is motivated by applications in molecular microscopy and image processing, where each measurement of an unknown object is subject to an independent random rotation from a rotational group. Equivalently, it is a Gaussian mixture model where the mixture centers belong to a group orbit. We show that fundamental properties of the likelihood landscape depend on the signal-to-noise ratio and the group structure. At low noise, this landscape is "benign" for any discrete group, possessing no spurious local optima and only strict saddle points. At high noise, this landscape may develop spurious local optima, depending on the specific group. We discuss several positive and negative examples, and provide a general condition that ensures a globally benign landscape. For cyclic permutations of coordinates on $\mathbb{R}^d$ (multi-reference alignment), there may be spurious local optima when $d \geq 6$, and we establish a correspondence between these local optima and those of a surrogate function of the phase variables in the Fourier domain. We show that the Fisher information matrix transitions from resembling that of a single Gaussian in low noise to having a graded eigenvalue structure in high noise, which is determined by the graded algebra of invariant polynomials under the group action. In a local neighborhood of the true object, the likelihood landscape is strongly convex in a reparametrized system of variables given by a transcendence basis of this polynomial algebra. We discuss implications for optimization algorithms, including slow convergence of expectation-maximization, and possible advantages of momentum-based acceleration and variable reparametrization for first- and second-order descent methods.

math.ST↗

arXiv2021

Testing correlation of unlabeled random graphs

We study the problem of detecting the edge correlation between two random graphs with $n$ unlabeled nodes. This is formalized as a hypothesis testing problem, where under the null hypothesis, the two graphs are independently generated; under the alternative, the two graphs are edge-correlated under some latent node correspondence, but have the same marginal distributions as the null. For both Gaussian-weighted complete graphs and dense Erdős-Rényi graphs (with edge probability $n^{-o(1)}$), we determine the sharp threshold at which the optimal testing error probability exhibits a phase transition from zero to one as $n\to \infty$. For sparse Erdős-Rényi graphs with edge probability $n^{-Ω(1)}$, we determine the threshold within a constant factor. The proof of the impossibility results is an application of the conditional second-moment method, where we bound the truncated second moment of the likelihood ratio by carefully conditioning on the typical behavior of the intersection graph (consisting of edges in both observed graphs) and taking into account the cycle structure of the induced random permutation on the edges. Notably, in the sparse regime, this is accomplished by leveraging the pseudoforest structure of subcritical Erdős-Rényi graphs and a careful enumeration of subpseudoforests that can be assembled from short orbits of the edge permutation.

math.ST↗

arXiv2021

EventAnchor: Reducing Human Interactions in Event Annotation of Racket Sports Videos

The popularity of racket sports (e.g., tennis and table tennis) leads to high demands for data analysis, such as notational analysis, on player performance. While sports videos offer many benefits for such analysis, retrieving accurate information from sports videos could be challenging. In this paper, we propose EventAnchor, a data analysis framework to facilitate interactive annotation of racket sports video with the support of computer vision algorithms. Our approach uses machine learning models in computer vision to help users acquire essential events from videos (e.g., serve, the ball bouncing on the court) and offers users a set of interactive tools for data annotation. An evaluation study on a table tennis annotation system built on this framework shows significant improvement of user performances in simple annotation tasks on objects of interest and complex annotation tasks requiring domain knowledge.

cs.HC↗

arXiv2021

On the origin of hard X-ray emissions from the behind-the-limb flare on 2014 September 1

The origin of hard X-rays and gamma-rays emitted from the solar atmosphere during occulted solar flares is still debated. The hard X-ray emissions could come from flaring loop tops rising above the limb or Coronal Mass Ejections (CME) shock waves, two by-products of energetic solar storms. For the shock scenario to work, accelerated particles must be released on magnetic field lines rooted on the visible disk and precipitate. We present a new Monte Carlo code that computes particle acceleration at shocks propagating along large coronal magnetic loops. A first implementation of the model is carried out for the 2014 September 1 event and the modeled electron spectra are compared with those inferred from Fermi Gamma-ray Burst Monitor (GBM) measurements. When particle diffusion processes are invoked our model can reproduce the hard electron spectra measured by GBM nearly ten minutes after the estimated on-disk hard X-rays appear to have ceased from the flare site.

astro-ph.SR↗

arXiv2021

Dualizing Le Cam's method for functional estimation, with applications to estimating the unseens

Le Cam's method (or the two-point method) is a commonly used tool for obtaining statistical lower bound and especially popular for functional estimation problems. This work aims to explain and give conditions for the tightness of Le Cam's lower bound in functional estimation from the perspective of convex duality. Under a variety of settings it is shown that the maximization problem that searches for the best two-point lower bound, upon dualizing, becomes a minimization problem that optimizes the bias-variance tradeoff among a family of estimators. For estimating linear functionals of a distribution our work strengthens prior results of Donoho-Liu \cite{DL91} (for quadratic loss) by dropping the Hölderian assumption on the modulus of continuity. For exponential families our results extend those of Juditsky-Nemirovski \cite{JN09} by characterizing the minimax risk for the quadratic loss under weaker assumptions on the exponential family. We also provide an extension to the high-dimensional setting for estimating separable functionals. Notably, coupled with tools from complex analysis, this method is particularly effective for characterizing the ``elbow effect'' -- the phase transition from parametric to nonparametric rates. As the main application we derive sharp minimax rates in the Distinct elements problem (given a fraction $p$ of colored balls from an urn containing $d$ balls, the optimal error of estimating the number of distinct colors is $\tilde Θ(d^{-\frac{1}{2}\min\{\frac{p}{1-p},1\}})$) and the Fisher's species problem (given $n$ iid observations from an unknown distribution, the optimal prediction error of the number of unseen symbols in the next (unobserved) $r \cdot n$ observations is $\tilde Θ(n^{-\min\{\frac{1}{r+1},\frac{1}{2}\}})$).

math.ST↗