arXiv subjects

Runze Li

Publications and source records attributed to Runze Li.

At least 109 records · Page 6Linked to original sources

arXiv2022

Central limit theorem and Berry-Esseen bounds for a branching random walk with immigration in a random environment

We consider a branching random walk on $d$-dimensional real space with immigration in a time-dependent random environment. Let $Z_n(\mathbf t)$ be the so-called partition function of the process, namely, the moment generating function of the counting measure describing the dispersion of individuals at time $n$. For $\mathbf t$ fixed, the logarithm $\log Z_n(\mathbf t)$ satisfies a central limit theorem. By studying the logarithmic moments of the intrinsic submartingale of the system and its convergence rates, we establish the uniform and non-uniform Berry-Esseen bounds corresponding to the central limit theorem, and discover the exact convergence rate in the central limit theorem.

math.PR↗

arXiv2022

Linear maps preserving the Lorentz spectrum of $3 \times 3$ matrices

For a given $3 \times 3$ real matrix $A$, the eigenvalue complementarity problem relative to the Lorentz cone consists of finding a real number $λ$ and a nonzero vector $x \in \mathbb{R}^3$ such that $x^T(A-λI)x=0$ and both $x$ and $(A-λI)x$ lie in the Lorentz cone, which is comprised of all vectors in $\mathbb{R}^3$ forming a $45^\circ$ or smaller angle with the positive $z$-axis. We refer to the set of all solutions $λ$ to this eigenvalue complementarity problem as the Lorentz spectrum of $A$. Our work concerns the characterization of the linear preservers of the Lorentz spectrum on the space $M_3$ of $3 \times 3$ real matrices, that is, the linear maps $ϕ: M_3 \to M_3$ such that the Lorentz spectra of $A$ and $ϕ(A)$ are the same for all $A$. We have proven that all such linear preservers take the form $ϕ(A) = (Q \oplus [1])A(Q^T \oplus [1])$, where $Q$ is an orthogonal $2 \times 2$ matrix.

math.RA↗

arXiv2022

MonoIndoor++:Towards Better Practice of Self-Supervised Monocular Depth Estimation for Indoor Environments

Self-supervised monocular depth estimation has seen significant progress in recent years, especially in outdoor environments. However, depth prediction results are not satisfying in indoor scenes where most of the existing data are captured with hand-held devices. As compared to outdoor environments, estimating depth of monocular videos for indoor environments, using self-supervised methods, results in two additional challenges: (i) the depth range of indoor video sequences varies a lot across different frames, making it difficult for the depth network to induce consistent depth cues for training; (ii) the indoor sequences recorded with handheld devices often contain much more rotational motions, which cause difficulties for the pose network to predict accurate relative camera poses. In this work, we propose a novel framework-MonoIndoor++ by giving special considerations to those challenges and consolidating a set of good practices for improving the performance of self-supervised monocular depth estimation for indoor environments. First, a depth factorization module with transformer-based scale regression network is proposed to estimate a global depth scale factor explicitly, and the predicted scale factor can indicate the maximum depth values. Second, rather than using a single-stage pose estimation strategy as in previous methods, we propose to utilize a residual pose estimation module to estimate relative camera poses across consecutive frames iteratively. Third, to incorporate extensive coordinates guidance for our residual pose estimation module, we propose to perform coordinate convolutional encoding directly over the inputs to pose networks. The proposed method is validated on a variety of benchmark indoor datasets, i.e., EuRoC MAV, NYUv2, ScanNet and 7-Scenes, demonstrating the state-of-the-art performance.

cs.CV↗

arXiv2022

Study of transfer learning from 2D supercritical airfoils to 3D transonic swept wings

Machine learning has been widely utilized in fluid mechanics studies and aerodynamic optimizations. However, most applications, especially flow field modeling and inverse design, involve two-dimensional flows and geometries. The dimensionality of three-dimensional problems is so high that it is too difficult and expensive to prepare sufficient samples. Therefore, transfer learning has become a promising approach to reuse well-trained two-dimensional models and greatly reduce the need for samples for three-dimensional problems. This paper proposes to reuse the baseline models trained on supercritical airfoils to predict finite-span swept supercritical wings, where the simple swept theory is embedded to improve the prediction accuracy. Two baseline models for transfer learning are investigated: one is commonly referred to as the forward problem of predicting the pressure coefficient distribution based on the geometry, and the other is the inverse problem that predicts the geometry based on the pressure coefficient distribution. Two transfer learning strategies are compared for both baseline models. The transferred models are then tested on the prediction of complete wings. The results show that transfer learning requires only approximately 500 wing samples to achieve good prediction accuracy on different wing planforms and different free stream conditions. Compared to the two baseline models, the transferred models reduce the prediction error by 60% and 80%, respectively.

physics.flu-dyn↗

arXiv2022

Model-Free Statistical Inference on High-Dimensional Data

This paper aims to develop an effective model-free inference procedure for high-dimensional data. We first reformulate the hypothesis testing problem via sufficient dimension reduction framework. With the aid of new reformulation, we propose a new test statistic and show that its asymptotic distribution is $χ^2$ distribution whose degree of freedom does not depend on the unknown population distribution. We further conduct power analysis under local alternative hypotheses. In addition, we study how to control the false discovery rate of the proposed $χ^2$ tests, which are correlated, to identify important predictors under a model-free framework. To this end, we propose a multiple testing procedure and establish its theoretical guarantees. Monte Carlo simulation studies are conducted to assess the performance of the proposed tests and an empirical analysis of a real-world data set is used to illustrate the proposed methodology.

stat.ME↗

arXiv2022

Multiple-Splitting Projection Test for High-Dimensional Mean Vectors

We propose a multiple-splitting projection test (MPT) for one-sample mean vectors in high-dimensional settings. The idea of projection test is to project high-dimensional samples to a 1-dimensional space using an optimal projection direction such that traditional tests can be carried out with projected samples. However, estimation of the optimal projection direction has not been systematically studied in the literature. In this work, we bridge the gap by proposing a consistent estimation via regularized quadratic optimization. To retain type I error rate, we adopt a data-splitting strategy when constructing test statistics. To mitigate the power loss due to data-splitting, we further propose a test via multiple splits to enhance the testing power. We show that the $p$-values resulted from multiple splits are exchangeable. Unlike existing methods which tend to conservatively combine dependent $p$-values, we develop an exact level $α$ test that explicitly utilizes the exchangeability structure to achieve better power. Numerical studies show that the proposed test well retains the type I error rate and is more powerful than state-of-the-art tests.

stat.ME↗

arXiv2022

Flowfield prediction of airfoil off-design conditions based on a modified variational autoencoder

Airfoil aerodynamic optimization based on single-point design may lead to poor off-design behaviors. Multipoint optimization that considers the off-design flow conditions is usually applied to improve the robustness and expand the flight envelope. Many deep learning models have been utilized for the rapid prediction or reconstruction of flowfields. However, the flowfield reconstruction accuracy may be insufficient for cruise efficiency optimization, and the model generalization ability is also questionable when facing airfoils different from the airfoils with which the model has been trained. Because a computational fluid dynamic evaluation of the cruise condition is usually necessary and affordable in industrial design, a novel deep learning framework is proposed to utilize the cruise flowfield as a prior reference for the off-design condition prediction. A prior variational autoencoder is developed to extract features from the cruise flowfield and to generate new flowfields under other free stream conditions. Physical-based loss functions based on aerodynamic force and conservation of mass are derived to minimize the prediction error of the flowfield reconstruction. The results demonstrate that the proposed model can reduce the prediction error on test airfoils by 30% compared to traditional models. The physical-based loss function can further reduce the prediction error by 4%. The proposed model illustrates a better balance of the time cost and the fidelity requirements of evaluation for cruise and off-design conditions, which makes the model more feasible for industrial applications.

physics.flu-dyn↗

arXiv2022

Physically Interpretable Feature Learning and Inverse Design of Supercritical Airfoils

Machine-learning models have demonstrated a great ability to learn complex patterns and make predictions. In high-dimensional nonlinear problems of fluid dynamics, data representation often greatly affects the performance and interpretability of machine learning algorithms. With the increasing application of machine learning in fluid dynamics studies, the need for physically explainable models continues to grow. This paper proposes a feature learning algorithm based on variational autoencoders, which is able to assign physical features to some latent variables of the variational autoencoder. In addition, it is theoretically proved that the remaining latent variables are independent of the physical features. The proposed algorithm is trained to include shock wave features in its latent variables for the reconstruction of supercritical pressure distributions. The reconstruction accuracy and physical interpretability are also compared with those of other variational autoencoders. Then, the proposed algorithm is used for the inverse design of supercritical airfoils, which enables the generation of airfoil geometries based on physical features rather than the complete pressure distributions. It also demonstrates the ability to manipulate certain pressure distribution features of the airfoil without changing the others.

physics.flu-dyn↗

arXiv2022

Invariance principle and CLT for the spiked eigenvalues of large-dimensional Fisher matrices and applications

This paper aims to derive asymptotical distributions of the spiked eigenvalues of the large-dimensional spiked Fisher matrices without Gaussian assumption and the restrictive assumptions on covariance matrices. We first establish invariance principle for the spiked eigenvalues of the Fisher matrix. That is, we show that the limiting distributions of the spiked eigenvalues are invariant over a large class of population distributions satisfying certain conditions. Using the invariance principle, we further established a central limit theorem (CLT) for the spiked eigenvalues. As some interesting applications, we use the CLT to derive the power functions of Roy Maximum root test for linear hypothesis in linear models and the test in signal detection. We conduct some Monte Carlo simulation to compare the proposed test with existing ones.

math.ST↗

arXiv2022

Causal Structural Learning on MPHIA Individual Dataset

The Population-based HIV Impact Assessment (PHIA) is an ongoing project that conducts nationally representative HIV-focused surveys for measuring national and regional progress toward UNAIDS' 90-90-90 targets, the primary strategy to end the HIV epidemic. We believe the PHIA survey offers a unique opportunity to better understand the key factors that drive the HIV epidemics in the most affected countries in sub-Saharan Africa. In this article, we propose a novel causal structural learning algorithm to discover important covariates and potential causal pathways for 90-90-90 targets. Existing constrained-based causal structural learning algorithms are quite aggressive in edge removal. The proposed algorithm preserves more information about important features and potential causal pathways. It is applied to the Malawi PHIA (MPHIA) data set and leads to interesting results. For example, it discovers age and condom usage to be important for female HIV awareness; the number of sexual partners to be important for male HIV awareness; and knowing the travel time to HIV care facilities leads to a higher chance of being treated for both females and males. We further compare and validate the proposed algorithm using BIC and using Monte Carlo simulations, and show that the proposed algorithm achieves improvement in true positive rates in important feature discovery over existing algorithms.

stat.ME↗

arXiv2021

Space Charge Driven Emittance Growth and the Effect of Octupoles in IOTA

The Integrable Optics Test Accelerator (IOTA) at Fermilab is a small machine dedicated to a broad frontier accelerator physics program. An important aspect of this program is to investigate the potential benefits of the resonance free tune spread achievable with integrable optics to store and accelerate high intensity proton beams for which space charge is significant. In this context, a good understanding of proton beam emittance growth and particle loss mechanisms is essential. Assuming nominal design parameters, simulations show that for a bunched beam, the bulk of emittance growth takes place immediately following injection, typically within tens of turns. We attempt to account for this growth using a simplified RMS mismatch theory; some of its limitations and possible improvements are briefly discussed. We then compare theoretical predictions to simulations performed using the PIC code pyORBIT. Further exploring ways to mitigate emittance growth and reduce particle loss, we compare two beam matching strategies: (1) matching at the injection point (2) matching at the center of the nonlinear (octupole) insertion region where $β_x = β_y$. To observe how nonlinearity affects emittance growth and whether it dominates growth due to mismatch, we track two different distributions. Finally, we explore the potential of using octupoles in a quasi-integrable configuration to mitigate growth using a variety of initial distributions both at reduced and full intensities.

physics.acc-ph↗

arXiv2021

Power-enhanced simultaneous test of high-dimensional mean vectors and covariance matrices with application to gene-set testing

Power-enhanced tests with high-dimensional data have received growing attention in theoretical and applied statistics in recent years. Existing tests possess their respective high-power regions, and we may lack prior knowledge about the alternatives when testing for a problem of interest in practice. There is a critical need of developing powerful testing procedures against more general alternatives. This paper studies the joint test of two-sample mean vectors and covariance matrices for high-dimensional data. We first expand the high-power region of high-dimensional mean tests or covariance tests to a wider alternative space and then combine their strengths together in the simultaneous test. We develop a new power-enhanced simultaneous test that is powerful to detect differences in either mean vectors or covariance matrices under either sparse or dense alternatives. We prove that the proposed testing procedures align with the power enhancement principles introduced by Fan et al. (2015) and achieve the accurate asymptotic size and consistent asymptotic power. We demonstrate the finite-sample performance using simulation studies and a real application to find differentially expressed gene-sets in cancer studies. Our findings in the empirical study are supported by the biological literature.

stat.ME↗

arXiv2021

Statistical Inference for Linear Mediation Models with High-dimensional Mediators and Application to Studying Stock Reaction to COVID-19 Pandemic

Mediation analysis draws increasing attention in many scientific areas such as genomics, epidemiology and finance. In this paper, we propose new statistical inference procedures for high dimensional mediation models, in which both the outcome model and the mediator model are linear with high dimensional mediators. Traditional procedures for mediation analysis cannot be used to make statistical inference for high dimensional linear mediation models due to high-dimensionality of the mediators. We propose an estimation procedure for the indirect effects of the models via a partial penalized least squares method, and further establish its theoretical properties. We further develop a partial penalized Wald test on the indirect effects, and prove that the proposed test has a $χ^2$ limiting null distribution. We also propose an $F$-type test for direct effects and show that the proposed test asymptotically follows a $χ^2$-distribution under null hypothesis and a noncentral $χ^2$-distribution under local alternatives. Monte Carlo simulations are conducted to examine the finite sample performance of the proposed tests and compare their performance with existing ones. We further apply the newly proposed statistical inference procedures to study stock reaction to COVID-19 pandemic via an empirical analysis of studying the mediation effects of financial metrics that bridge company's sector and stock return.

stat.ME↗

arXiv2021

Transferring Knowledge with Attention Distillation for Multi-Domain Image-to-Image Translation

Gradient-based attention modeling has been used widely as a way to visualize and understand convolutional neural networks. However, exploiting these visual explanations during the training of generative adversarial networks (GANs) is an unexplored area in computer vision research. Indeed, we argue that this kind of information can be used to influence GANs training in a positive way. For this reason, in this paper, it is shown how gradient based attentions can be used as knowledge to be conveyed in a teacher-student paradigm for multi-domain image-to-image translation tasks in order to improve the results of the student architecture. Further, it is demonstrated how "pseudo"-attentions can also be employed during training when teacher and student networks are trained on different domains which share some similarities. The approach is validated on multi-domain facial attributes transfer and human expression synthesis showing both qualitative and quantitative results.

cs.CV↗

arXiv2021

MonoIndoor: Towards Good Practice of Self-Supervised Monocular Depth Estimation for Indoor Environments

Self-supervised depth estimation for indoor environments is more challenging than its outdoor counterpart in at least the following two aspects: (i) the depth range of indoor sequences varies a lot across different frames, making it difficult for the depth network to induce consistent depth cues, whereas the maximum distance in outdoor scenes mostly stays the same as the camera usually sees the sky; (ii) the indoor sequences contain much more rotational motions, which cause difficulties for the pose network, while the motions of outdoor sequences are pre-dominantly translational, especially for driving datasets such as KITTI. In this paper, special considerations are given to those challenges and a set of good practices are consolidated for improving the performance of self-supervised monocular depth estimation in indoor environments. The proposed method mainly consists of two novel modules, \ie, a depth factorization module and a residual pose estimation module, each of which is designed to respectively tackle the aforementioned challenges. The effectiveness of each module is shown through a carefully conducted ablation study and the demonstration of the state-of-the-art performance on three indoor datasets, \ie, EuRoC, NYUv2, and 7-scenes.

cs.CV↗

arXiv2021

Learning Local Recurrent Models for Human Mesh Recovery

We consider the problem of estimating frame-level full human body meshes given a video of a person with natural motion dynamics. While much progress in this field has been in single image-based mesh estimation, there has been a recent uptick in efforts to infer mesh dynamics from video given its role in alleviating issues such as depth ambiguity and occlusions. However, a key limitation of existing work is the assumption that all the observed motion dynamics can be modeled using one dynamical/recurrent model. While this may work well in cases with relatively simplistic dynamics, inference with in-the-wild videos presents many challenges. In particular, it is typically the case that different body parts of a person undergo different dynamics in the video, e.g., legs may move in a way that may be dynamically different from hands (e.g., a person dancing). To address these issues, we present a new method for video mesh recovery that divides the human mesh into several local parts following the standard skeletal model. We then model the dynamics of each local part with separate recurrent models, with each model conditioned appropriately based on the known kinematic structure of the human body. This results in a structure-informed local recurrent learning architecture that can be trained in an end-to-end fashion with available annotations. We conduct a variety of experiments on standard video mesh recovery benchmark datasets such as Human3.6M, MPI-INF-3DHP, and 3DPW, demonstrating the efficacy of our design of modeling local dynamics as well as establishing state-of-the-art results based on standard evaluation metrics.

cs.CV↗

arXiv2021

Modeling Transverse Space Charge effects in IOTA with pyORBIT

The role and mitigation of space charge effects are important aspects of the beam physics research to be performed at the Integrable Optics Test Accelerator (IOTA) at Fermilab. The impact of nonlinear integrability (partial and complete) on space charge driven incoherent and coherent resonances will be a new feature of this accelerator and has the potential to influence the design of future low energy proton synchrotrons. In this report we model transverse space charge effects using the PIC code pyORBIT. First we benchmark the single particle tracking results against MADX with checks on symplecticity, tune footprints, and dynamic aperture in a partially integrable lattice realized with a special octupole string insert. Our space charge calculations begin with an examination of the 4D symplecticity. Short term tracking is done first with the initial bare lattice and then with a matching of the rms values with space charge. Next, we explore slow initialization of charge as a technique to establish steady state and reduce emittance growth and beam loss following injection into a mismatched lattice. We establish values of space charge simulation parameters so as to ensure numerical convergence. Finally, we compare the simulated space charge induced tune shifts and footprints against theory.

physics.acc-ph↗

arXiv2021

Doubly Robust Feature Selection with Mean and Variance Outlier Detection and Oracle Properties

We propose a general approach to handle data contaminations that might disrupt the performance of feature selection and estimation procedures for high-dimensional linear models. Specifically, we consider the co-occurrence of mean-shift and variance-inflation outliers, which can be modeled as additional fixed and random components, respectively, and evaluated independently. Our proposal performs feature selection while detecting and down-weighting variance-inflation outliers, detecting and excluding mean-shift outliers, and retaining non-outlying cases with full weights. Feature selection and mean-shift outlier detection are performed through a robust class of nonconcave penalization methods. Variance-inflation outlier detection is based on the penalization of the restricted posterior mode. The resulting approach satisfies a robust oracle property for feature selection in the presence of data contamination -- which allows the number of features to exponentially increase with the sample size -- and detects truly outlying cases of each type with asymptotic probability one. This provides an optimal trade-off between a high breakdown point and efficiency. Computationally efficient heuristic procedures are also presented. We illustrate the finite-sample performance of our proposal through an extensive simulation study and a real-world application.

stat.ME↗