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Wei Dai

Publications and source records attributed to Wei Dai.

At least 199 records · Page 11Linked to original sources
arXiv2022

Orthogonal Stochastic Configuration Networks with Adaptive Construction Parameter for Data Analytics

As a randomized learner model, SCNs are remarkable that the random weights and biases are assigned employing a supervisory mechanism to ensure universal approximation and fast learning. However, the randomness makes SCNs more likely to generate approximate linear correlative nodes that are redundant and low quality, thereby resulting in non-compact network structure. In the light of a fundamental principle in machine learning, that is, a model with fewer parameters holds improved generalization. This paper proposes orthogonal SCN, termed OSCN, to filtrate out the low-quality hidden nodes for network structure reduction by incorporating Gram-Schmidt orthogonalization technology. The universal approximation property of OSCN and an adaptive setting for the key construction parameters have been presented in details. In addition, an incremental updating scheme is developed to dynamically determine the output weights, contributing to improved computational efficiency. Finally, experimental results on two numerical examples and several real-world regression and classification datasets substantiate the effectiveness and feasibility of the proposed approach.

cs.LG↗
arXiv2022

Blind Two-Dimensional Super-Resolution and Its Performance Guarantee (Extended Version)

We study the problem of identifying the parameters of a linear system from its response to multiple unknown waveforms. We assume that the system response is a scaled superposition of time-delayed and frequency-shifted versions of the unknown waveforms. Such kind of problem is severely ill-posed and does not yield a unique solution without introducing further constraints. To fully characterize the system, we assume that the unknown waveforms lie in a common known low-dimensional subspace that satisfies certain properties. Then, we develop a blind two-dimensional (2D) super-resolution framework that applies to a large number of applications. In this framework, we show that under a minimum separation between the time-frequency shifts, all the unknowns that characterize the system can be recovered precisely and with high probability provided that a lower bound on the number of the observed samples is satisfied. The proposed framework is based on a 2D atomic norm minimization problem, which is shown to be reformulated and solved via semidefinite programming. Simulation results that confirm the theoretical findings of the paper are provided.

cs.IT↗
arXiv2022

Maximum principles and the method of moving planes for the uniformly elliptic nonlocal Bellman operator and applications

In this paper, we establish various maximum principles and develop the method of moving planes and the sliding method (on general unbounded domains) for equations involving the uniformly elliptic nonlocal Bellman operator. As a consequence, we derive multiple applications of these maximum principles and the moving planes method. For instance, we prove symmetry, monotonicity and uniqueness results and asymptotic properties for solutions to various equations involving the uniformly elliptic nonlocal Bellman operator in bounded domains, unbounded domains, epigraph or $\mathbb{R}^{n}$. In particular, the uniformly elliptic nonlocal Monge-Ampère operator introduced by Caffarelli and Charro in \cite{CC} is a typical example of the uniformly elliptic nonlocal Bellman operator.

math.AP↗
arXiv2022

Data-Efficient Modeling for Precise Power Consumption Estimation of Quadrotor Operations Using Ensemble Learning

Electric Take-Off and Landing (eVTOL) aircraft is considered as the major aircraft type in the emerging urban air mobility. Accurate power consumption estimation is crucial to eVTOL, supporting advanced power management strategies and improving the efficiency and safety performance of flight operations. In this study, a framework for power consumption modeling of eVTOL aircraft was established. We employed an ensemble learning method, namely stacking, to develop a data-driven model using flight records of three different types of quadrotors. Random forest and extreme gradient boosting, showing advantages in prediction, were chosen as base-models, and a linear regression model was used as the meta-model. The established stacking model can accurately estimate the power of a quadrotor. Error analysis shows that about 80% prediction errors fall within one standard deviation interval and less than 0.5% error in the prediction for an entire flight can be expected with a confidence of more than 80%. Our model outperforms the existing models in two aspects: firstly, our model has a better prediction performance, and secondly, our model is more data-efficient, requiring a much smaller dataset. Our model provides a powerful tool for operators of eVTOL aircraft in mission management and contributes to promoting safe and energy-efficient urban air traffic.

cs.LG↗
arXiv2022

Probing the in-medium $P_T$-broadening by $γ$+HF angular de-correlations

Angular correlations between vector boson and heavy flavors~(HF) are potentially new effective tools to gain insight into the partonic interactions in the quark-gluon plasma (QGP). In this paper, we present the theoretical study of the azimuthal angular de-correlations of $γ+$HF in nucleus-nucleus collisions as a new probe of the in-medium $P_T$-broadening effect. The initial production of $γ+$HF in p+p is generated by SHERPA which matches the next-to-leading hard processes with parton shower. The in-medium heavy quark evolution is implemented by a Monte Carlo Langevin simulation, which takes into account the collisional and radiative energy loss. We observe considerable suppression at $Δϕ_{γD}\simπ$ and enhancement at $Δϕ_{γD}<2.8$ in $γ+$D azimuthal angular distribution in $0-10\%$ Pb+Pb collisions at $\sqrt{s_{NN}}=$5.02 TeV compared to the p+p baseline, which indicates evident in-medium $P_T$-broadening of charm quarks. We also find that the overall modification patterns of $γ+$D angular distribution are sensitive to the selection cut of D meson $p_T$. Furthermore, by constructing the 2D ($x_{J}^{γD}, Δϕ_{γD}$) correlation diagram, it's possible to display the respective impacts of the two aspects of jet quenching, energy loss and $P_T$-broadening, on the final-state $γ+$D observable simultaneously. Additionally, we find weaker angular de-correlations of $γ+$B compared to $γ+$D which may be helpful to understand the mass hierarchy in heavy-ion collisions. Finally, the nuclear modification of $Δϕ_{γD}$ distributions in central $0-10\%$ Au+Au collisions at RHIC energy is provided for completeness.

nucl-th↗
arXiv2022

Digging into Primary Financial Market: Challenges and Opportunities of Adopting Blockchain

Since the emergence of blockchain technology, its application in the financial market has always been an area of focus and exploration by all parties. With the characteristics of anonymity, trust, tamper-proof, etc., blockchain technology can effectively solve some problems faced by the financial market, such as trust issues and information asymmetry issues. To deeply understand the application scenarios of blockchain in the financial market, the issue of securities issuance and trading in the primary market is a problem that must be studied clearly. We conducted an empirical study to investigate the main difficulties faced by primary market participants in their business practices and the potential challenges of the deepening application of blockchain technology in the primary market. We adopted a hybrid method combining interviews (qualitative methods) and surveys (quantitative methods) to conduct this research in two stages. In the first stage, we interview 15 major primary market participants with different backgrounds and expertise. In the second phase, we conducted a verification survey of 54 primary market practitioners to confirm various insights from the interviews, including challenges and desired improvements. Our interviews and survey results revealed several significant challenges facing blockchain applications in the primary market: complex due diligence, mismatch, and difficult monitoring. On this basis, we believe that our future research can focus on some aspects of these challenges.

q-fin.ST↗
arXiv2022

A New Learning Paradigm for Stochastic Configuration Network: SCN+

Learning using privileged information (LUPI) paradigm, which pioneered teacher-student interaction mechanism, makes the learning models use additional information in training stage. This paper is the first to propose an incremental learning algorithm with LUPI paradigm for stochastic configuration network (SCN), named SCN+. This novel algorithm can leverage privileged information into SCN in the training stage, which provides a new method to train SCN. Moreover, the convergences have been studied in this paper. Finally, experimental results indicate that SCN+ indeed performs favorably.

cs.LG↗
arXiv2022

Benchmarking Robustness of Deep Learning Classifiers Using Two-Factor Perturbation

Accuracies of deep learning (DL) classifiers are often unstable in that they may change significantly when retested on adversarial images, imperfect images, or perturbed images. This paper adds to the fundamental body of work on benchmarking the robustness of DL classifiers on defective images. To measure robust DL classifiers, previous research reported on single-factor corruption. We created comprehensive 69 benchmarking image sets, including a clean set, sets with single factor perturbations, and sets with two-factor perturbation conditions. The state-of-the-art two-factor perturbation includes (a) two digital perturbations (salt & pepper noise and Gaussian noise) applied in both sequences, and (b) one digital perturbation (salt & pepper noise) and a geometric perturbation (rotation) applied in both sequences. Previous research evaluating DL classifiers has often used top-1/top-5 accuracy. We innovate a new two-dimensional, statistical matrix to evaluating robustness of DL classifiers. Also, we introduce a new visualization tool, including minimum accuracy, maximum accuracy, mean accuracies, and coefficient of variation (CV), for benchmarking robustness of DL classifiers. Comparing with single factor corruption, we first report that using two-factor perturbed images improves both robustness and accuracy of DL classifiers. All source codes and related image sets are shared on the Website at http://cslinux.semo.edu/david/data to support future academic research and industry projects.

cs.CV↗
arXiv2021

An Empirical Evaluation On the Applicability of the DALiuGE Execution Framework

The Square Kilometre Array (SKA) project is an international cooperation project to build the largest radio telescope worldwide. Data processing is one of the biggest challenges of building the SKA telescope. As a distributed execution framework, the Data Activated Liu Graph Engine (DALiuGE) was proposed to be one of the candidates for addressing the massive data of the SKA. DALiuGE has many distinctive features, but its actual ability to handle scientific data is still not evident. In this paper, we perform an objective evaluation of the usability of DALiuGE concerning the execution performance, developer workload, and implementation difficulty of porting the SAGECal to DALiuGE. The evaluation results showed that the DALiuGE enables fast integration of astronomical software, but there are significant differences in the efficiency of different parallel granularities. Even with the deep optimization of the program, there is still a gap between the current DALiuGE and the traditional MPI in execution performance. Therefore, we come to a preliminary conclusion that the DALiuGE has no performance advantage in batch processing of massive data, while it may be more suitable for application scenarios with more customized computational tasks, such as SKA science regional centers.

astro-ph.IM↗
arXiv2021

Short-and-Sparse Deconvolution Via Rank-One Constrained Optimization (ROCO)

Short-and-sparse deconvolution (SaSD) aims to recover a short kernel and a long and sparse signal from their convolution. In the literature, formulations of blind deconvolution is either a convex programming via a matrix lifting of convolution, or a bilinear Lasso. Optimization solvers are typically based on bilinear factorizations. In this paper, we formulate SaSD as a non-convex optimization with a rank-one matrix constraint, hence referred to as Rank-One Constrained Optimization (ROCO). The solver is based on alternating direction method of multipliers (ADMM). It operates on the full rank-one matrix rather than bilinear factorizations. Closed form updates are derived for the efficiency of ADMM. Simulations include both synthetic data and real images. Results show substantial improvements in recovery accuracy (at least 19dB in PSNR for real images) and comparable runtime compared with benchmark algorithms based on bilinear factorization.

eess.SP↗
arXiv2021

Long time existence for semilinear wave equations with the inverse-square potential

In this paper, we study the semilinear wave equations with the inverse-square potential. By transferring the original equation to a "fractional dimensional" wave equation and analyzing the properties of its fundamental solution, we establish a long-time existence result, for sufficiently small, spherically symmetric initial data. Together with the previously known blow-up result, we determine the critical exponent which divides the global existence and finite time blow-up. Moreover, the sharp lower bounds of the lifespan are obtained, except for certain borderline case. In addition, our technology allows us to handle an extreme case for the potential, which has hardly been discussed in literature.

math.AP↗
arXiv2021

Liouville type theorems for fractional and higher order Hénon-Hardy type equations via the method of scaling spheres

In this paper, we are concerned with the fractional and higher order Hénon-Hardy type equations \begin{equation*} (-Δ)^{\fracα{2}}u(x)=f(x,u(x)) \,\,\,\,\,\,\,\,\,\,\,\, \text{in} \,\,\, \mathbb{R}^{n}, \,\,\, \mathbb{R}^{n}_{+} \,\,\, \text{or} \,\,\, Ω\end{equation*} with $n>α$, $0<α<2$ or $α=2m$ with $1\leq m<\frac{n}{2}$. We first consider the typical case $f(x,u)=|x|^{a}u^{p}$ with $a\in(-α,\infty)$ and $0 0$, we covered the gap $p\in\big[\frac{n+α+a}{n-α},p_{c}(a)\big)$. In particular, when $α=2$, our results give an affirmative answer to the conjecture posed by Phan and Souplet \cite{PS}. As a consequence, we derive a priori estimates and existence of positive solutions to higher order Lane-Emden equations in bounded domains for all $1<p<\frac{n+2m}{n-2m}$. Our theorems improve the results in \cite{CFL,DPQ} remarkably to the maximal range of $p$. For bounded domains $Ω$, we also apply the method of scaling spheres to derive Liouville theorems for super-critical problems. Extensions to PDEs and IEs with general nonlinearities $f(x,u)$ are also included. We believe the method of scaling spheres developed here can be applied conveniently to various fractional or higher order problems with singularities or without translation invariance or in the cases the method of moving planes in conjunction with Kelvin transforms do not work.

math.AP↗
arXiv2021

Dictionary Learning Using Rank-One Atomic Decomposition (ROAD)

Dictionary learning aims at seeking a dictionary under which the training data can be sparsely represented. Methods in the literature typically formulate the dictionary learning problem as an optimization w.r.t. two variables, i.e., dictionary and sparse coefficients, and solve it by alternating between two stages: sparse coding and dictionary update. The key contribution of this work is a Rank-One Atomic Decomposition (ROAD) formulation where dictionary learning is cast as an optimization w.r.t. a single variable which is a set of rank one matrices. The resulting algorithm is hence single-stage. Compared with two-stage algorithms, ROAD minimizes the sparsity of the coefficients whilst keeping the data consistency constraint throughout the whole learning process. An alternating direction method of multipliers (ADMM) is derived to solve the optimization problem and the lower bound of the penalty parameter is computed to guarantees a global convergence despite non-convexity of the optimization formulation. From practical point of view, ROAD reduces the number of tuning parameters required in other benchmark algorithms. Numerical tests demonstrate that ROAD outperforms other benchmark algorithms for both synthetic data and real data, especially when the number of training samples is small.

eess.SP↗
arXiv2021

Dictionary Learning with Convex Update (ROMD)

Dictionary learning aims to find a dictionary under which the training data can be sparsely represented, and it is usually achieved by iteratively applying two stages: sparse coding and dictionary update. Typical methods for dictionary update focuses on refining both dictionary atoms and their corresponding sparse coefficients by using the sparsity patterns obtained from sparse coding stage, and hence it is a non-convex bilinear inverse problem. In this paper, we propose a Rank-One Matrix Decomposition (ROMD) algorithm to recast this challenge into a convex problem by resolving these two variables into a set of rank-one matrices. Different from methods in the literature, ROMD updates the whole dictionary at a time using convex programming. The advantages hence include both convergence guarantees for dictionary update and faster convergence of the whole dictionary learning. The performance of ROMD is compared with other benchmark dictionary learning algorithms. The results show the improvement of ROMD in recovery accuracy, especially in the cases of high sparsity level and fewer observation data.

eess.SP↗
arXiv2021

VMAF And Variants: Towards A Unified VQA

Video quality assessment (VQA) is now a fast-growing subject, maturing in the full reference (FR) case, yet challenging in the exploding no reference (NR) case. We investigate variants of the popular VMAF video quality assessment algorithm for the FR case, using both support vector regression and feedforward neural networks. We extend it to the NR case, using some different features but similar learning, to develop a partially unified framework for VQA. When fully trained, FR algorithms such as VMAF perform very well on test datasets, reaching 90%+ match in PCC and SRCC; but for predicting performance in the wild, we train/test from scratch for each database. With an 80/20 train/test split, we still achieve about 90% performance on average in both PCC and SRCC, with up to 7-9% gains over VMAF, using an improved motion feature and better regression. Moreover, we even get decent performance (about 75%) if we ignore the reference, treating FR as NR, partly justifying our attempts at unification. In the true NR case, we reduce complexity vs. leading recent algorithms VIDEVAL, RAPIQUE, yet achieve performance within 3-5%. Moreover, we develop a method to analyze the saliency of features, and conclude that for both VIDEVAL and RAPIQUE, a small subset of their features are providing the bulk of the performance. In short, we find encouraging improvements in trainability in FR, while constraining training complexity against leading methods in NR, elucidating the saliency of features for feature selection.

eess.IV↗
arXiv2021

CAN3D: Fast 3D Medical Image Segmentation via Compact Context Aggregation

Direct automatic segmentation of objects from 3D medical imaging, such as magnetic resonance (MR) imaging, is challenging as it often involves accurately identifying a number of individual objects with complex geometries within a large volume under investigation. To address these challenges, most deep learning approaches typically enhance their learning capability by substantially increasing the complexity or the number of trainable parameters within their models. Consequently, these models generally require long inference time on standard workstations operating clinical MR systems and are restricted to high-performance computing hardware due to their large memory requirement. Further, to fit 3D dataset through these large models using limited computer memory, trade-off techniques such as patch-wise training are often used which sacrifice the fine-scale geometric information from input images which could be clinically significant for diagnostic purposes. To address these challenges, we present a compact convolutional neural network with a shallow memory footprint to efficiently reduce the number of model parameters required for state-of-art performance. This is critical for practical employment as most clinical environments only have low-end hardware with limited computing power and memory. The proposed network can maintain data integrity by directly processing large full-size 3D input volumes with no patches required and significantly reduces the computational time required for both training and inference. We also propose a novel loss function with extra shape constraint to improve the accuracy for imbalanced classes in 3D MR images.

eess.IV↗
arXiv2021

Conflict-Free Four-Dimensional Path Planning for Urban Air Mobility Considering Airspace Occupations

Urban air mobility (UAM) has attracted the attention of aircraft manufacturers, air navigation service providers and governments in recent years. Preventing the conflict among urban aircraft is crucial to UAM traffic safety, which is a key in enabling large scale UAM operation. Pre-flight conflict-free path planning can provide a strategic layer in the maintenance of safety performance, thus becomes an important element in UAM. This paper aims at tackling conflict-free path planning problem for UAM operation with a consideration of four-dimensional airspace management. In the first place, we introduced and extended a four-dimensional airspace management concept, AirMatrix. On the basis of AirMatrix, we formulated the shortest flight time path planning problem considering resolution of conflicts with both static and dynamic obstacles. A Conflict-Free A-Star algorithm was developed for planning four-dimensional paths based on first-come-first-served scheme. The algorithm contains a novel design of heuristic function as well as a conflict detection and resolution strategy. Numerical experiment was carried out in Jurong East area in Singapore, and the results show that the algorithm can generate paths resolving a significant number of potential conflicts in airspace utilization, with acceptable computational time and flight delay. The contributions of this study provide references for stakeholders to support the development of UAM.

eess.SY↗