arXiv subjects

Wenjia Wang

Publications and source records attributed to Wenjia Wang.

At least 73 records · Page 4Linked to original sources

arXiv2023

Uncertainty Quantification for Bayesian Optimization

Bayesian optimization is a class of global optimization techniques. In Bayesian optimization, the underlying objective function is modeled as a realization of a Gaussian process. Although the Gaussian process assumption implies a random distribution of the Bayesian optimization outputs, quantification of this uncertainty is rarely studied in the literature. In this work, we propose a novel approach to assess the output uncertainty of Bayesian optimization algorithms, which proceeds by constructing confidence regions of the maximum point (or value) of the objective function. These regions can be computed efficiently, and their confidence levels are guaranteed by the uniform error bounds for sequential Gaussian process regression newly developed in the present work. Our theory provides a unified uncertainty quantification framework for all existing sequential sampling policies and stopping criteria.

math.ST↗

arXiv2023

HuMMan: Multi-Modal 4D Human Dataset for Versatile Sensing and Modeling

4D human sensing and modeling are fundamental tasks in vision and graphics with numerous applications. With the advances of new sensors and algorithms, there is an increasing demand for more versatile datasets. In this work, we contribute HuMMan, a large-scale multi-modal 4D human dataset with 1000 human subjects, 400k sequences and 60M frames. HuMMan has several appealing properties: 1) multi-modal data and annotations including color images, point clouds, keypoints, SMPL parameters, and textured meshes; 2) popular mobile device is included in the sensor suite; 3) a set of 500 actions, designed to cover fundamental movements; 4) multiple tasks such as action recognition, pose estimation, parametric human recovery, and textured mesh reconstruction are supported and evaluated. Extensive experiments on HuMMan voice the need for further study on challenges such as fine-grained action recognition, dynamic human mesh reconstruction, point cloud-based parametric human recovery, and cross-device domain gaps.

cs.CV↗

arXiv2023

Deciphering the Projection Head: Representation Evaluation Self-supervised Learning

Self-supervised learning (SSL) aims to learn intrinsic features without labels. Despite the diverse architectures of SSL methods, the projection head always plays an important role in improving the performance of the downstream task. In this work, we systematically investigate the role of the projection head in SSL. Specifically, the projection head targets the uniformity part of SSL, which pushes the dissimilar samples away from each other, thus enabling the encoder to focus on extracting semantic features. Based on this understanding, we propose a Representation Evaluation Design (RED) in SSL models in which a shortcut connection between the representation and the projection vectors is built. Extensive experiments with different architectures, including SimCLR, MoCo-V2, and SimSiam, on various datasets, demonstrate that the representation evaluation design can consistently improve the baseline models in the downstream tasks. The learned representation from the RED-SSL models shows superior robustness to unseen augmentations and out-of-distribution data.

cs.LG↗

arXiv2023

Functional-Input Gaussian Processes with Applications to Inverse Scattering Problems

Surrogate modeling based on Gaussian processes (GPs) has received increasing attention in the analysis of complex problems in science and engineering. Despite extensive studies on GP modeling, the developments for functional inputs are scarce. Motivated by an inverse scattering problem in which functional inputs representing the support and material properties of the scatterer are involved in the partial differential equations, a new class of kernel functions for functional inputs is introduced for GPs. Based on the proposed GP models, the asymptotic convergence properties of the resulting mean squared prediction errors are derived and the finite sample performance is demonstrated by numerical examples. In the application to inverse scattering, a surrogate model is constructed with functional inputs, which is crucial to recover the reflective index of an inhomogeneous isotropic scattering region of interest for a given far-field pattern.

stat.ME↗

arXiv2022

An automated approach to extracting positive and negative clinical research results

Failure is common in clinical trials since the successful failures presented in negative results always indicate the ways that should not be taken. In this paper, we proposed an automated approach to extracting positive and negative clinical research results by introducing a PICOE (Population, Intervention, Comparation, Outcome, and Effect) framework to represent randomized controlled trials (RCT) reports, where E indicates the effect between a specific I and O. We developed a pipeline to extract and assign the corresponding statistical effect to a specific I-O pair from natural language RCT reports. The extraction models achieved a high degree of accuracy for ICO and E descriptive words extraction through two rounds of training. By defining a threshold of p-value, we find in all Covid-19 related intervention-outcomes pairs with statistical tests, negative results account for nearly 40%. We believe that this observation is noteworthy since they are extracted from the published literature, in which there is an inherent risk of reporting bias, preferring to report positive results rather than negative results. We provided a tool to systematically understand the current level of clinical evidence by distinguishing negative results from the positive results.

cs.IR↗

arXiv2022

Convergence of Gaussian process regression: Optimality, robustness, and relationship with kernel ridge regression

In this work, we investigate Gaussian process regression used to recover a function based on noisy observations. We derive upper and lower error bounds for Gaussian process regression with possibly misspecified correlation functions. The optimal convergence rate can be attained even if the smoothness of the imposed correlation function exceeds that of the true correlation function and the sampling scheme is quasi-uniform. As byproducts, we also obtain convergence rates of kernel ridge regression with misspecified kernel function, where the underlying truth is a deterministic function. The convergence rates of Gaussian process regression and kernel ridge regression are closely connected, which is aligned with the relationship between sample paths of Gaussian process and the corresponding reproducing kernel Hilbert space.

math.ST↗

arXiv2022

WegFormer: Transformers for Weakly Supervised Semantic Segmentation

Although convolutional neural networks (CNNs) have achieved remarkable progress in weakly supervised semantic segmentation (WSSS), the effective receptive field of CNN is insufficient to capture global context information, leading to sub-optimal results. Inspired by the great success of Transformers in fundamental vision areas, this work for the first time introduces Transformer to build a simple and effective WSSS framework, termed WegFormer. Unlike existing CNN-based methods, WegFormer uses Vision Transformer (ViT) as a classifier to produce high-quality pseudo segmentation masks. To this end, we introduce three tailored components in our Transformer-based framework, which are (1) a Deep Taylor Decomposition (DTD) to generate attention maps, (2) a soft erasing module to smooth the attention maps, and (3) an efficient potential object mining (EPOM) to filter noisy activation in the background. Without any bells and whistles, WegFormer achieves state-of-the-art 70.5% mIoU on the PASCAL VOC dataset, significantly outperforming the previous best method. We hope WegFormer provides a new perspective to tap the potential of Transformer in weakly supervised semantic segmentation. Code will be released.

cs.CV↗

arXiv2022

Differentiable and Scalable Generative Adversarial Models for Data Imputation

Data imputation has been extensively explored to solve the missing data problem. The dramatically increasing volume of incomplete data makes the imputation models computationally infeasible in many real-life applications. In this paper, we propose an effective scalable imputation system named SCIS to significantly speed up the training of the differentiable generative adversarial imputation models under accuracy-guarantees for large-scale incomplete data. SCIS consists of two modules, differentiable imputation modeling (DIM) and sample size estimation (SSE). DIM leverages a new masking Sinkhorn divergence function to make an arbitrary generative adversarial imputation model differentiable, while for such a differentiable imputation model, SSE can estimate an appropriate sample size to ensure the user-specified imputation accuracy of the final model. Extensive experiments upon several real-life large-scale datasets demonstrate that, our proposed system can accelerate the generative adversarial model training by 7.1x. Using around 7.6% samples, SCIS yields competitive accuracy with the state-of-the-art imputation methods in a much shorter computation time.

cs.LG↗

arXiv2021

Understanding Square Loss in Training Overparametrized Neural Network Classifiers

Deep learning has achieved many breakthroughs in modern classification tasks. Numerous architectures have been proposed for different data structures but when it comes to the loss function, the cross-entropy loss is the predominant choice. Recently, several alternative losses have seen revived interests for deep classifiers. In particular, empirical evidence seems to promote square loss but a theoretical justification is still lacking. In this work, we contribute to the theoretical understanding of square loss in classification by systematically investigating how it performs for overparametrized neural networks in the neural tangent kernel (NTK) regime. Interesting properties regarding the generalization error, robustness, and calibration error are revealed. We consider two cases, according to whether classes are separable or not. In the general non-separable case, fast convergence rate is established for both misclassification rate and calibration error. When classes are separable, the misclassification rate improves to be exponentially fast. Further, the resulting margin is proven to be lower bounded away from zero, providing theoretical guarantees for robustness. We expect our findings to hold beyond the NTK regime and translate to practical settings. To this end, we conduct extensive empirical studies on practical neural networks, demonstrating the effectiveness of square loss in both synthetic low-dimensional data and real image data. Comparing to cross-entropy, square loss has comparable generalization error but noticeable advantages in robustness and model calibration.

stat.ML↗

arXiv2021

High-Dimensional Non-Parametric Density Estimation in Mixed Smooth Sobolev Spaces

Density estimation plays a key role in many tasks in machine learning, statistical inference, and visualization. The main bottleneck in high-dimensional density estimation is the prohibitive computational cost and the slow convergence rate. In this paper, we propose novel estimators for high-dimensional non-parametric density estimation called the adaptive hyperbolic cross density estimators, which enjoys nice convergence properties in the mixed smooth Sobolev spaces. As modifications of the usual Sobolev spaces, the mixed smooth Sobolev spaces are more suitable for describing high-dimensional density functions in some applications. We prove that, unlike other existing approaches, the proposed estimator does not suffer the curse of dimensionality under Integral Probability Metric, including Hölder Integral Probability Metric, where Total Variation Metric and Wasserstein Distance are special cases. Applications of the proposed estimators to generative adversarial networks (GANs) and goodness of fit test for high-dimensional data are discussed to illustrate the proposed estimator's good performance in high-dimensional problems. Numerical experiments are conducted and illustrate the efficiency of our proposed method.

cs.LG↗

arXiv2021

On the Inference of Applying Gaussian Process Modeling to a Deterministic Function

Gaussian process modeling is a standard tool for building emulators for computer experiments, which are usually used to study deterministic functions, for example, a solution to a given system of partial differential equations. This work investigates applying Gaussian process modeling to a deterministic function from prediction and uncertainty quantification perspectives, where the Gaussian process model is misspecified. Specifically, we consider the case where the underlying function is fixed and from a reproducing kernel Hilbert space generated by some kernel function, and the same kernel function is used in the Gaussian process modeling as the correlation function for prediction and uncertainty quantification. While upper bounds and the optimal convergence rate of prediction in the Gaussian process modeling have been extensively studied in the literature, a comprehensive exploration of convergence rates and theoretical study of uncertainty quantification is lacking. We prove that, if one uses maximum likelihood estimation to estimate the variance in Gaussian process modeling, under different choices of the regularization parameter value, the predictor is not optimal and/or the confidence interval is not reliable. In particular, lower bounds of the prediction error under different choices of the regularization parameter value are obtained. The results indicate that, if one directly applies Gaussian process modeling to a fixed function, the reliability of the confidence interval and the optimality of the predictor cannot be achieved at the same time.

math.ST↗

arXiv2021

Regularization Matters: A Nonparametric Perspective on Overparametrized Neural Network

Overparametrized neural networks trained by gradient descent (GD) can provably overfit any training data. However, the generalization guarantee may not hold for noisy data. From a nonparametric perspective, this paper studies how well overparametrized neural networks can recover the true target function in the presence of random noises. We establish a lower bound on the $L_2$ estimation error with respect to the GD iterations, which is away from zero without a delicate scheme of early stopping. In turn, through a comprehensive analysis of $\ell_2$-regularized GD trajectories, we prove that for overparametrized one-hidden-layer ReLU neural network with the $\ell_2$ regularization: (1) the output is close to that of the kernel ridge regression with the corresponding neural tangent kernel; (2) minimax {optimal} rate of $L_2$ estimation error can be achieved. Numerical experiments confirm our theory and further demonstrate that the $\ell_2$ regularization approach improves the training robustness and works for a wider range of neural networks.

stat.ML↗

arXiv2021

Eigenvector-based sparse canonical correlation analysis: Fast computation for estimation of multiple canonical vectors

Classical canonical correlation analysis (CCA) requires matrices to be low dimensional, i.e. the number of features cannot exceed the sample size. Recent developments in CCA have mainly focused on the high-dimensional setting, where the number of features in both matrices under analysis greatly exceeds the sample size. These approaches impose penalties in the optimization problems that are needed to be solve iteratively, and estimate multiple canonical vectors sequentially. In this work, we provide an explicit link between sparse multiple regression with sparse canonical correlation analysis, and an efficient algorithm that can estimate multiple canonical pairs simultaneously rather than sequentially. Furthermore, the algorithm naturally allows parallel computing. These properties make the algorithm much efficient. We provide theoretical results on the consistency of canonical pairs. The algorithm and theoretical development are based on solving an eigenvectors problem, which significantly differentiate our method with existing methods. Simulation results support the improved performance of the proposed approach. We apply eigenvector-based CCA to analysis of the GTEx thyroid histology images, analysis of SNPs and RNA-seq gene expression data, and a microbiome study. The real data analysis also shows improved performance compared to traditional sparse CCA.

stat.ME↗

arXiv2021

Gaussian Processes with Input Location Error and Applications to the Composite Parts Assembly Process

In this paper, we investigate Gaussian process modeling with input location error, where the inputs are corrupted by noise. Here, the best linear unbiased predictor for two cases is considered, according to whether there is noise at the target unobserved location or not. We show that the mean squared prediction error converges to a non-zero constant if there is noise at the target unobserved location, and provide an upper bound of the mean squared prediction error if there is no noise at the target unobserved location. We investigate the use of stochastic Kriging in the prediction of Gaussian processes with input location error, and show that stochastic Kriging is a good approximation when the sample size is large. Several numeric examples are given to illustrate the results, and a case study on the assembly of composite parts is presented. Technical proofs are provided in the Appendix.

math.ST↗

arXiv2021

Segmenting Transparent Object in the Wild with Transformer

This work presents a new fine-grained transparent object segmentation dataset, termed Trans10K-v2, extending Trans10K-v1, the first large-scale transparent object segmentation dataset. Unlike Trans10K-v1 that only has two limited categories, our new dataset has several appealing benefits. (1) It has 11 fine-grained categories of transparent objects, commonly occurring in the human domestic environment, making it more practical for real-world application. (2) Trans10K-v2 brings more challenges for the current advanced segmentation methods than its former version. Furthermore, a novel transformer-based segmentation pipeline termed Trans2Seg is proposed. Firstly, the transformer encoder of Trans2Seg provides the global receptive field in contrast to CNN's local receptive field, which shows excellent advantages over pure CNN architectures. Secondly, by formulating semantic segmentation as a problem of dictionary look-up, we design a set of learnable prototypes as the query of Trans2Seg's transformer decoder, where each prototype learns the statistics of one category in the whole dataset. We benchmark more than 20 recent semantic segmentation methods, demonstrating that Trans2Seg significantly outperforms all the CNN-based methods, showing the proposed algorithm's potential ability to solve transparent object segmentation.

cs.CV↗

arXiv2020

Neural Network Gaussian Process Considering Input Uncertainty for Composite Structures Assembly

Developing machine learning enabled smart manufacturing is promising for composite structures assembly process. To improve production quality and efficiency of the assembly process, accurate predictive analysis on dimensional deviations and residual stress of the composite structures is required. The novel composite structures assembly involves two challenges: (i) the highly nonlinear and anisotropic properties of composite materials; and (ii) inevitable uncertainty in the assembly process. To overcome those problems, we propose a neural network Gaussian process model considering input uncertainty for composite structures assembly. Deep architecture of our model allows us to approximate a complex process better, and consideration of input uncertainty enables robust modeling with complete incorporation of the process uncertainty. Based on simulation and case study, the NNGPIU can outperform other benchmark methods when the response function is nonsmooth and nonlinear. Although we use composite structure assembly as an example, the proposed methodology can be applicable to other engineering systems with intrinsic uncertainties.

stat.ML↗

arXiv2020

Kriging prediction with isotropic Matérn correlations: Robustness and experimental design

This work investigates the prediction performance of the kriging predictors. We derive some error bounds for the prediction error in terms of non-asymptotic probability under the uniform metric and $L_p$ metrics when the spectral densities of both the true and the imposed correlation functions decay algebraically. The Matérn family is a prominent class of correlation functions of this kind. Our analysis shows that, when the smoothness of the imposed correlation function exceeds that of the true correlation function, the prediction error becomes more sensitive to the space-filling property of the design points. In particular, the kriging predictor can still reach the optimal rate of convergence, if the experimental design scheme is quasi-uniform. Lower bounds of the kriging prediction error are also derived under the uniform metric and $L_p$ metrics. An accurate characterization of this error is obtained, when an oversmoothed correlation function and a space-filling design is used.

math.ST↗

arXiv2020

Efficient and Accurate Arbitrary-Shaped Text Detection with Pixel Aggregation Network

Scene text detection, an important step of scene text reading systems, has witnessed rapid development with convolutional neural networks. Nonetheless, two main challenges still exist and hamper its deployment to real-world applications. The first problem is the trade-off between speed and accuracy. The second one is to model the arbitrary-shaped text instance. Recently, some methods have been proposed to tackle arbitrary-shaped text detection, but they rarely take the speed of the entire pipeline into consideration, which may fall short in practical applications.In this paper, we propose an efficient and accurate arbitrary-shaped text detector, termed Pixel Aggregation Network (PAN), which is equipped with a low computational-cost segmentation head and a learnable post-processing. More specifically, the segmentation head is made up of Feature Pyramid Enhancement Module (FPEM) and Feature Fusion Module (FFM). FPEM is a cascadable U-shaped module, which can introduce multi-level information to guide the better segmentation. FFM can gather the features given by the FPEMs of different depths into a final feature for segmentation. The learnable post-processing is implemented by Pixel Aggregation (PA), which can precisely aggregate text pixels by predicted similarity vectors. Experiments on several standard benchmarks validate the superiority of the proposed PAN. It is worth noting that our method can achieve a competitive F-measure of 79.9% at 84.2 FPS on CTW1500.

cs.CV↗