In this work we propose lifted regression/reconstruction networks (LRRNs), which combine lifted neural networks with a guaranteed Lipschitz continuity property for the output layer. Lifted neural networks explicitly optimize an energy model to infer the unit activations and therefore---in contrast to standard feed-forward neural networks---allow bidirectional feedback between layers. So far lifted neural networks have been modelled around standard feed-forward architectures. We propose to take further advantage of the feedback property by letting the layers simultaneously perform regression and reconstruction. The resulting lifted network architecture allows to control the desired amount of Lipschitz continuity, which is an important feature to obtain adversarially robust regression and classification methods. We analyse and numerically demonstrate applications for unsupervised and supervised learning.
We consider the problem of discriminatively learning restricted Boltzmann machines in the presence of relational data. Unlike previous approaches that employ a rule learner (for structure learning) and a weight learner (for parameter learning) sequentially, we develop a gradient-boosted approach that performs both simultaneously. Our approach learns a set of weak relational regression trees, whose paths from root to leaf are conjunctive clauses and represent the structure, and whose leaf values represent the parameters. When the learned relational regression trees are transformed into a lifted…
City University of Hong Kong（香港城市大学）；SenseTime Research（商汤科技研究院）；Harbin Institute of Technology（哈尔滨工业大学）
Capturing visual image with a hyperspectral camera has been successfully applied to many areas due to its narrow-band imaging technology. Hyperspectral reconstruction from RGB images denotes a reverse process of hyperspectral imaging by discovering an inverse response function. Current works mainly map RGB images directly to corresponding spectrum but do not consider context information explicitly. Moreover, the use of encoder-decoder pair in current algorithms leads to loss of information. To address these problems, we propose a 4-level Hierarchical Regression Network (HRNet) with PixelShuffl…
This paper introduces an interpolation-based method, called the reconstruction approach, for nonparametric regression. Based on the fact that interpolation usually has negligible errors compared to statistical estimation, the reconstruction approach uses an interpolator to parameterize the regression function with its values at finite knots, and then estimates these values by (regularized) least squares. Some popular methods including kernel ridge regression can be viewed as its special cases. It is shown that, the reconstruction idea not only provides different angles to look into existing me…
In recent years, anomaly detection has become an essential field in medical image analysis. Most current anomaly detection methods for medical images are based on image reconstruction. In this work, we propose a novel anomaly detection approach based on coordinate regression. Our method estimates the position of patches within a volume, and is trained only on data of healthy subjects. During inference, we can detect and localize anomalies by considering the error of the position estimate of a given patch. We apply our method to 3D CT volumes and evaluate it on patients with intracranial haemor…
INR-Bench: A Unified Benchmark for Implicit Neural Representations in Multi-Domain Regression and Reconstruction
School of Computer Science and Technology, Tongji University（同济大学计算机科学与技术学院）；School of Electrical Engineering and Computer Science, The University of Queensland（昆士兰大学电气工程与计算机科学学院）；Department of Automation, Shanghai Jiao Tong University（上海交通大学自动化学院）
Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学与系统科学研究院）；School of Mathematical Sciences, University of Chinese Academy of Sciences（中国科学院大学数学科学学院）；H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology（佐治亚理工学院H. Milton Stewart工业与系统工程学院）；Beijing Institute of Spacecraft System Engineering（北京航天器系统工程研究所）；Department of Statistics, Purdue University（普渡大学统计系）
Because of the widespread existence of noise and data corruption, recovering the true regression parameters with a certain proportion of corrupted response variables is an essential task. Methods to overcome this problem often involve robust least-squares regression, but few methods perform well when confronted with severe adaptive adversarial attacks. In many applications, prior knowledge is often available from historical data or engineering experience, and by incorporating prior information into a robust regression method, we develop an effective robust regression method that can resist ada…
Defense Innovation Institute, Academy of Military Sciences（军事科学院国防科技创新研究院）
Temperature monitoring during the life time of heat source components in engineering systems becomes essential to guarantee the normal work and the working life of these components. However, prior methods, which mainly use the interpolate estimation to reconstruct the temperature field from limited monitoring points, require large amounts of temperature tensors for an accurate estimation. This may decrease the availability and reliability of the system and sharply increase the monitoring cost. To solve this problem, this work develops a novel physics-informed deep reversible regression models …
College of Aerospace Science and Engineering National University of Defense Technology（国防科技大学航空航天学院）；Defense Innovation Institute Chinese Academy of Military Science（中国人民解放军军事科学院国防创新研究院）
For the temperature field reconstruction (TFR), a complex image-to-image regression problem, the convolutional neural network (CNN) is a powerful surrogate model due to the convolutional layer's good image feature extraction ability. However, a lot of labeled data is needed to train CNN, and the common CNN can not quantify the aleatoric uncertainty caused by data noise. In actual engineering, the noiseless and labeled training data is hardly obtained for the TFR. To solve these two problems, this paper proposes a deep Monte Carlo quantile regression (Deep MC-QR) method for reconstructing the t…
University of Michigan（密歇根大学）；University of Michigan - Shanghai Jiao Tong University Joint Institute（上海交通大学密西根学院）；Shanghai Jiao Tong University（上海交通大学）
Obtaining accurate and reliable images from low-dose computed tomography (CT) is challenging. Regression convolutional neural network (CNN) models that are learned from training data are increasingly gaining attention in low-dose CT reconstruction. This paper modifies the architecture of an iterative regression CNN, BCD-Net, for fast, stable, and accurate low-dose CT reconstruction, and presents the convergence property of the modified BCD-Net. Numerical results with phantom data show that applying faster numerical solvers to model-based image reconstruction (MBIR) modules of BCD-Net leads to …
Aalto University（阿尔托大学）；University of Turku（图尔库大学）
This paper proposes a novel method for learning highly nonlinear, multivariate functions from examples. Our method takes advantage of the property that continuous functions can be approximated by polynomials, which in turn are representable by tensors. Hence the function learning problem is transformed into a tensor reconstruction problem, an inverse problem of the tensor decomposition. Our method incrementally builds up the unknown tensor from rank-one terms, which lets us control the complexity of the learned model and reduce the chance of overfitting. For learning the models, we present an …
Towards a Unified Analysis of Neural Networks in Nonparametric Instrumental Variable Regression: Optimization and Generalization
University College London（伦敦大学学院）；Nanyang Technological University（南洋理工大学）；The University of Tokyo（东京大学）；RIKEN Center for Advanced Intelligence Project（理化学研究所革新智能综合研究中心）
NVIDIA（英伟达）；New York University（纽约大学）；ETH Zürich（苏黎世联邦理工学院）；University of Toronto（多伦多大学）；Vector Institute（矢量研究所）
We present Neural Kernel Fields: a novel method for reconstructing implicit 3D shapes based on a learned kernel ridge regression. Our technique achieves state-of-the-art results when reconstructing 3D objects and large scenes from sparse oriented points, and can reconstruct shape categories outside the training set with almost no drop in accuracy. The core insight of our approach is that kernel methods are extremely effective for reconstructing shapes when the chosen kernel has an appropriate inductive bias. We thus factor the problem of shape reconstruction into two parts: (1) a backbone neur…
Anomaly detection on time series data is increasingly common across various industrial domains that monitor metrics in order to prevent potential accidents and economic losses. However, a scarcity of labeled data and ambiguous definitions of anomalies can complicate these efforts. Recent unsupervised machine learning methods have made remarkable progress in tackling this problem using either single-timestamp predictions or time series reconstructions. While traditionally considered separately, these methods are not mutually exclusive and can offer complementary perspectives on anomaly detectio…
Can input reconstruction be used to directly estimate uncertainty of a regression U-Net model? -- Application to proton therapy dose prediction for head and neck cancer patients
Institut de Recherche Expérimentale et Clinique (IREC), UCLouvain（比利时鲁汶大学实验与临床研究所（IREC））；UT Southwestern Medical Center（德克萨斯大学西南医学中心）
本文提出一种基于输入重建误差的直接不确定性估计方法，用于回归 U-Net 模型，并在头颈癌质子治疗剂量预测中验证其比 MCDO 和 DE 具有更高相关性、更强 OOD 检测能力和更低计算开销。
Duke University（杜克大学）；Oak Ridge National Laboratory（橡树岭国家实验室）；Fermi National Accelerator Laboratory（费米国家加速器实验室）
We present a deep learning approach for vertex reconstruction of neutrino-nucleus interaction events, a problem in the domain of high energy physics. In this approach, we combine both energy and timing data that are collected in the MINERvA detector to perform classification and regression tasks. We show that the resulting network achieves higher accuracy than previous results while requiring a smaller model size and less training time. In particular, the proposed model outperforms the state-of-the-art by 4.00% on classification accuracy. For the regression task, our model achieves 0.9919 on t…
Gaussian processes (GPs) with derivatives are useful in many applications, including Bayesian optimization, implicit surface reconstruction, and terrain reconstruction. Fitting a GP to function values and derivatives at $n$ points in $d$ dimensions requires linear solves and log determinants with an ${n(d+1) \times n(d+1)}$ positive definite matrix -- leading to prohibitive $\mathcal{O}(n^3d^3)$ computations for standard direct methods. We propose iterative solvers using fast $\mathcal{O}(nd)$ matrix-vector multiplications (MVMs), together with pivoted Cholesky preconditioning that cuts the it…
Faculty of Information Technology（信息技术学院）；Czech Technical University in Prague（捷克布拉格技术大学）
In real-world applications, we can encounter situations when a well-trained model has to be used to predict from a damaged dataset. The damage caused by missing or corrupted values can be either on the level of individual instances or on the level of entire features. Both situations have a negative impact on the usability of the model on such a dataset. This paper focuses on the scenario where entire features are missing which can be understood as a specific case of transfer learning. Our aim is to experimentally research the influence of various imputation methods on the performance of severa…
School of Electrical Engineering, Korea Advanced Institute of Science and Technology（韩国科学技术院电气工程学院）
We consider the classical sparse regression problem of recovering a sparse signal $x_0$ given a measurement vector $y = Φx_0+w$. We propose a tree search algorithm driven by the deep neural network for sparse regression (TSN). TSN improves the signal reconstruction performance of the deep neural network designed for sparse regression by performing a tree search with pruning. It is observed in both noiseless and noisy cases, TSN recovers synthetic and real signals with lower complexity than a conventional tree search and is superior to existing algorithms by a large margin for various types of …
University of Electronic Science and Technology of China（电子科技大学）；Macau University of Science and Technology（澳门科技大学）
Nonlinear sparse data regression and generation have been a long-term challenge, to cite the flow field reconstruction as a typical example. The huge computational cost of computational fluid dynamics (CFD) makes it much expensive for large scale CFD data producing, which is the reason why we need some cheaper ways to do this, of which the traditional reduced order models (ROMs) were promising but they couldn't generate a large number of full domain flow field data (FFD) to realize high-precision flow field reconstructions. Motivated by the problems of existing approaches and inspired by the s…
Amazon Web Services（亚马逊网络服务公司）；University of Southern California（南加州大学）；Los Angeles, CA, USA（美国加利福尼亚州洛杉矶）
Estimation of uncertainty in deep learning models is of vital importance, especially in medical imaging, where reliance on inference without taking into account uncertainty could lead to misdiagnosis. Recently, the probabilistic Variational AutoEncoder (VAE) has become a popular model for anomaly detection in applications such as lesion detection in medical images. The VAE is a generative graphical model that is used to learn the data distribution from samples and then generate new samples from this distribution. By training on normal samples, the VAE can be used to detect inputs that deviate …
Manchester Metropolitan University（曼彻斯特城市大学）；CERN（欧洲核子研究组织）；Florida State University（佛罗里达州立大学）；Massachusetts Institute of Technology（麻省理工学院）；Staffordshire University（斯塔福德郡大学）
We present an end-to-end reconstruction algorithm to build particle candidates from detector hits in next-generation granular calorimeters similar to that foreseen for the high-luminosity upgrade of the CMS detector. The algorithm exploits a distance-weighted graph neural network, trained with object condensation, a graph segmentation technique. Through a single-shot approach, the reconstruction task is paired with energy regression. We describe the reconstruction performance in terms of efficiency as well as in terms of energy resolution. In addition, we show the jet reconstruction performanc…
Machine-learned particle flow as a foundation model for collider physics
University of California San Diego（加州大学圣地亚哥分校）；National Institute of Chemical Physics and Biophysics（化学物理与生物物理国家研究所）；SLAC National Accelerator Laboratory（斯坦福线性加速器中心国家加速器实验室）
Oilfield development related decisions are made using reservoir simulation-based optimization study in which different production scenarios and well controls are compared. Such simulations are computationally expensive and so surrogate models are used to accelerate studies. Deep learning has been used in past to generate surrogates, but such models often fail to quantify prediction uncertainty and are not interpretable. In this work, beta-VAE based regression is proposed to generate simulation surrogates for use in optimization workflow. beta-VAE enables interpretable, factorized representatio…
Complex network reconstruction is a hot topic in many fields. Currently, the most popular data-driven reconstruction framework is based on lasso. However, it is found that, in the presence of noise, lasso loses efficiency for weighted networks. This paper builds a new framework to cope with this problem. The key idea is to employ a series of linear regression problems to model the relationship between network nodes, and then to use an efficient variational Bayesian algorithm to infer the unknown coefficients. The numerical experiments conducted on both synthetic and real data demonstrate that …
