arXiv subjects

Jie Chen

Publications and source records attributed to Jie Chen.

At least 631 records · Page 35Linked to original sources

arXiv2019

Learning ReLU Networks on Linearly Separable Data: Algorithm, Optimality, and Generalization

Neural networks with REctified Linear Unit (ReLU) activation functions (a.k.a. ReLU networks) have achieved great empirical success in various domains. Nonetheless, existing results for learning ReLU networks either pose assumptions on the underlying data distribution being e.g. Gaussian, or require the network size and/or training size to be sufficiently large. In this context, the problem of learning a two-layer ReLU network is approached in a binary classification setting, where the data are linearly separable and a hinge loss criterion is adopted. Leveraging the power of random noise perturbation, this paper presents a novel stochastic gradient descent (SGD) algorithm, which can \emph{provably} train any single-hidden-layer ReLU network to attain global optimality, despite the presence of infinitely many bad local minima, maxima, and saddle points in general. This result is the first of its kind, requiring no assumptions on the data distribution, training/network size, or initialization. Convergence of the resultant iterative algorithm to a global minimum is analyzed by establishing both an upper bound and a lower bound on the number of non-zero updates to be performed. Moreover, generalization guarantees are developed for ReLU networks trained with the novel SGD leveraging classic compression bounds. These guarantees highlight a key difference (at least in the worst case) between reliably learning a ReLU network as well as a leaky ReLU network in terms of sample complexity. Numerical tests using both synthetic data and real images validate the effectiveness of the algorithm and the practical merits of the theory.

stat.ML↗

arXiv2019

Stratified Labeling for Surface Consistent Parallax Correction and Occlusion Completion

The light field faithfully records the spatial and angular configurations of the scene, which facilitates a wide range of imaging possibilities. In this work, we propose an LF synthesis algorithm which renders high quality novel LF views far outside the range of angular baselines of the given references. A stratified synthesis strategy is adopted which parses the scene content based on stratified disparity layers and across a varying range of spatial granularities. Such a stratified methodology proves to help preserve scene structures over large perspective shifts, and it provides informative clues for inferring the textures of occluded regions. A generative-adversarial network model is further adopted for parallax correction and occlusion completion conditioned on the stratified synthesis features. Experiments show that our proposed model can provide more reliable novel view synthesis quality at large baseline extension ratios. Over 3dB quality improvement has been achieved against state-of-the-art LF view synthesis algorithms.

cs.CV↗

arXiv2019

SRN: Side-output Residual Network for Object Reflection Symmetry Detection and Beyond

In this paper, we establish a baseline for object reflection symmetry detection in complex backgrounds by presenting a new benchmark and an end-to-end deep learning approach, opening up a promising direction for symmetry detection in the wild. The new benchmark, Sym-PASCAL, spans challenges including object diversity, multi-objects, part-invisibility, and various complex backgrounds that are far beyond those in existing datasets. The end-to-end deep learning approach, referred to as a side-output residual network (SRN), leverages the output residual units (RUs) to fit the errors between the object ground-truth symmetry and the side-outputs of multiple stages. By cascading RUs in a deep-to-shallow manner, SRN exploits the 'flow' of errors among multiple stages to address the challenges of fitting complex output with limited convolutional layers, suppressing the complex backgrounds, and effectively matching object symmetry at different scales. SRN is further upgraded to a multi-task side-output residual network (MT-SRN) for joint symmetry and edge detection, demonstrating its generality to image-to-mask learning tasks. Experimental results validate both the challenging aspects of Sym-PASCAL benchmark related to real-world images and the state-of-the-art performance of the proposed SRN approach.

cs.CV↗

arXiv2019

A Sequential Set Generation Method for Predicting Set-Valued Outputs

Consider a general machine learning setting where the output is a set of labels or sequences. This output set is unordered and its size varies with the input. Whereas multi-label classification methods seem a natural first resort, they are not readily applicable to set-valued outputs because of the growth rate of the output space; and because conventional sequence generation doesn't reflect sets' order-free nature. In this paper, we propose a unified framework--sequential set generation (SSG)--that can handle output sets of labels and sequences. SSG is a meta-algorithm that leverages any probabilistic learning method for label or sequence prediction, but employs a proper regularization such that a new label or sequence is generated repeatedly until the full set is produced. Though SSG is sequential in nature, it does not penalize the ordering of the appearance of the set elements and can be applied to a variety of set output problems, such as a set of classification labels or sequences. We perform experiments with both benchmark and synthetic data sets and demonstrate SSG's strong performance over baseline methods.

cs.LG↗

arXiv2019

Oriented Three-Dimensional Magnetic Biskyrmion in MnNiGa Bulk Crystals

A biskyrmion consists of two bound, topologically stable skyrmion spin textures. These coffee-bean-shaped objects have been observed in real-space in thin plates using Lorentz transmission electron microscopy (LTEM). From LTEM imaging alone, it is not clear whether biskyrmions are surface-confined objects, or, analogously to skyrmions in non-centrosymmetric helimagnets, three-dimensional tube-like structures in bulk sample. Here, we investigate the biskyrmion form factor in single- and polycrystalline MnNiGa samples using small angle neutron scattering (SANS). We find that biskyrmions are not long-range ordered, not even in single-crystals. Surprisingly all of the disordered biskyrmions have their in-plane symmetry axis aligned along certain directions, governed by the magnetocrystalline anisotropy. This anisotropic nature of biskyrmions may be further exploited to encode information.

cond-mat.mtrl-sci↗

arXiv2019

A laboratory-created dataset with ground-truth for hyperspectral unmixing evaluation

Spectral unmixing is an important and challenging problem in hyperspectral data processing. This topic has been extensively studied and a variety of unmixing algorithms have been proposed in the literature. However, the lack of publicly available dataset with ground-truth makes it difficult to evaluate and compare the performance of unmixing algorithms in a quantitative and objective manner. Most of the existing works rely on the use of numerical synthetic data and an intuitive inspection of the results of real data. To alleviate this dilemma, in this study, we design several experimental scenes in our laboratory, including printed checkerboards, mixed quartz sands, and reflection with a vertical board. A dataset is then created by imaging these scenes with the hyperspectral camera in our laboratory, providing 36 mixtures with more than 130, 000 pixels with 256 wavelength bands ranging from 400nm to 1000nm. The experimental settings are strictly controlled so that pure material spectral signatures and material compositions are known. To the best of our knowledge, this dataset is the first publicly available dataset created in a systematic manner with ground-truth for spectral unmixing. Some typical linear and nonlinear unmixing algorithms are also tested with this dataset and lead to meaningful results.

cs.CV↗

arXiv2019

Relaxation-Based Coarsening for Multilevel Hypergraph Partitioning

Multilevel partitioning methods that are inspired by principles of multiscaling are the most powerful practical hypergraph partitioning solvers. Hypergraph partitioning has many applications in disciplines ranging from scientific computing to data science. In this paper we introduce the concept of algebraic distance on hypergraphs and demonstrate its use as an algorithmic component in the coarsening stage of multilevel hypergraph partitioning solvers. The algebraic distance is a vertex distance measure that extends hyperedge weights for capturing the local connectivity of vertices which is critical for hypergraph coarsening schemes. The practical effectiveness of the proposed measure and corresponding coarsening scheme is demonstrated through extensive computational experiments on a diverse set of problems. Finally, we propose a benchmark of hypergraph partitioning problems to compare the quality of other solvers.

cs.DM↗

arXiv2019

Robust and Scalable Power System State Estimation via Composite Optimization

In today's cyber-enabled smart grids, high penetration of uncertain renewables, purposeful manipulation of meter readings, and the need for wide-area situational awareness, call for fast, accurate, and robust power system state estimation. The least-absolute-value (LAV) estimator is known for its robustness relative to the weighted least-squares (WLS) one. However, due to nonconvexity and nonsmoothness, existing LAV solvers based on linear programming are typically slow, hence inadequate for real-time system monitoring. This paper develops two novel algorithms for efficient LAV estimation, which draw from recent advances in composite optimization. The first is a deterministic linear proximal scheme that handles a sequence of convex quadratic problems, each efficiently solvable either via off-the-shelf algorithms or through the alternating direction method of multipliers. Leveraging the sparse connectivity inherent to power networks, the second scheme is stochastic, and updates only \emph{a few} entries of the complex voltage state vector per iteration. In particular, when voltage magnitude and (re)active power flow measurements are used only, this number reduces to one or two, \emph{regardless of} the number of buses in the network. This computational complexity evidently scales well to large-size power systems. Furthermore, by carefully \emph{mini-batching} the voltage and power flow measurements, accelerated implementation of the stochastic iterations becomes possible. The developed algorithms are numerically evaluated using a variety of benchmark power networks. Simulated tests corroborate that improved robustness can be attained at comparable or markedly reduced computation times for medium- or large-size networks relative to the "workhorse" WLS-based Gauss-Newton iterations.

eess.SY↗

arXiv2018

Scalable Graph Learning for Anti-Money Laundering: A First Look

Organized crime inflicts human suffering on a genocidal scale: the Mexican drug cartels have murdered 150,000 people since 2006, upwards of 700,000 people per year are "exported" in a human trafficking industry enslaving an estimated 40 million people. These nefarious industries rely on sophisticated money laundering schemes to operate. Despite tremendous resources dedicated to anti-money laundering (AML) only a tiny fraction of illicit activity is prevented. The research community can help. In this brief paper, we map the structural and behavioral dynamics driving the technical challenge. We review AML methods, current and emergent. We provide a first look at scalable graph convolutional neural networks for forensic analysis of financial data, which is massive, dense, and dynamic. We report preliminary experimental results using a large synthetic graph (1M nodes, 9M edges) generated by a data simulator we created called AMLSim. We consider opportunities for high performance efficiency, in terms of computation and memory, and we share results from a simple graph compression experiment. Our results support our working hypothesis that graph deep learning for AML bears great promise in the fight against criminal financial activity.

cs.SI↗

arXiv2018

Automatic Seismic Salt Interpretation with Deep Convolutional Neural Networks

One of the most crucial tasks in seismic reflection imaging is to identify the salt bodies with high precision. Traditionally, this is accomplished by visually picking the salt/sediment boundaries, which requires a great amount of manual work and may introduce systematic bias. With recent progress of deep learning algorithm and growing computational power, a great deal of efforts have been made to replace human effort with machine power in salt body interpretation. Currently, the method of Convolutional neural networks (CNN) is revolutionizing the computer vision field and has been a hot topic in the image analysis. In this paper, the benefits of CNN-based classification are demonstrated by using a state-of-art network structure U-Net, along with the residual learning framework ResNet, to delineate salt body with high precision. Network adjustments, including the Exponential Linear Units (ELU) activation function, the Lovász-Softmax loss function, and stratified $K$-fold cross-validation, have been deployed to further improve the prediction accuracy. The preliminary result using SEG Advanced Modeling (SEAM) data shows good agreement between the predicted salt body and manually interpreted salt body, especially in areas with weak reflections. This indicates the great potential of applying CNN for salt-related interpretations.

physics.geo-ph↗

arXiv2018

Mean-square Stabilizability via Output Feedback for Non-minimum Phase Networked Feedback Systems

This work studies mean-square stabilizability via output feedback for a networked linear time invariant (LTI) feedback system with a non-minimum phase plant. In the feedback system, the control signals are transmitted to the plant over a set of parallel communication channels with possible packet dropout. Our goal is to analytically describe intrinsic constraints among channel packet dropout probabilities and the plant's characteristics, such as unstable poles, non-minimum phase zeros in the mean-square stabilizability of the system. It turns out that this is a very hard problem. Here, we focus on the case in which the plant has relative degree one and each non-minimum zero of the plant is only associated with one of control input channels. Then, the admissible region of packet dropout probabilities in the mean-square stabilizability of the system is obtained. Moreover, a set of hyper-rectangles in this region is presented in terms of the plant's non-minimum phase zeros, unstable poles and Wonham decomposition forms which is related to the structure of controllable subspace of the plant. When the non-minimum phase zeros are void, it is found that the supremum of packet dropout probabilities' product in the admissible region is determined by the product of plant's unstable poles only. A numerical example is presented to illustrate the fundamental constraints in the mean-square stabilizability of the networked system.

eess.SY↗

arXiv2018

On the algebraic Gordian distance

Using Blanchfield pairings, we show that two Alexander polynomials cannot be realized by a pair of matrices with Gordian distance one if a corresponding quadratic equation does not have an integer solution. We also give an example of how our results help in calculating the Gordian distances, algebraic Gordian distances and polynomial distances.

math.GT↗

arXiv2018

From BoW to CNN: Two Decades of Texture Representation for Texture Classification

Texture is a fundamental characteristic of many types of images, and texture representation is one of the essential and challenging problems in computer vision and pattern recognition which has attracted extensive research attention. Since 2000, texture representations based on Bag of Words (BoW) and on Convolutional Neural Networks (CNNs) have been extensively studied with impressive performance. Given this period of remarkable evolution, this paper aims to present a comprehensive survey of advances in texture representation over the last two decades. More than 200 major publications are cited in this survey covering different aspects of the research, which includes (i) problem description; (ii) recent advances in the broad categories of BoW-based, CNN-based and attribute-based methods; and (iii) evaluation issues, specifically benchmark datasets and state of the art results. In retrospect of what has been achieved so far, the survey discusses open challenges and directions for future research.

cs.CV↗

arXiv2018

Learning Low-Complexity Autoregressive Models via Proximal Alternating Minimization

We consider the estimation of the state transition matrix in vector autoregressive models, when time sequence data is limited but nonsequence steady-state data is abundant. To leverage both sources of data, we formulate the least squares minimization problem regularized by a Lyapunov penalty. We impose cardinality or rank constraints to reduce the complexity of the autoregressive model. We solve the resulting nonconvex, nonsmooth problem by using the proximal alternating linearization method (PALM). We show that PALM is globally convergent to a critical point and that the estimation error monotonically decreases. Furthermore, we obtain explicit formulas for the proximal operators to facilitate the implementation of PALM. We demonstrate the effectiveness of the developed method on synthetic and real-world data. Our experiments show that PALM outperforms the gradient projection method in both computational efficiency and solution quality.

math.OC↗

arXiv2018

Constrained Generation of Semantically Valid Graphs via Regularizing Variational Autoencoders

Deep generative models have achieved remarkable success in various data domains, including images, time series, and natural languages. There remain, however, substantial challenges for combinatorial structures, including graphs. One of the key challenges lies in the difficulty of ensuring semantic validity in context. For examples, in molecular graphs, the number of bonding-electron pairs must not exceed the valence of an atom; whereas in protein interaction networks, two proteins may be connected only when they belong to the same or correlated gene ontology terms. These constraints are not easy to be incorporated into a generative model. In this work, we propose a regularization framework for variational autoencoders as a step toward semantic validity. We focus on the matrix representation of graphs and formulate penalty terms that regularize the output distribution of the decoder to encourage the satisfaction of validity constraints. Experimental results confirm a much higher likelihood of sampling valid graphs in our approach, compared with others reported in the literature.

cs.LG↗

arXiv2018

Revisiting Random Binning Features: Fast Convergence and Strong Parallelizability

Kernel method has been developed as one of the standard approaches for nonlinear learning, which however, does not scale to large data set due to its quadratic complexity in the number of samples. A number of kernel approximation methods have thus been proposed in the recent years, among which the random features method gains much popularity due to its simplicity and direct reduction of nonlinear problem to a linear one. The Random Binning (RB) feature, proposed in the first random-feature paper \cite{rahimi2007random}, has drawn much less attention than the Random Fourier (RF) feature. In this work, we observe that the RB features, with right choice of optimization solver, could be orders-of-magnitude more efficient than other random features and kernel approximation methods under the same requirement of accuracy. We thus propose the first analysis of RB from the perspective of optimization, which by interpreting RB as a Randomized Block Coordinate Descent in the infinite-dimensional space, gives a faster convergence rate compared to that of other random features. In particular, we show that by drawing $R$ random grids with at least $κ$ number of non-empty bins per grid in expectation, RB method achieves a convergence rate of $O(1/(κR))$, which not only sharpens its $O(1/\sqrt{R})$ rate from Monte Carlo analysis, but also shows a $κ$ times speedup over other random features under the same analysis framework. In addition, we demonstrate another advantage of RB in the L1-regularized setting, where unlike other random features, a RB-based Coordinate Descent solver can be parallelized with guaranteed speedup proportional to $κ$. Our extensive experiments demonstrate the superior performance of the RB features over other random features and kernel approximation methods. Our code and data is available at { \url{https://github.com/teddylfwu/RB_GEN}}.

cs.LG↗

arXiv2018

Model Interpretation: A Unified Derivative-based Framework for Nonparametric Regression and Supervised Machine Learning

Interpreting a nonparametric regression model with many predictors is known to be a challenging problem. There has been renewed interest in this topic due to the extensive use of machine learning algorithms and the difficulty in understanding and explaining their input-output relationships. This paper develops a unified framework using a derivative-based approach for existing tools in the literature, including the partial-dependence plots, marginal plots and accumulated effects plots. It proposes a new interpretation technique called the accumulated total derivative effects plot and demonstrates how its components can be used to develop extensive insights in complex regression models with correlated predictors. The techniques are illustrated through simulation results.

stat.ML↗

arXiv2018

Application of Machine Learning in Rock Facies Classification with Physics-Motivated Feature Augmentation

With recent progress in algorithms and the availability of massive amounts of computation power, application of machine learning techniques is becoming a hot topic in the oil and gas industry. One of the most promising aspects to apply machine learning to the upstream field is the rock facies classification in reservoir characterization, which is crucial in determining the net pay thickness of reservoirs, thus a definitive factor in drilling decision making process. For complex machine learning tasks like facies classification, feature engineering is often critical. This paper shows the inclusion of physics-motivated feature interaction in feature augmentation can further improve the capability of machine learning in rock facies classification. We demonstrate this approach with the SEG 2016 machine learning contest dataset and the top winning algorithms. The improvement is roboust and can be $\sim5\%$ better than current existing best F-1 score, where F-1 is an evaluation metric used to quantify average prediction accuracy.

stat.ML↗