arXiv subjects

Tong Zhang

Publications and source records attributed to Tong Zhang.

At least 667 records · Page 37Linked to original sources

arXiv2016

Isolating Mice and Elephant in Data Centers

Data centers traffic is composed by numerous latency-sensitive "mice" flows, which is consisted of only several packets, and a few throughput-sensitive "elephant" flows, which occupy more than 80% of overall load. Generally, the short-lived "mice" flows induce transient congestion and the long-lived "elephant" flows cause persistent congestion. The network congestion is a major performance inhibitor. Conventionally, the hop-by-hop and end-to-end flow control mechanisms are employed to relief transient and persistent congestion, respectively. However, in face of the mixture of elephants and mice, we find the hybrid congestion control scheme including hop-by-hop and end-to-end flow control mechanisms suffers from serious performance impairments. As a step further, our in-depth analysis reveals that the hybrid scheme performs poor at latency of mice and throughput of elephant. Motivated by this understanding, we argue for isolating mice and elephants in different queues, such that the hop-by-hop and end-to-end flow control mechanisms are independently imposed to short-lived and long-lived flows, respectively. Our solution is readily-deployable and compatible with current commodity network devices and can leverage various congestion control mechanisms. Extensive simulations show that our proposal of isolation can simultaneously improve the latency of mice by at least 30% and the link utilization to almost 100%.

cs.NI↗

arXiv2016

Supervised and Semi-Supervised Text Categorization using LSTM for Region Embeddings

One-hot CNN (convolutional neural network) has been shown to be effective for text categorization (Johnson & Zhang, 2015). We view it as a special case of a general framework which jointly trains a linear model with a non-linear feature generator consisting of `text region embedding + pooling'. Under this framework, we explore a more sophisticated region embedding method using Long Short-Term Memory (LSTM). LSTM can embed text regions of variable (and possibly large) sizes, whereas the region size needs to be fixed in a CNN. We seek effective and efficient use of LSTM for this purpose in the supervised and semi-supervised settings. The best results were obtained by combining region embeddings in the form of LSTM and convolution layers trained on unlabeled data. The results indicate that on this task, embeddings of text regions, which can convey complex concepts, are more useful than embeddings of single words in isolation. We report performances exceeding the previous best results on four benchmark datasets.

stat.ML↗

arXiv2016

Efficient Distributed Learning with Sparsity

We propose a novel, efficient approach for distributed sparse learning in high-dimensions, where observations are randomly partitioned across machines. Computationally, at each round our method only requires the master machine to solve a shifted ell_1 regularized M-estimation problem, and other workers to compute the gradient. In respect of communication, the proposed approach provably matches the estimation error bound of centralized methods within constant rounds of communications (ignoring logarithmic factors). We conduct extensive experiments on both simulated and real world datasets, and demonstrate encouraging performances on high-dimensional regression and classification tasks.

stat.ML↗

arXiv2016

Learning Sparse Low-Threshold Linear Classifiers

We consider the problem of learning a non-negative linear classifier with a $1$-norm of at most $k$, and a fixed threshold, under the hinge-loss. This problem generalizes the problem of learning a $k$-monotone disjunction. We prove that we can learn efficiently in this setting, at a rate which is linear in both $k$ and the size of the threshold, and that this is the best possible rate. We provide an efficient online learning algorithm that achieves the optimal rate, and show that in the batch case, empirical risk minimization achieves this rate as well. The rates we show are tighter than the uniform convergence rate, which grows with $k^2$.

stat.ML↗

arXiv2015

Improved Analyses of the Randomized Power Method and Block Lanczos Method

The power method and block Lanczos method are popular numerical algorithms for computing the truncated singular value decomposition (SVD) and eigenvalue decomposition problems. Especially in the literature of randomized numerical linear algebra, the power method is widely applied to improve the quality of randomized sketching, and relative-error bounds have been well established. Recently, Musco & Musco (2015) proposed a block Krylov subspace method that fully exploits the intermediate results of the power iteration to accelerate convergence. They showed spectral gap-independent bounds which are stronger than the power method by order-of-magnitude. This paper offers novel error analysis techniques and significantly improves the bounds of both the randomized power method and the block Lanczos method. This paper also establishes the first gap-independent bound for the warm-start block Lanczos method.

math.NA↗

arXiv2015

Sparse Nonlinear Regression: Parameter Estimation and Asymptotic Inference

We study parameter estimation and asymptotic inference for sparse nonlinear regression. More specifically, we assume the data are given by $y = f( x^\top β^* ) + ε$, where $f$ is nonlinear. To recover $β^*$, we propose an $\ell_1$-regularized least-squares estimator. Unlike classical linear regression, the corresponding optimization problem is nonconvex because of the nonlinearity of $f$. In spite of the nonconvexity, we prove that under mild conditions, every stationary point of the objective enjoys an optimal statistical rate of convergence. In addition, we provide an efficient algorithm that provably converges to a stationary point. We also access the uncertainty of the obtained estimator. Specifically, based on any stationary point of the objective, we construct valid hypothesis tests and confidence intervals for the low dimensional components of the high-dimensional parameter $β^*$. Detailed numerical results are provided to back up our theory.

stat.ML↗

arXiv2015

Semi-supervised Convolutional Neural Networks for Text Categorization via Region Embedding

This paper presents a new semi-supervised framework with convolutional neural networks (CNNs) for text categorization. Unlike the previous approaches that rely on word embeddings, our method learns embeddings of small text regions from unlabeled data for integration into a supervised CNN. The proposed scheme for embedding learning is based on the idea of two-view semi-supervised learning, which is intended to be useful for the task of interest even though the training is done on unlabeled data. Our models achieve better results than previous approaches on sentiment classification and topic classification tasks.

stat.ML↗

arXiv2015

On the Duality Gap Convergence of ADMM Methods

This paper provides a duality gap convergence analysis for the standard ADMM as well as a linearized version of ADMM. It is shown that under appropriate conditions, both methods achieve linear convergence. However, the standard ADMM achieves a faster accelerated convergence rate than that of the linearized ADMM. A simple numerical example is used to illustrate the difference in convergence behavior.

math.OC↗

arXiv2015

Effective Use of Word Order for Text Categorization with Convolutional Neural Networks

Convolutional neural network (CNN) is a neural network that can make use of the internal structure of data such as the 2D structure of image data. This paper studies CNN on text categorization to exploit the 1D structure (namely, word order) of text data for accurate prediction. Instead of using low-dimensional word vectors as input as is often done, we directly apply CNN to high-dimensional text data, which leads to directly learning embedding of small text regions for use in classification. In addition to a straightforward adaptation of CNN from image to text, a simple but new variation which employs bag-of-word conversion in the convolution layer is proposed. An extension to combine multiple convolution layers is also explored for higher accuracy. The experiments demonstrate the effectiveness of our approach in comparison with state-of-the-art methods.

cs.CL↗

arXiv2015

Adjusting Leverage Scores by Row Weighting: A Practical Approach to Coherent Matrix Completion

Low-rank matrix completion is an important problem with extensive real-world applications. When observations are uniformly sampled from the underlying matrix entries, existing methods all require the matrix to be incoherent. This paper provides the first working method for coherent matrix completion under the standard uniform sampling model. Our approach is based on the weighted nuclear norm minimization idea proposed in several recent work, and our key contribution is a practical method to compute the weighting matrices so that the leverage scores become more uniform after weighting. Under suitable conditions, we are able to derive theoretical results, showing the effectiveness of our approach. Experiments on synthetic data show that our approach recovers highly coherent matrices with high precision, whereas the standard unweighted method fails even on noise-free data.

cs.LG↗

arXiv2015

Optimal computational and statistical rates of convergence for sparse nonconvex learning problems

We provide theoretical analysis of the statistical and computational properties of penalized $M$-estimators that can be formulated as the solution to a possibly nonconvex optimization problem. Many important estimators fall in this category, including least squares regression with nonconvex regularization, generalized linear models with nonconvex regularization and sparse elliptical random design regression. For these problems, it is intractable to calculate the global solution due to the nonconvex formulation. In this paper, we propose an approximate regularization path-following method for solving a variety of learning problems with nonconvex objective functions. Under a unified analytic framework, we simultaneously provide explicit statistical and computational rates of convergence for any local solution attained by the algorithm. Computationally, our algorithm attains a global geometric rate of convergence for calculating the full regularization path, which is optimal among all first-order algorithms. Unlike most existing methods that only attain geometric rates of convergence for one single regularization parameter, our algorithm calculates the full regularization path with the same iteration complexity. In particular, we provide a refined iteration complexity bound to sharply characterize the performance of each stage along the regularization path. Statistically, we provide sharp sample complexity analysis for all the approximate local solutions along the regularization path. In particular, our analysis improves upon existing results by providing a more refined sample complexity bound as well as an exact support recovery result for the final estimator. These results show that the final estimator attains an oracle statistical property due to the usage of nonconvex penalty.

stat.ML↗

arXiv2015

Stochastic Optimization with Importance Sampling

Uniform sampling of training data has been commonly used in traditional stochastic optimization algorithms such as Proximal Stochastic Gradient Descent (prox-SGD) and Proximal Stochastic Dual Coordinate Ascent (prox-SDCA). Although uniform sampling can guarantee that the sampled stochastic quantity is an unbiased estimate of the corresponding true quantity, the resulting estimator may have a rather high variance, which negatively affects the convergence of the underlying optimization procedure. In this paper we study stochastic optimization with importance sampling, which improves the convergence rate by reducing the stochastic variance. Specifically, we study prox-SGD (actually, stochastic mirror descent) with importance sampling and prox-SDCA with importance sampling. For prox-SGD, instead of adopting uniform sampling throughout the training process, the proposed algorithm employs importance sampling to minimize the variance of the stochastic gradient. For prox-SDCA, the proposed importance sampling scheme aims to achieve higher expected dual value at each dual coordinate ascent step. We provide extensive theoretical analysis to show that the convergence rates with the proposed importance sampling methods can be significantly improved under suitable conditions both for prox-SGD and for prox-SDCA. Experiments are provided to verify the theoretical analysis.

stat.ML↗

arXiv2014

Randomized Dual Coordinate Ascent with Arbitrary Sampling

We study the problem of minimizing the average of a large number of smooth convex functions penalized with a strongly convex regularizer. We propose and analyze a novel primal-dual method (Quartz) which at every iteration samples and updates a random subset of the dual variables, chosen according to an arbitrary distribution. In contrast to typical analysis, we directly bound the decrease of the primal-dual error (in expectation), without the need to first analyze the dual error. Depending on the choice of the sampling, we obtain efficient serial, parallel and distributed variants of the method. In the serial case, our bounds match the best known bounds for SDCA (both with uniform and importance sampling). With standard mini-batching, our bounds predict initial data-independent speedup as well as additional data-driven speedup which depends on spectral and sparsity properties of the data. We calculate theoretical speedup factors and find that they are excellent predictors of actual speedup in practice. Moreover, we illustrate that it is possible to design an efficient mini-batch importance sampling. The distributed variant of Quartz is the first distributed SDCA-like method with an analysis for non-separable data.

math.OC↗

arXiv2014

Joint Multi-Cell Resource Allocation Using Pure Binary-Integer Programming for LTE Uplink

Due to high system capacity requirement, 3GPP Long Term Evolution (LTE) is likely to adopt frequency reuse factor 1 at the cost of suffering severe inter-cell interference (ICI). One of combating ICI strategies is network cooperation of resource allocation (RA). For LTE uplink RA, requiring all the subcarriers to be allocated adjacently complicates the RA problem greatly. This paper investigates the joint multi-cell RA problem for LTE uplink. We model the uplink RA and ICI mitigation problem using pure binary-integer programming (BIP), with integrative consideration of all users' channel state information (CSI). The advantage of the pure BIP model is that it can be solved by branch-and-bound search (BBS) algorithm or other BIP solving algorithms, rather than resorting to exhaustive search. The system-level simulation results show that it yields 14.83% and 22.13% gains over single-cell optimal RA in average spectrum efficiency and 5th percentile of user throughput, respectively.

cs.IT↗

arXiv2014

Experimental demonstration of longitudinal beam phase space linearizer in a free-electron laser facility by corrugated structures

Removal of residual linear energy chirp and intrinsic nonlinear energy curvature in the relativistic electron beam from radiofrequency linear accelerator is of paramount importance for efficient lasing of a high-gain free-electron laser. Recently, it was theoretically and experimentally demonstrated that the longitudinal wakefield excited by the electrons itself in the corrugated structure allows for precise control of the electron beam phase space. In this Letter, we report the first utilization of a corrugated structure as beam linearizer in the operation of a seeded free-electron laser driven by a 140 MeV linear accelerator, where a gain of ~10,000 over spontaneous emission was achieved at the second harmonic of the 1047 nm seed laser, and a free-electron laser bandwidth narrowing by about 50% was observed, in good agreement with the theoretical expectations.

physics.acc-ph↗

arXiv2014

Learning Nonlinear Functions Using Regularized Greedy Forest

We consider the problem of learning a forest of nonlinear decision rules with general loss functions. The standard methods employ boosted decision trees such as Adaboost for exponential loss and Friedman's gradient boosting for general loss. In contrast to these traditional boosting algorithms that treat a tree learner as a black box, the method we propose directly learns decision forests via fully-corrective regularized greedy search using the underlying forest structure. Our method achieves higher accuracy and smaller models than gradient boosting (and Adaboost with exponential loss) on many datasets.

stat.ML↗

arXiv2014

Adaptive Stochastic Alternating Direction Method of Multipliers

The Alternating Direction Method of Multipliers (ADMM) has been studied for years. The traditional ADMM algorithm needs to compute, at each iteration, an (empirical) expected loss function on all training examples, resulting in a computational complexity proportional to the number of training examples. To reduce the time complexity, stochastic ADMM algorithms were proposed to replace the expected function with a random loss function associated with one uniformly drawn example plus a Bregman divergence. The Bregman divergence, however, is derived from a simple second order proximal function, the half squared norm, which could be a suboptimal choice. In this paper, we present a new family of stochastic ADMM algorithms with optimal second order proximal functions, which produce a new family of adaptive subgradient methods. We theoretically prove that their regret bounds are as good as the bounds which could be achieved by the best proximal function that can be chosen in hindsight. Encouraging empirical results on a variety of real-world datasets confirm the effectiveness and efficiency of the proposed algorithms.

stat.ML↗

arXiv2014

Compensating the electron beam energy spread by the natural transverse gradient of laser undulator in all-optical x-ray light sources

All-optical ideas provide a potential to dramatically cut off the size and cost of x-ray light sources to the university-laboratory scale, with the combination of the laser-plasma accelerator and the laser undulator. However, the large longitudinal energy spread of the electron beam from laser-plasma accelerator may hinder the way to high brightness of these all-optical light sources. In this paper, the beam energy spread effect is proposed to be significantly compensated by the natural transverse gradient of a laser undulator when properly transverse-dispersing the electron beam. Theoretical analysis and numerical simulations on conventional laser-Compton scattering sources and high-gain all-optical x-ray free-electron lasers with the electron beams from laser-plasma accelerators are presented.

physics.acc-ph↗