arXiv subjects

Songtao Lu

Publications and source records attributed to Songtao Lu.

67 records · Page 4Linked to original sources

arXiv2019

Leveraging Two Reference Functions in Block Bregman Proximal Gradient Descent for Non-convex and Non-Lipschitz Problems

In the applications of signal processing and data analytics, there is a wide class of non-convex problems whose objective function is freed from the common global Lipschitz continuous gradient assumption (e.g., the nonnegative matrix factorization (NMF) problem). Recently, this type of problem with some certain special structures has been solved by Bregman proximal gradient (BPG). This inspires us to propose a new Block-wise two-references Bregman proximal gradient (B2B) method, which adopts two reference functions so that a closed-form solution in the Bregman projection is obtained. Based on the relative smoothness, we prove the global convergence of the proposed algorithms for various block selection rules. In particular, we establish the global convergence rate of $O(\frac{\sqrt{s}}{\sqrt{k}})$ for the greedy and randomized block updating rule for B2B, which is $O(\sqrt{s})$ times faster than the cyclic variant, i.e., $O(\frac{s}{\sqrt{k}} )$, where $s$ is the number of blocks, and $k$ is the number of iterations. Multiple numerical results are provided to illustrate the superiority of the proposed B2B compared to the state-of-the-art works in solving NMF problems.

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arXiv2019

Learn Electronic Health Records by Fully Decentralized Federated Learning

Federated learning opens a number of research opportunities due to its high communication efficiency in distributed training problems within a star network. In this paper, we focus on improving the communication efficiency for fully decentralized federated learning over a graph, where the algorithm performs local updates for several iterations and then enables communications among the nodes. In such a way, the communication rounds of exchanging the common interest of parameters can be saved significantly without loss of optimality of the solutions. Multiple numerical simulations based on large, real-world electronic health record databases showcase the superiority of the decentralized federated learning compared with classic methods.

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arXiv2019

Improving the Sample and Communication Complexity for Decentralized Non-Convex Optimization: A Joint Gradient Estimation and Tracking Approach

Many modern large-scale machine learning problems benefit from decentralized and stochastic optimization. Recent works have shown that utilizing both decentralized computing and local stochastic gradient estimates can outperform state-of-the-art centralized algorithms, in applications involving highly non-convex problems, such as training deep neural networks. In this work, we propose a decentralized stochastic algorithm to deal with certain smooth non-convex problems where there are $m$ nodes in the system, and each node has a large number of samples (denoted as $n$). Differently from the majority of the existing decentralized learning algorithms for either stochastic or finite-sum problems, our focus is given to both reducing the total communication rounds among the nodes, while accessing the minimum number of local data samples. In particular, we propose an algorithm named D-GET (decentralized gradient estimation and tracking), which jointly performs decentralized gradient estimation (which estimates the local gradient using a subset of local samples) and gradient tracking (which tracks the global full gradient using local estimates). We show that, to achieve certain $ε$ stationary solution of the deterministic finite sum problem, the proposed algorithm achieves an $\mathcal{O}(mn^{1/2}ε^{-1})$ sample complexity and an $\mathcal{O}(ε^{-1})$ communication complexity. These bounds significantly improve upon the best existing bounds of $\mathcal{O}(mnε^{-1})$ and $\mathcal{O}(ε^{-1})$, respectively. Similarly, for online problems, the proposed method achieves an $\mathcal{O}(m ε^{-3/2})$ sample complexity and an $\mathcal{O}(ε^{-1})$ communication complexity, while the best existing bounds are $\mathcal{O}(mε^{-2})$ and $\mathcal{O}(ε^{-2})$, respectively.

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arXiv2019

SNAP: Finding Approximate Second-Order Stationary Solutions Efficiently for Non-convex Linearly Constrained Problems

This paper proposes low-complexity algorithms for finding approximate second-order stationary points (SOSPs) of problems with smooth non-convex objective and linear constraints. While finding (approximate) SOSPs is computationally intractable, we first show that generic instances of the problem can be solved efficiently. More specifically, for a generic problem instance, certain strict complementarity (SC) condition holds for all Karush-Kuhn-Tucker (KKT) solutions (with probability one). The SC condition is then used to establish an equivalence relationship between two different notions of SOSPs, one of which is computationally easy to verify. Based on this particular notion of SOSP, we design an algorithm named the Successive Negative-curvature grAdient Projection (SNAP), which successively performs either conventional gradient projection or some negative curvature based projection steps to find SOSPs. SNAP and its first-order extension SNAP$^+$, require $\mathcal{O}(1/ε^{2.5})$ iterations to compute an $(ε, \sqrtε)$-SOSP, and their per-iteration computational complexities are polynomial in the number of constraints and problem dimension. To our knowledge, this is the first time that first-order algorithms with polynomial per-iteration complexity and global sublinear rate have been designed to find SOSPs of the important class of non-convex problems with linear constraints.

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arXiv2019

Signal Demodulation with Machine Learning Methods for Physical Layer Visible Light Communications: Prototype Platform, Open Dataset and Algorithms

In this paper, we investigate the design and implementation of machine learning (ML) based demodulation methods in the physical layer of visible light communication (VLC) systems. We build a flexible hardware prototype of an end-to-end VLC system, from which the received signals are collected as the real data. The dataset is available online, which contains eight types of modulated signals. Then, we propose three ML demodulators based on convolutional neural network (CNN), deep belief network (DBN), and adaptive boosting (AdaBoost), respectively. Specifically, the CNN based demodulator converts the modulated signals to images and recognizes the signals by the image classification. The proposed DBN based demodulator contains three restricted Boltzmann machines (RBMs) to extract the modulation features. The AdaBoost method includes a strong classifier that is constructed by the weak classifiers with the k-nearest neighbor (KNN) algorithm. These three demodulators are trained and tested by our online open dataset. Experimental results show that the demodulation accuracy of the three data-driven demodulators drops as the transmission distance increases. A higher modulation order negatively influences the accuracy for a given transmission distance. Among the three ML methods, the AdaBoost modulator achieves the best performance.

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arXiv2019

Deep Learning for Signal Demodulation in Physical Layer Wireless Communications: Prototype Platform, Open Dataset, and Analytics

In this paper, we investigate deep learning (DL)-enabled signal demodulation methods and establish the first open dataset of real modulated signals for wireless communication systems. Specifically, we propose a flexible communication prototype platform for measuring real modulation dataset. Then, based on the measured dataset, two DL-based demodulators, called deep belief network (DBN)-support vector machine (SVM) demodulator and adaptive boosting (AdaBoost) based demodulator, are proposed. The proposed DBN-SVM based demodulator exploits the advantages of both DBN and SVM, i.e., the advantage of DBN as a feature extractor and SVM as a feature classifier. In DBN-SVM based demodulator, the received signals are normalized before being fed to the DBN network. Furthermore, an AdaBoost based demodulator is developed, which employs the $k$-Nearest Neighbor (KNN) as a weak classifier to form a strong combined classifier. Finally, experimental results indicate that the proposed DBN-SVM based demodulator and AdaBoost based demodulator are superior to the single classification method using DBN, SVM, and maximum likelihood (MLD) based demodulator.

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arXiv2018

Power Market Price Forecasting via Deep Learning

A study on power market price forecasting by deep learning is presented. As one of the most successful deep learning frameworks, the LSTM (Long short-term memory) neural network is utilized. The hourly prices data from the New England and PJM day-ahead markets are used in this study. First, a LSTM network is formulated and trained. Then the raw input and output data are preprocessed by unit scaling, and the trained network is tested on the real price data under different input lengths, forecasting horizons and data sizes. Its performance is also compared with other existing methods. The forecasted results demonstrate that, the LSTM deep neural network can outperform the others under different application settings in this problem.

cs.LG↗

arXiv2018

On the Sublinear Convergence of Randomly Perturbed Alternating Gradient Descent to Second Order Stationary Solutions

The alternating gradient descent (AGD) is a simple but popular algorithm which has been applied to problems in optimization, machine learning, data ming, and signal processing, etc. The algorithm updates two blocks of variables in an alternating manner, in which a gradient step is taken on one block, while keeping the remaining block fixed. When the objective function is nonconvex, it is well-known the AGD converges to the first-order stationary solution with a global sublinear rate. In this paper, we show that a variant of AGD-type algorithms will not be trapped by "bad" stationary solutions such as saddle points and local maximum points. In particular, we consider a smooth unconstrained optimization problem, and propose a perturbed AGD (PA-GD) which converges (with high probability) to the set of second-order stationary solutions (SS2) with a global sublinear rate. To the best of our knowledge, this is the first alternating type algorithm which takes $\mathcal{O}(\text{polylog}(d)/ε^{7/3})$ iterations to achieve SS2 with high probability [where polylog$(d)$ is polynomial of the logarithm of dimension $d$ of the problem].

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arXiv2017

A Nonconvex Splitting Method for Symmetric Nonnegative Matrix Factorization: Convergence Analysis and Optimality

Symmetric nonnegative matrix factorization (SymNMF) has important applications in data analytics problems such as document clustering, community detection and image segmentation. In this paper, we propose a novel nonconvex variable splitting method for solving SymNMF. The proposed algorithm is guaranteed to converge to the set of Karush-Kuhn-Tucker (KKT) points of the nonconvex SymNMF problem. Furthermore, it achieves a global sublinear convergence rate. We also show that the algorithm can be efficiently implemented in parallel. Further, sufficient conditions are provided which guarantee the global and local optimality of the obtained solutions. Extensive numerical results performed on both synthetic and real data sets suggest that the proposed algorithm converges quickly to a local minimum solution.

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arXiv2016

Inexact Block Coordinate Descent Methods For Symmetric Nonnegative Matrix Factorization

Symmetric nonnegative matrix factorization (SNMF) is equivalent to computing a symmetric nonnegative low rank approximation of a data similarity matrix. It inherits the good data interpretability of the well-known nonnegative matrix factorization technique and have better ability of clustering nonlinearly separable data. In this paper, we focus on the algorithmic aspect of the SNMF problem and propose simple inexact block coordinate decent methods to address the problem, leading to both serial and parallel algorithms. The proposed algorithms have guaranteed stationary convergence and can efficiently handle large-scale and/or sparse SNMF problems. Extensive simulations verify the effectiveness of the proposed algorithms compared to recent state-of-the-art algorithms.

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arXiv2016

Achievable Rates and Training Optimization for Uplink Multiuser Massive MIMO Systems

We study the performance of uplink transmission in a large-scale (massive) MIMO system, where all the transmitters have single antennas and the base station has a large number of antennas. Specifically, we first derive the rates that are possible through minimum mean-squared error (MMSE) channel estimation and three linear receivers: maximum ratio combining (MRC), zero-forcing (ZF), and MMSE. Based on the derived rates, we quantify the amount of energy savings that are possible through increased number of base-station antennas or increased coherence interval. We also analyze achievable total degrees of freedom (DoF) of such a system without assuming channel state information at the receiver, which is shown to be the same as that of a point-to-point MIMO channel. Linear receiver is sufficient to achieve total DoF when the number of users is less than the number of antennas. When the number of users is equal to or larger than the number of antennas, nonlinear processing is necessary to achieve the full degrees of freedom. Finally, the training period and optimal training energy allocation under the average and peak power constraints are optimized jointly to maximize the achievable sum rate when either MRC or ZF receiver is adopted at the receiver.

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arXiv2014

Joint Optimization of Power Allocation and Training Duration for Uplink Multiuser MIMO Communications

In this paper, we consider a multiuser multiple-input multiple-output (MU-MIMO) communication system between a base station equipped with multiple antennas and multiple mobile users each equipped with a single antenna. The uplink scenario is considered. The uplink channels are acquired by the base station through a training phase. Two linear processing schemes are considered, namely maximum-ratio combining (MRC) and zero-forcing (ZF). We optimize the training period and optimal training energy under the average and peak power constraint so that an achievable sum rate is maximized.

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arXiv2012

Amplitude Space Sharing among the Macro-Cell and Small-Cell Users

The crushing demand for wireless data services will soon exceed the capability of the current homogeneous cellular architecture. An emerging solution is to overlay small-cell networks with the macro-cell networks. In this paper, we propose an amplitude space sharing (ASS) method among the macro-cell user and small-cell users. By transmit layer design and data-rate optimization, the signals and interferences are promised to be separable at each receiver and the network sum-rate is maximized. The Han-Koboyashi coding is employed and optimal power allocation is derived for the one small-cell scenario, and a simple ASS transmission scheme is developed for the multiple small-cells scenarios. Simulation results show great superiority over other interference management schemes.

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