面向绿色边缘AI推理的稀疏优化

Sparse Group Lasso: Optimal Sample Complexity, Convergence Rate, and Statistical Inference

We study sparse group Lasso for high-dimensional double sparse linear regression, where the parameter of interest is simultaneously element-wise and group-wise sparse. This problem is an important instance of the simultaneously structured model -- an actively studied topic in statistics and machine learning. In the noiseless case, matching upper and lower bounds on sample complexity are established for the exact recovery of sparse vectors and for stable estimation of approximately sparse vectors, respectively. In the noisy case, upper and matching minimax lower bounds for estimation error are …

Scalable Inference of Sparsely-changing Markov Random Fields with Strong Statistical Guarantees

In this paper, we study the problem of inferring time-varying Markov random fields (MRF), where the underlying graphical model is both sparse and changes sparsely over time. Most of the existing methods for the inference of time-varying MRFs rely on the regularized maximum likelihood estimation (MLE), that typically suffer from weak statistical guarantees and high computational time. Instead, we introduce a new class of constrained optimization problems for the inference of sparsely-changing MRFs. The proposed optimization problem is formulated based on the exact $\ell_0$ regularization, and c…

稀疏深度学习中变分推理的收敛速度

Convergence Rates of Variational Inference in Sparse Deep Learning

变分推理在贝叶斯统计和机器学习中越来越多地用于逼近难以处理的后验分布。与此同时，最近的一些工作为深度神经网络提供了理论依据和新的见解，用于在非参数回归等通常设置中估计平滑函数。在本文中，我们证明了稀疏深度学习的变分推理保留了与精确贝叶斯推理相同的泛化特性。特别是，我们强调估计和逼近论之间的连接，通过经典的偏差方差权衡，并表明它导致近极小极大的收敛速度的Hölder光滑函数。此外，我们表明，通过ELBO最大化的神经网络架构的模型选择框架不会过拟合，并自适应地实现了最佳的收敛速率。

Partitioning sparse deep neural networks for scalable training and inference

The state-of-the-art deep neural networks (DNNs) have significant computational and data management requirements. The size of both training data and models continue to increase. Sparsification and pruning methods are shown to be effective in removing a large fraction of connections in DNNs. The resulting sparse networks present unique challenges to further improve the computational efficiency of training and inference in deep learning. Both the feedforward (inference) and backpropagation steps in stochastic gradient descent (SGD) algorithm for training sparse DNNs involve consecutive sparse ma…

绿色云RAN的组稀疏波束形成

Group Sparse Beamforming for Green Cloud-RAN

云无线接入网络（Cloud-RAN）是一种网络架构，有望满足移动数据流量的爆炸性增长。在这种架构中，所有基带信号处理都转移到单个基带单元（BBU）池，这实现了高效的资源分配和干扰管理。与此同时，传统的强大基站可以被低成本低功率的远程无线电头（RRH）取代，从而产生绿色和低成本的基础设施。然而，由于所有RRH都需要通过光传输链路连接到BBU池，因此传输网络功耗变得很大。在本文中，我们提出了一个新的框架来设计一个绿色的Cloud-RAN，这是制定为一个联合RRH选择和功率最小化波束成形问题。为了有效地解决这个问题，我们首先提出了一个贪婪的选择算法，它被证明提供了接近最优的性能。为了进一步降低算法复杂度，提出了一种新的分组稀疏波束形成方法，该方法通过加权$\ell_1/\ell_2$范数最小化来诱导波束形成器的分组稀疏性，其中分组稀疏模式指示可以关闭的RRH。仿真结果表明，所提出的算法显着降低了网络功耗，并证明了考虑传输链路功耗的重要性。

基于组稀疏功率控制的下行异构网络半动态绿色资源管理

Semi-dynamic Green Resource Management in Downlink Heterogeneous Networks by Group Sparse Power Control

针对异构网络下行链路的节能问题，提出了在满足用户速率需求的前提下，最小化基站总功耗的节能方案。这项工作的基本思想是利用系统的灵活性和可扩展性，以便通过有效的资源管理获得更多的好处。这促使我们提出一种灵活的BS功耗模型，该模型可以以能量有效的方式而不是BS的“开/关”二进制睡眠方式来控制系统资源，诸如天线、频率载波和发射功率分配。为了表示这些功率节省模式，我们采用发射功率向量的组稀疏度而不是{0，1}变量。基于该功率模型，提出了一种半动态绿色资源管理机制，通过基于大尺度衰落值的分组稀疏功率控制，联合解决基站关联、频率载波分配和发射功率分配等一系列资源管理问题。特别是，连续凸逼近（SCA）为基础的算法，以解决原来的非凸问题的固定解决方案。仿真结果也验证了所提出的基站功率模型和绿色资源管理机制。