arXiv subjects

Dong Yin

Publications and source records attributed to Dong Yin.

42 records · Page 3Linked to original sources

arXiv2018

Sub-linear Time Support Recovery for Compressed Sensing using Sparse-Graph Codes

We study the support recovery problem for compressed sensing, where the goal is to reconstruct the a high-dimensional $K$-sparse signal $\mathbf{x}\in\mathbb{R}^N$, from low-dimensional linear measurements with and without noise. Our key contribution is a new compressed sensing framework through a new family of carefully designed sparse measurement matrices associated with minimal measurement costs and a low-complexity recovery algorithm. The measurement matrix in our framework is designed based on the well-crafted sparsification through capacity-approaching sparse-graph codes, where the sparse coefficients can be recovered efficiently in a few iterations by performing simple error decoding over the observations. We formally connect this general recovery problem with sparse-graph decoding in packet communication systems, and analyze our framework in terms of the measurement cost, time complexity and recovery performance. In the noiseless setting, our framework can recover any arbitrary $K$-sparse signal in $O(K)$ time using $2K$ measurements asymptotically with high probability. In the noisy setting, when the sparse coefficients take values in a finite and quantized alphabet, our framework can achieve the same goal in time $O(K\log(N/K))$ using $O(K\log(N/K))$ measurements obtained from measurement matrix with elements $\{-1,0,1\}$. When the sparsity $K$ is sub-linear in the signal dimension $K=O(N^δ)$ for some $0<δ<1$, our results are order-optimal in terms of measurement costs and run-time, both of which are sub-linear in the signal dimension $N$. The sub-linear measurement cost and run-time can also be achieved with continuous-valued sparse coefficients, with a slight increment in the logarithmic factors. This offers the desired scalability of our framework that can potentially enable real-time or near-real-time processing for massive datasets featuring sparsity.

cs.IT↗

arXiv2018

Gradient Diversity: a Key Ingredient for Scalable Distributed Learning

It has been experimentally observed that distributed implementations of mini-batch stochastic gradient descent (SGD) algorithms exhibit speedup saturation and decaying generalization ability beyond a particular batch-size. In this work, we present an analysis hinting that high similarity between concurrently processed gradients may be a cause of this performance degradation. We introduce the notion of gradient diversity that measures the dissimilarity between concurrent gradient updates, and show its key role in the performance of mini-batch SGD. We prove that on problems with high gradient diversity, mini-batch SGD is amenable to better speedups, while maintaining the generalization performance of serial (one sample) SGD. We further establish lower bounds on convergence where mini-batch SGD slows down beyond a particular batch-size, solely due to the lack of gradient diversity. We provide experimental evidence indicating the key role of gradient diversity in distributed learning, and discuss how heuristics like dropout, Langevin dynamics, and quantization can improve it.

cs.LG↗

arXiv2017

PhaseCode: Fast and Efficient Compressive Phase Retrieval based on Sparse-Graph-Codes

We consider the problem of recovering a $K$-sparse complex signal $x$ from $m$ intensity measurements. We propose the PhaseCode algorithm, and show that in the noiseless case, PhaseCode can recover an arbitrarily-close-to-one fraction of the $K$ non-zero signal components using only slightly more than $4K$ measurements when the support of the signal is uniformly random, with order-optimal time and memory complexity of $Θ(K)$. It is known that the fundamental limit for the number of measurements in compressive phase retrieval problem is $4K - o(K)$ to recover the signal exactly and with no assumptions on its support distribution. This shows that under mild relaxation of the conditions, our algorithm is the first constructive \emph{capacity-approaching} compressive phase retrieval algorithm: in fact, our algorithm is also order-optimal in complexity and memory. Next, motivated by some important practical classes of optical systems, we consider a Fourier-friendly constrained measurement setting, and show that its performance matches that of the unconstrained setting. In the Fourier-friendly setting that we consider, the measurement matrix is constrained to be a cascade of Fourier matrices and diagonal matrices. We further demonstrate how PhaseCode can be robustified to noise. Throughout, we provide extensive simulation results that validate the practical power of our proposed algorithms for the sparse unconstrained and Fourier-friendly measurement settings, for noiseless and noisy scenarios. A key contribution of our work is the novel use of coding-theoretic tools like density evolution methods for the design and analysis of fast and efficient algorithms for compressive phase-retrieval problems.

cs.IT↗

arXiv2017

Distributed Sequence Memory of Multidimensional Inputs in Recurrent Networks

Recurrent neural networks (RNNs) have drawn interest from machine learning researchers because of their effectiveness at preserving past inputs for time-varying data processing tasks. To understand the success and limitations of RNNs, it is critical that we advance our analysis of their fundamental memory properties. We focus on echo state networks (ESNs), which are RNNs with simple memoryless nodes and random connectivity. In most existing analyses, the short-term memory (STM) capacity results conclude that the ESN network size must scale linearly with the input size for unstructured inputs. The main contribution of this paper is to provide general results characterizing the STM capacity for linear ESNs with multidimensional input streams when the inputs have common low-dimensional structure: sparsity in a basis or significant statistical dependence between inputs. In both cases, we show that the number of nodes in the network must scale linearly with the information rate and poly-logarithmically with the ambient input dimension. The analysis relies on advanced applications of random matrix theory and results in explicit non-asymptotic bounds on the recovery error. Taken together, this analysis provides a significant step forward in our understanding of the STM properties in RNNs.

cs.IT↗

arXiv2016

Fast and Robust Compressive Phase Retrieval with Sparse-Graph Codes

In this paper, we tackle the compressive phase retrieval problem in the presence of noise. The noisy compressive phase retrieval problem is to recover a $K$-sparse complex signal $s \in \mathbb{C}^n$, from a set of $m$ noisy quadratic measurements: $ y_i=| a_i^H s |^2+w_i$, where $a_i^H\in\mathbb{C}^n$ is the $i$th row of the measurement matrix $A\in\mathbb{C}^{m\times n}$, and $w_i$ is the additive noise to the $i$th measurement. We consider the regime where $K=βn^δ$, with constants $β>0$ and $δ\in(0,1)$. We use the architecture of PhaseCode algorithm, and robustify it using two schemes: the almost-linear scheme and the sublinear scheme. We prove that with high probability, the almost-linear scheme recovers $s$ with sample complexity $Θ(K \log(n))$ and computational complexity $Θ(n \log(n))$, and the sublinear scheme recovers $s$ with sample complexity $Θ(K\log^3(n))$ and computational complexity $Θ(K\log^3(n))$. To the best of our knowledge, this is the first scheme that achieves sublinear computational complexity for compressive phase retrieval problem. Finally, we provide simulation results that support our theoretical contributions.

cs.IT↗

arXiv2015

Sliding-Window Optimization on an Ambiguity-Clearness Graph for Multi-object Tracking

Multi-object tracking remains challenging due to frequent occurrence of occlusions and outliers. In order to handle this problem, we propose an Approximation-Shrink Scheme for sequential optimization. This scheme is realized by introducing an Ambiguity-Clearness Graph to avoid conflicts and maintain sequence independent, as well as a sliding window optimization framework to constrain the size of state space and guarantee convergence. Based on this window-wise framework, the states of targets are clustered in a self-organizing manner. Moreover, we show that the traditional online and batch tracking methods can be embraced by the window-wise framework. Experiments indicate that with only a small window, the optimization performance can be much better than online methods and approach to batch methods.

cs.CV↗