arXiv subjects

Xiaoyun Li

Publications and source records attributed to Xiaoyun Li.

25 records · Page 2Linked to original sources

arXiv2021

C-MinHash: Rigorously Reducing $K$ Permutations to Two

Minwise hashing (MinHash) is an important and practical algorithm for generating random hashes to approximate the Jaccard (resemblance) similarity in massive binary (0/1) data. The basic theory of MinHash requires applying hundreds or even thousands of independent random permutations to each data vector in the dataset, in order to obtain reliable results for (e.g.,) building large-scale learning models or approximate near neighbor search in massive data. In this paper, we propose {\bf Circulant MinHash (C-MinHash)} and provide the surprising theoretical results that we just need \textbf{two} independent random permutations. For C-MinHash, we first conduct an initial permutation on the data vector, then we use a second permutation to generate hash values. Basically, the second permutation is re-used $K$ times via circulant shifting to produce $K$ hashes. Unlike classical MinHash, these $K$ hashes are obviously correlated, but we are able to provide rigorous proofs that we still obtain an unbiased estimate of the Jaccard similarity and the theoretical variance is uniformly smaller than that of the classical MinHash with $K$ independent permutations. The theoretical proofs of C-MinHash require some non-trivial efforts. Numerical experiments are conducted to justify the theory and demonstrate the effectiveness of C-MinHash.

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arXiv2021

Quantization Algorithms for Random Fourier Features

The method of random projection (RP) is the standard technique in machine learning and many other areas, for dimensionality reduction, approximate near neighbor search, compressed sensing, etc. Basically, RP provides a simple and effective scheme for approximating pairwise inner products and Euclidean distances in massive data. Closely related to RP, the method of random Fourier features (RFF) has also become popular, for approximating the Gaussian kernel. RFF applies a specific nonlinear transformation on the projected data from random projections. In practice, using the (nonlinear) Gaussian kernel often leads to better performance than the linear kernel (inner product), partly due to the tuning parameter $(γ)$ introduced in the Gaussian kernel. Recently, there has been a surge of interest in studying properties of RFF. After random projections, quantization is an important step for efficient data storage, computation, and transmission. Quantization for RP has also been extensive studied in the literature. In this paper, we focus on developing quantization algorithms for RFF. The task is in a sense challenging due to the tuning parameter $γ$ in the Gaussian kernel. For example, the quantizer and the quantized data might be tied to each specific tuning parameter $γ$. Our contribution begins with an interesting discovery, that the marginal distribution of RFF is actually free of the Gaussian kernel parameter $γ$. This small finding significantly simplifies the design of the Lloyd-Max (LM) quantization scheme for RFF in that there would be only one LM quantizer for RFF (regardless of $γ$). We also develop a variant named LM$^2$-RFF quantizer, which in certain cases is more accurate. Experiments confirm that the proposed quantization schemes perform well.

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arXiv2020

When Services Computing Meets Blockchain: Challenges and Opportunities

Services computing can offer a high-level abstraction to support diverse applications via encapsulating various computing infrastructures. Though services computing has greatly boosted the productivity of developers, it is faced with three main challenges: privacy and security risks, information silo, and pricing mechanisms and incentives. The recent advances of blockchain bring opportunities to address the challenges of services computing due to its build-in encryption as well as digital signature schemes, decentralization feature, and intrinsic incentive mechanisms. In this paper, we present a survey to investigate the integration of blockchain with services computing. The integration of blockchain with services computing mainly exhibits merits in two aspects: i) blockchain can potentially address key challenges of services computing and ii) services computing can also promote blockchain development. In particular, we categorize the current literature of services computing based on blockchain into five types: services creation, services discovery, services recommendation, services composition, and services arbitration. Moreover, we generalize Blockchain as a Service (BaaS) architecture and summarize the representative BaaS platforms. In addition, we also outline open issues of blockchain-based services computing and BaaS.

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arXiv2020

An Optimistic Acceleration of AMSGrad for Nonconvex Optimization

We propose a new variant of AMSGrad, a popular adaptive gradient based optimization algorithm widely used for training deep neural networks. Our algorithm adds prior knowledge about the sequence of consecutive mini-batch gradients and leverages its underlying structure making the gradients sequentially predictable. By exploiting the predictability and ideas from optimistic online learning, the proposed algorithm can accelerate the convergence and increase sample efficiency. After establishing a tighter upper bound under some convexity conditions on the regret, we offer a complimentary view of our algorithm which generalizes the offline and stochastic version of nonconvex optimization. In the nonconvex case, we establish a non-asymptotic convergence bound independently of the initialization. We illustrate the practical speedup on several deep learning models via numerical experiments.

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arXiv2020

FedSKETCH: Communication-Efficient and Private Federated Learning via Sketching

Communication complexity and privacy are the two key challenges in Federated Learning where the goal is to perform a distributed learning through a large volume of devices. In this work, we introduce FedSKETCH and FedSKETCHGATE algorithms to address both challenges in Federated learning jointly, where these algorithms are intended to be used for homogeneous and heterogeneous data distribution settings respectively. The key idea is to compress the accumulation of local gradients using count sketch, therefore, the server does not have access to the gradients themselves which provides privacy. Furthermore, due to the lower dimension of sketching used, our method exhibits communication-efficiency property as well. We provide, for the aforementioned schemes, sharp convergence guarantees. Finally, we back up our theory with various set of experiments.

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arXiv2020

Randomized Kernel Multi-view Discriminant Analysis

In many artificial intelligence and computer vision systems, the same object can be observed at distinct viewpoints or by diverse sensors, which raises the challenges for recognizing objects from different, even heterogeneous views. Multi-view discriminant analysis (MvDA) is an effective multi-view subspace learning method, which finds a discriminant common subspace by jointly learning multiple view-specific linear projections for object recognition from multiple views, in a non-pairwise way. In this paper, we propose the kernel version of multi-view discriminant analysis, called kernel multi-view discriminant analysis (KMvDA). To overcome the well-known computational bottleneck of kernel methods, we also study the performance of using random Fourier features (RFF) to approximate Gaussian kernels in KMvDA, for large scale learning. Theoretical analysis on stability of this approximation is developed. We also conduct experiments on several popular multi-view datasets to illustrate the effectiveness of our proposed strategy.

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arXiv2020

IVFS: Simple and Efficient Feature Selection for High Dimensional Topology Preservation

Feature selection is an important tool to deal with high dimensional data. In unsupervised case, many popular algorithms aim at maintaining the structure of the original data. In this paper, we propose a simple and effective feature selection algorithm to enhance sample similarity preservation through a new perspective, topology preservation, which is represented by persistent diagrams from the context of computational topology. This method is designed upon a unified feature selection framework called IVFS, which is inspired by random subset method. The scheme is flexible and can handle cases where the problem is analytically intractable. The proposed algorithm is able to well preserve the pairwise distances, as well as topological patterns, of the full data. We demonstrate that our algorithm can provide satisfactory performance under a sharp sub-sampling rate, which supports efficient implementation of our proposed method to large scale datasets. Extensive experiments validate the effectiveness of the proposed feature selection scheme.

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