Preconditioned Data Sparsification for Big Data with Applications to PCA and K-means

We analyze a compression scheme for large data sets that randomly keeps a small percentage of the components of each data sample. The benefit is that the output is a sparse matrix and therefore subsequent processing, such as PCA or K-means, is significantly faster, especially in a distributed-data setting. Furthermore, the sampling is single-pass and applicable to streaming data. The sampling mechanism is a variant of previous methods proposed in the literature combined with a randomized preconditioning to smooth the data. We provide guarantees for PCA in terms of the covariance matrix, and guarantees for K-means in terms of the error in the center estimators at a given step. We present numerical evidence to show both that our bounds are nearly tight and that our algorithms provide a real benefit when applied to standard test data sets, as well as providing certain benefits over related sampling approaches.Comment: 28 pages, 10 figure

Performance analysis and optimization of automatic speech recognition

© 2018 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes,creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.Fast and accurate Automatic Speech Recognition (ASR) is emerging as a key application for mobile devices. Delivering ASR on such devices is challenging due to the compute-intensive nature of the problem and the power constraints of embedded systems. In this paper, we provide a performance and energy characterization of Pocketsphinx, a popular toolset for ASR that targets mobile devices. We identify the computation of the Gaussian Mixture Model (GMM) as the main bottleneck, consuming more than 80 percent of the execution time. The CPI stack analysis shows that branches and main memory accesses are the main performance limiting factors for GMM computation. We propose several software-level optimizations driven by the power/performance analysis. Unlike previous proposals that trade accuracy for performance by reducing the number of Gaussians evaluated, we maintain accuracy and improve performance by effectively using the underlying CPU microarchitecture. First, we use a refactored implementation of the innermost loop of the GMM evaluation code to ameliorate the impact of branches. Second, we exploit the vector unit available on most modern CPUs to boost GMM computation, introducing a novel memory layout for storing the means and variances of the Gaussians in order to maximize the effectiveness of vectorization. Third, we compute the Gaussians for multiple frames in parallel, so means and variances can be fetched once in the on-chip caches and reused across multiple frames, significantly reducing memory bandwidth usage. We evaluate our optimizations using both hardware counters on real CPUs and simulations. Our experimental results show that the proposed optimizations provide 2.68x speedup over the baseline Pocketsphinx decoder on a high-end Intel Skylake CPU, while achieving 61 percent energy savings. On a modern ARM Cortex-A57 mobile processor our techniques improve performance by 1.85x, while providing 59 percent energy savings without any loss in the accuracy of the ASR system.Peer ReviewedPostprint (author's final draft

Random Walkers with Shrinking Steps in d-Dimensions and Their Long Term Memory

We study, in d-dimensions, the random walker with geometrically shrinking step sizes at each hop. We emphasize the integrated quantities such as expectation values, cumulants and moments rather than a direct study of the probability distribution. We develop a 1/d expansion technique and study various correlations of the first step to the position as ti me goes to infinity. We also show and substantiate with a study of the cumulants that to order 1/d the system admits a continuum counterpart equation which can be obtained with a generalization of the ordinary technique to obtain the continuum limit. We also advocate that this continuum counterpart equation, which is nothing but the ordinary diffusion equation with a diffusion constant decaying exponentially in continuous time, captures all the qualitative aspects of t he discrete system and is often a good starting point for quantitative approximations