Diffusion Approximations for Online Principal Component Estimation and Global Convergence

In this paper, we propose to adopt the diffusion approximation tools to study the dynamics of Oja's iteration which is an online stochastic gradient descent method for the principal component analysis. Oja's iteration maintains a running estimate of the true principal component from streaming data and enjoys less temporal and spatial complexities. We show that the Oja's iteration for the top eigenvector generates a continuous-state discrete-time Markov chain over the unit sphere. We characterize the Oja's iteration in three phases using diffusion approximation and weak convergence tools. Our three-phase analysis further provides a finite-sample error bound for the running estimate, which matches the minimax information lower bound for principal component analysis under the additional assumption of bounded samples.Comment: Appeared in NIPS 201

Load-Varying LINPACK: A Benchmark for Evaluating Energy Efficiency in High-End Computing

For decades, performance has driven the high-end computing (HEC) community. However, as highlighted in recent exascale studies that chart a path from petascale to exascale computing, power consumption is fast becoming the major design constraint in HEC. Consequently, the HEC community needs to address this issue in future petascale and exascale computing systems. Current scientific benchmarks, such as LINPACK and SPEChpc, only evaluate HEC systems when running at full throttle, i.e., 100% workload, resulting in a focus on performance and ignoring the issues of power and energy consumption. In contrast, efforts like SPECpower evaluate the energy efficiency of a compute server at varying workloads. This is analogous to evaluating the energy efficiency (i.e., fuel efficiency) of an automobile at varying speeds (e.g., miles per gallon highway versus city). SPECpower, however, only evaluates the energy efficiency of a single compute server rather than a HEC system; furthermore, it is based on SPEC's Java Business Benchmarks (SPECjbb) rather than a scientific benchmark. Given the absence of a load-varying scientific benchmark to evaluate the energy efficiency of HEC systems at different workloads, we propose the load-varying LINPACK (LV-LINPACK) benchmark. In this paper, we identify application parameters that affect performance and provide a methodology to vary the workload of LINPACK, thus enabling a more rigorous study of energy efficiency in supercomputers, or more generally, HEC