Evaluation Mappings of Spatial Accelerator Based On Data Placement

The scheduling strategies of workloads are critical to fully exploiting the performance of spatial accelerators, accurate performance models are required to evaluate the mapping of workloads.Recent works proposed various cost-model to describe the dataflow of the spatial accelerator. However, they are less expressive about customized memory hierarchies and thus lead to inaccurate performance models. In this paper, we propose, PolyAcc, a framework for evaluating the mappings of workload on spatial accelerator based on data placement. The Data placement relation describes the temporal-spatial relation of data at different memory levels, which can accurately capture the runtime behavior of hardware units. Based on data placement relations, polyAcc accurately analyzes the data volume for different reuse patterns and estimate metrics, including data reuse, latency, and energy. Overall, polyAcc closely matches the ideal execution time and PE utilization for GEMM and Conv workloads, respectively achieves 0.82%, 18.8% improvements for execution time and energy consumption estimates in validation against Eyeriss architecture compared to the state-of-the-art framework.Comment: 7 pages,8 figures,3 table

Robust High-dimensional Tuning Free Multiple Testing

A stylized feature of high-dimensional data is that many variables have heavy tails, and robust statistical inference is critical for valid large-scale statistical inference. Yet, the existing developments such as Winsorization, Huberization and median of means require the bounded second moments and involve variable-dependent tuning parameters, which hamper their fidelity in applications to large-scale problems. To liberate these constraints, this paper revisits the celebrated Hodges-Lehmann (HL) estimator for estimating location parameters in both the one- and two-sample problems, from a non-asymptotic perspective. Our study develops Berry-Esseen inequality and Cram\'{e}r type moderate deviation for the HL estimator based on newly developed non-asymptotic Bahadur representation, and builds data-driven confidence intervals via a weighted bootstrap approach. These results allow us to extend the HL estimator to large-scale studies and propose \emph{tuning-free} and \emph{moment-free} high-dimensional inference procedures for testing global null and for large-scale multiple testing with false discovery proportion control. It is convincingly shown that the resulting tuning-free and moment-free methods control false discovery proportion at a prescribed level. The simulation studies lend further support to our developed theory.Comment: In this paper, we develop tuning-free and moment-free high dimensional inference procedures

Spectral Ranking Inferences based on General Multiway Comparisons

This paper studies the performance of the spectral method in the estimation and uncertainty quantification of the unobserved preference scores of compared entities in a very general and more realistic setup in which the comparison graph consists of hyper-edges of possible heterogeneous sizes and the number of comparisons can be as low as one for a given hyper-edge. Such a setting is pervasive in real applications, circumventing the need to specify the graph randomness and the restrictive homogeneous sampling assumption imposed in the commonly-used Bradley-Terry-Luce (BTL) or Plackett-Luce (PL) models. Furthermore, in the scenarios when the BTL or PL models are appropriate, we unravel the relationship between the spectral estimator and the Maximum Likelihood Estimator (MLE). We discover that a two-step spectral method, where we apply the optimal weighting estimated from the equal weighting vanilla spectral method, can achieve the same asymptotic efficiency as the MLE. Given the asymptotic distributions of the estimated preference scores, we also introduce a comprehensive framework to carry out both one-sample and two-sample ranking inferences, applicable to both fixed and random graph settings. It is noteworthy that it is the first time effective two-sample rank testing methods are proposed. Finally, we substantiate our findings via comprehensive numerical simulations and subsequently apply our developed methodologies to perform statistical inferences on statistics journals and movie rankings