The Degrees of Freedom of Partial Least Squares Regression

The derivation of statistical properties for Partial Least Squares regression can be a challenging task. The reason is that the construction of latent components from the predictor variables also depends on the response variable. While this typically leads to good performance and interpretable models in practice, it makes the statistical analysis more involved. In this work, we study the intrinsic complexity of Partial Least Squares Regression. Our contribution is an unbiased estimate of its Degrees of Freedom. It is defined as the trace of the first derivative of the fitted values, seen as a function of the response. We establish two equivalent representations that rely on the close connection of Partial Least Squares to matrix decompositions and Krylov subspace techniques. We show that the Degrees of Freedom depend on the collinearity of the predictor variables: The lower the collinearity is, the higher the Degrees of Freedom are. In particular, they are typically higher than the naive approach that defines the Degrees of Freedom as the number of components. Further, we illustrate how the Degrees of Freedom approach can be used for the comparison of different regression methods. In the experimental section, we show that our Degrees of Freedom estimate in combination with information criteria is useful for model selection.Comment: to appear in the Journal of the American Statistical Associatio

RPPM : Rapid Performance Prediction of Multithreaded workloads on multicore processors

Analytical performance modeling is a useful complement to detailed cycle-level simulation to quickly explore the design space in an early design stage. Mechanistic analytical modeling is particularly interesting as it provides deep insight and does not require expensive offline profiling as empirical modeling. Previous work in mechanistic analytical modeling, unfortunately, is limited to single-threaded applications running on single-core processors. This work proposes RPPM, a mechanistic analytical performance model for multi-threaded applications on multicore hardware. RPPM collects microarchitecture-independent characteristics of a multi-threaded workload to predict performance on a previously unseen multicore architecture. The profile needs to be collected only once to predict a range of processor architectures. We evaluate RPPM's accuracy against simulation and report a performance prediction error of 11.2% on average (23% max). We demonstrate RPPM's usefulness for conducting design space exploration experiments as well as for analyzing parallel application performance

Checkpointing algorithms and fault prediction

This paper deals with the impact of fault prediction techniques on checkpointing strategies. We extend the classical first-order analysis of Young and Daly in the presence of a fault prediction system, characterized by its recall and its precision. In this framework, we provide an optimal algorithm to decide when to take predictions into account, and we derive the optimal value of the checkpointing period. These results allow to analytically assess the key parameters that impact the performance of fault predictors at very large scale.Comment: Supported in part by ANR Rescue. Published in Journal of Parallel and Distributed Computing. arXiv admin note: text overlap with arXiv:1207.693

Boosting Additive Models using Component-wise P-Splines

We consider an efficient approximation of Bühlmann & Yu’s L2Boosting algorithm with component-wise smoothing splines. Smoothing spline base-learners are replaced by P-spline base-learners which yield similar prediction errors but are more advantageous from a computational point of view. In particular, we give a detailed analysis on the effect of various P-spline hyper-parameters on the boosting fit. In addition, we derive a new theoretical result on the relationship between the boosting stopping iteration and the step length factor used for shrinking the boosting estimates

Racing to hardware-validated simulation

Processor simulators rely on detailed timing models of the processor pipeline to evaluate performance. The diversity in real-world processor designs mandates building flexible simulators that expose parts of the underlying model to the user in the form of configurable parameters. Consequently, the accuracy of modeling a real processor relies on both the accuracy of the pipeline model itself, and the accuracy of adjusting the configuration parameters according to the modeled processor. Unfortunately, processor vendors publicly disclose only a subset of their design decisions, raising the probability of introducing specification inaccuracies when modeling these processors. Inaccurately tuning model parameters deviates the simulated processor from the actual one. In the worst case, using improper parameters may lead to imbalanced pipeline models compromising the simulation output. Therefore, simulation models should be hardware-validated before using them for performance evaluation. As processors increase in complexity and diversity, validating a simulator model against real hardware becomes increasingly more challenging and time-consuming. In this work, we propose a methodology for validating simulation models against real hardware. We create a framework that relies on micro-benchmarks to collect performance statistics on real hardware, and machine learning-based algorithms to fine-tune the unknown parameters based on the accumulated statistics. We overhaul the Sniper simulator to support the ARM AArch64 instruction-set architecture (ISA), and introduce two new timing models for ARM-based in-order and out-of-order cores. Using our proposed simulator validation framework, we tune the in-order and out-of-order models to match the performance of a real-world implementation of the Cortex-A53 and Cortex-A72 cores with an average error of 7% and 15%, respectively, across a set of SPEC CPU2017 benchmarks

A PAUC-based Estimation Technique for Disease Classification and Biomarker Selection.

The partial area under the receiver operating characteristic curve (PAUC) is a well-established performance measure to evaluate biomarker combinations for disease classification. Because the PAUC is defined as the area under the ROC curve within a restricted interval of false positive rates, it enables practitioners to quantify sensitivity rates within pre-specified specificity ranges. This issue is of considerable importance for the development of medical screening tests. Although many authors have highlighted the importance of PAUC, there exist only few methods that use the PAUC as an objective function for finding optimal combinations of biomarkers. In this paper, we introduce a boosting method for deriving marker combinations that is explicitly based on the PAUC criterion. The proposed method can be applied in high-dimensional settings where the number of biomarkers exceeds the number of observations. Additionally, the proposed method incorporates a recently proposed variable selection technique (stability selection) that results in sparse prediction rules incorporating only those biomarkers that make relevant contributions to predicting the outcome of interest. Using both simulated data and real data, we demonstrate that our method performs well with respect to both variable selection and prediction accuracy. Specifically, if the focus is on a limited range of specificity values, the new method results in better predictions than other established techniques for disease classification

Model-driven performance evaluation for service engineering

Service engineering and service-oriented architecture as an integration and platform technology is a recent approach to software systems integration. Software quality aspects such as performance are of central importance for the integration of heterogeneous, distributed service-based systems. Empirical performance evaluation is a process of measuring and calculating performance metrics of the implemented software. We present an approach for the empirical, model-based performance evaluation of services and service compositions in the context of model-driven service engineering. Temporal databases theory is utilised for the empirical performance evaluation of model-driven developed service systems

Bayesian Nonstationary Spatial Modeling for Very Large Datasets

With the proliferation of modern high-resolution measuring instruments mounted on satellites, planes, ground-based vehicles and monitoring stations, a need has arisen for statistical methods suitable for the analysis of large spatial datasets observed on large spatial domains. Statistical analyses of such datasets provide two main challenges: First, traditional spatial-statistical techniques are often unable to handle large numbers of observations in a computationally feasible way. Second, for large and heterogeneous spatial domains, it is often not appropriate to assume that a process of interest is stationary over the entire domain. We address the first challenge by using a model combining a low-rank component, which allows for flexible modeling of medium-to-long-range dependence via a set of spatial basis functions, with a tapered remainder component, which allows for modeling of local dependence using a compactly supported covariance function. Addressing the second challenge, we propose two extensions to this model that result in increased flexibility: First, the model is parameterized based on a nonstationary Matern covariance, where the parameters vary smoothly across space. Second, in our fully Bayesian model, all components and parameters are considered random, including the number, locations, and shapes of the basis functions used in the low-rank component. Using simulated data and a real-world dataset of high-resolution soil measurements, we show that both extensions can result in substantial improvements over the current state-of-the-art.Comment: 16 pages, 2 color figure