Subsampling Approach Research Articles

Estimation of the asymptotic variance of univariate and multivariate random fields and statistical inference

Correlated random fields are a common way to model dependence structures in high-dimensional data, especially for data collected in imaging. One important parameter characterizing the degree of dependence is the asymptotic variance which adds up all autocovariances in the temporal and spatial domain. Especially, it arises in the standardization of test statistics based on partial sums of random fields and thus the construction of tests requires its estimation. In this paper we propose consistent estimators for this parameter for strictly stationary $\varphi $-mixing random fields with arbitrary dimension of the domain and taking values in a Euclidean space of arbitrary dimension, thus allowing for multivariate random fields. We establish consistency, provide central limit theorems and show that distributional approximations of related test statistics based on sample autocovariances of random fields can be obtained by the subsampling approach. As in applications the spatial-temporal correlations are often quite local, such that a large number of autocovariances vanish or are negligible, we also investigate a thresholding approach where sample autocovariances of small magnitude are omitted. Extensive simulation studies show that the proposed estimators work well in practice and, when used to standardize image test statistics, can provide highly accurate image testing procedures. Having in mind automatized applications on a big data scale as arising in data science problems, these examinations also cover the proposed data-adaptive procedures to select method parameters.

Market Efficiency in Indian Exchange Rates: Adaptive Market Hypothesis

This paper utilizes the automatic variance ratio test and Belaire-Franch and Contreras (2004) rank-based tests to examine the adaptive market hypothesis in Indian exchange rates relative to US dollar (USD), Great British pound (GBP), Euro and Japanese yen (Yen). We use overlapping and non-overlapping moving subsample approach to examine the sensitivity of the results to a particular sample period. Our findings provide evidence in support of violation of the martingale hypothesis of Indian exchange rates relative to the US dollar and Japanese yen for whole sample period. Our findings also provide evidence that the predictability of returns of Indian exchange rates occurs from time to time and depends on occurrence of major macroeconomic events. These findings are consistent with the validity of adaptive market hypothesis in Indian exchange rates.

A novel case-control subsampling approach for rapid model exploration of large clustered binary data.

In many settings, an analysis goal is the identification of a factor, or set of factors associated with an event or outcome. Often, these associations are then used for inference and prediction. Unfortunately, in the big data era, the model building and exploration phases of analysis can be time-consuming, especially if constrained by computing power (ie, a typical corporate workstation). To speed up this model development, we propose a novel subsampling scheme to enable rapid model exploration of clustered binary data using flexible yet complex model set-ups (GLMMs with additive smoothing splines). By reframing the binary response prospective cohort study into a case-control-type design, and using our knowledge of sampling fractions, we show one can approximate the model estimates as would be calculated from a full cohort analysis. This idea is extended to derive cluster-specific sampling fractions and thereby incorporate cluster variation into an analysis. Importantly, we demonstrate that previously computationally prohibitive analyses can be conducted in a timely manner on a typical workstation. The approach is applied to analysing risk factors associated with adverse reactions relating to blood donation.

Quantifying the importance of geographic replication and representativeness when estimating demographic rates, using a coastal species as a case study

Demographic rates are rarely estimated over an entire species range, limiting empirical tests of ecological patterns and theories, and raising questions about the representativeness of studies that use data from a small part of a range. The uncertainty that results from using demographic rates from just a few sites is especially pervasive in population projections, which are critical for a wide range of questions in ecology and conservation. We developed a simple simulation to quantify how this lack of geographic representativeness can affect inferences about the global mean and variance of growth rates, which has implications for the robust design of a wide range of population studies. Using a coastal songbird, saltmarsh sparrow Ammodramus caudacutus, as a case study, we first estimated survival, fecundity, and population growth rates at 21 sites distributed across much of their breeding range. We then subsampled this large, representative dataset according to five sampling scenarios in order to simulate a variety of geographic biases in study design. We found spatial variation in demographic rates, but no large systematic patterns. Estimating the global mean and variance of growth rates using subsets of the data suggested that at least 10–15 sites were required for reasonably unbiased estimates, highlighting how relying on demographic data from just a few sites can lead to biased results when extrapolating across a species range. Sampling at the full 21 sites, however, offered diminishing returns, raising the possibility that for some species accepting some geographical bias in sampling can still allow for robust range‐wide inferences. The subsampling approach presented here, while conceptually simple, could be used with both new and existing data to encourage efficiency in the design of long‐term or large‐scale ecological studies.

Blackbox modeling of central heating and cooling plant equipment performance

The current article presents an analysis conducted upon the sensor data gathered from the distribution control system of a central heating and cooling plant in Ottawa, Canada. After observing that the performance of four boilers and five chillers of this plant vary substantially in time under steady-state conditions, data-driven models were developed to explain this variability from the archived sensor data. By employing a forward stepwise regression and a repeated random sub-sampling cross-validation approach, two-layer feed-forward artificial neural network models with 7 to 15 hidden-nodes were selected for each boiler and chiller. The selected boiler models could explain 84% to 95% of the variability in a boiler's efficiency, and the selected chiller models could explain 65% to 94% of the variability in a chiller's coefficient of performance. Among studied nine variables, the most informative ones to predict a boiler's efficiency were identified as follows: flue gas O2 concentration, pressure, part-load ratio, forced draft fan state, and return water flow rate. Unlike boilers, all four studied variables were found useful in predicting a chiller's coefficient of performance. These four variables were the return water flow rate, part-load ratio, outdoor temperature, and return water temperature. A residual analysis was conducted to verify the appropriateness of the selected models to the datasets. In addition, potential use cases for the selected models were discussed with illustrative examples.

Comparison of Machine Learning Approaches Toward Assessing the Risk of Developing Cardiovascular Disease as a Long-Term Diabetes Complication.

The estimation of long-term diabetes complications risk is essential in the process of medical decision making. Guidelines for the management of Type 2 Diabetes Mellitus (T2DM) advocate calculating the Cardiovascular Disease (CVD) risk to initiate appropriate treatment. The objective of this study is to investigate the use of sophisticated machine learning techniques toward the development of personalized models able to predict the risk of fatal or nonfatal CVD incidence in T2DM patients. The important challenge of handling the unbalanced nature of the available dataset is addressed by applying novel ensemble strategies. Hybrid Wavelet Neural Networks (HWNNs) and Self-Organizing Maps (SOMs) constitute the primary models for building ensembles following a subsampling approach. Different methods for combining the decisions of the primary models are applied and comparatively assessed. Data from the 5-year follow up of 560 patients with T2DM are used for development and evaluation purposes. The highest discrimination performance (Area Under the Curve (AUC): 71.48%) is achieved by taking into account both the HWNN- and SOM- based primary models' outputs. The proposed method is superior to the Binomial Linear Regression (BLR) model justifying the need to apply more sophisticated techniques in order to produce reliable CVD risk scores.

Nyström type subsampling analyzed as a regularized projection

In the statistical learning theory the Nyström type subsampling methods are considered as tools for dealing with big data. In this paper we consider Nyström subsampling as a special form of the projected Lavrentiev regularization, and study it using the approaches developed in the regularization theory. As a result, we prove that the same capacity independent learning rates that are guaranteed for standard algorithms running with quadratic computational complexity can be obtained with subquadratic complexity by the Nyström subsampling approach, provided that the subsampling size is chosen properly. We propose a priori rule for choosing the subsampling size and a posteriori strategy for dealing with uncertainty in the choice of it. The theoretical results are illustrated by numerical experiments.

Subsampling for nonstationary time series with non-zero mean function

In this paper a subsampling approach for nonstationary time series with a non-zero mean function is proposed. It is applied for periodically and almost periodically processes. Two statistical tests are constructed. An example with real data is presented.

The Repertoire Dissimilarity Index as a method to compare lymphocyte receptor repertoires

BackgroundThe B and T cells of the human adaptive immune system leverage a highly diverse repertoire of antigen-specific receptors to protect the human body from pathogens. The sequencing and analysis of immune repertoires is emerging as an important tool to understand immune responses, whether beneficial or harmful (in the case of autoimmunity). However, methods for studying these repertoires, and for directly comparing different immune repertoires, are lacking.ResultsIn this paper, we present a non-parametric method for directly comparing sequencing repertoires, with the goal of rigorously quantifying differences in V, D, and J gene segment utilization. This method, referred to as the Repertoire Dissimilarity Index (RDI), uses a bootstrapped subsampling approach to account for variance in sequencing depth, and, coupled with a data simulation approach, allows for direct quantification of the average variation between repertoires. We use the RDI method to recapitulate known differences in the formation of the CD4+ and CD8+ T cell repertoires, and further show that antigen-driven activation of naïve CD8+ T cells is more selective than in the CD4+ repertoire, resulting in a more specialized CD8+ memory repertoire.ConclusionsWe prove that the RDI method is an accurate and versatile method for comparisons of immune repertoires. The RDI method has been implemented as an R package, and is available for download through Bitbucket.

Inference from high-frequency data: A subsampling approach

In this paper, we show how to estimate the asymptotic (conditional) covariance matrix, which appears in central limit theorems in high-frequency estimation of asset return volatility. We provide a recipe for the estimation of this matrix by subsampling; an approach that computes rescaled copies of the original statistic based on local stretches of high-frequency data, and then it studies the sampling variation of these. We show that our estimator is consistent both in frictionless markets and models with additive microstructure noise. We derive a rate of convergence for it and are also able to determine an optimal rate for its tuning parameters (e.g., the number of subsamples). Subsampling does not require an extra set of estimators to do inference, which renders it trivial to implement. As a variance–covariance matrix estimator, it has the attractive feature that it is positive semi-definite by construction. Moreover, the subsampler is to some extent automatic, as it does not exploit explicit knowledge about the structure of the asymptotic covariance. It therefore tends to adapt to the problem at hand and be robust against misspecification of the noise process. As such, this paper facilitates assessment of the sampling errors inherent in high-frequency estimation of volatility. We highlight the finite sample properties of the subsampler in a Monte Carlo study, while some initial empirical work demonstrates its use to draw feasible inference about volatility in financial markets.

DIFFERENT WAYS TO CUT A CAKE: COMPARING EXPERT-BASED AND STATISTICAL TYPOLOGIES TO TARGET SUSTAINABLE INTENSIFICATION TECHNOLOGIES, A CASE-STUDY IN SOUTHERN ETHIOPIA

SUMMARYUnderstanding farm diversity is essential to delineate recommendation domains for new technologies, but diversity is a subjective concept, and can be described differently depending on the way it is perceived. Historically, new technologies have been targeted primarily based on agro-ecological conditions, largely ignoring socioeconomic conditions. Based on 273 farm households' surveys in Ethiopia, we compare two approaches for the delineation of farm type recommendation domains for crop and livestock technologies: one based on expert knowledge and one based on statistical methods. The expert-based typology used a simple discriminant key for stakeholders in the field to define four farm types based on Tropical Livestock Unit, total cultivated surface and the ratio of these two indicators. This simple key took only a few minutes to make inferences about the potential of adoption of crop and livestock technologies. The PCA-HC analysis included a greater number of variables describing the farm (land use, household size, cattle, fertilizer, off-farm work, hiring labour, production). This analysis emphasized the multi-dimensional potential of such a statistical approach and, in principle, its usefulness to grasp the full complexity of farming systems to identify their needs in crop and livestock technologies. A sub-sampling approach was used to test the impact of data selection on the diversity represented in the statistical approach. Our results show that diversity structure is significantly impacted according to the choice of a sub-sample of 15 of the 20 variables available. This paper shows the complementarity of the two approaches and demonstrates the influence of data selection within large baseline data sets on the total diversity represented in the clusters identified.

Sea level regulated tetrapod diversity dynamics through the Jurassic/Cretaceous interval.

Reconstructing deep time trends in biodiversity remains a central goal for palaeobiologists, but our understanding of the magnitude and tempo of extinctions and radiations is confounded by uneven sampling of the fossil record. In particular, the Jurassic/Cretaceous (J/K) boundary, 145 million years ago, remains poorly understood, despite an apparent minor extinction and the radiation of numerous important clades. Here we apply a rigorous subsampling approach to a comprehensive tetrapod fossil occurrence data set to assess the group's macroevolutionary dynamics through the J/K transition. Although much of the signal is exclusively European, almost every higher tetrapod group was affected by a substantial decline across the boundary, culminating in the extinction of several important clades and the ecological release and radiation of numerous modern tetrapod groups. Variation in eustatic sea level was the primary driver of these patterns, controlling biodiversity through availability of shallow marine environments and via allopatric speciation on land.

Measurement Validation for the Extension of Emission Measurements in Alternative Test Sites Above 1 GHz

Measurement procedures for determining the radiated disturbances from electronic equipment are described in several IEC/CISPR standards and are well probed for frequencies up to 1 GHz. Above that frequency, radiation pattern of EUTs evolve complex forms so that the direction and magnitude of the maximum directivity is not known by design. Hence, standardized sampling approaches might underestimate the “true” maximum of the radiated emission. In this paper, an extension of these measurement procedures is proposed. The method uses a stochastic approach for estimating the maximum directivity based on the electrical size of the EUT. This is combined with a total radiated power measurement for a reduced sampling procedure to predict the maximum free-space, far-zone electric field. For validation purposes, an extensive 3-D scan of the radiation pattern of a generic EUT is performed. Different subsampling approaches are then investigated while the new prediction method is applied. It can be shown that the accuracy of the measurement procedures can be increased due to the proposed method.

Ensemble approach for improving prediction in kernel regression and classification

Ensemble methods often help increase prediction ability in various predictive models by combining multiple weak learners and reducing the variability of the final predictive model. In this work, we demonstrate that ensemble methods also enhance the accuracy of prediction under kernel ridge regression and kernel logistic regression classification. Here we apply bagging and random forests to two kernel-based predictive models; and present the procedure of how bagging and random forests can be embedded in kernel-based predictive models. Our proposals are tested under numerous synthetic and real datasets; subsequently, they are compared with plain kernel-based predictive models and their subsampling approach. Numerical studies demonstrate that ensemble approach outperforms plain kernel-based predictive models.

Testing for Granger-causality in quantiles

ABSTRACTThis paper proposes a consistent parametric test of Granger-causality in quantiles. Although the concept of Granger-causality is defined in terms of the conditional distribution, most articles have tested Granger-causality using conditional mean regression models in which the causal relations are linear. Rather than focusing on a single part of the conditional distribution, we develop a test that evaluates nonlinear causalities and possible causal relations in all conditional quantiles, which provides a sufficient condition for Granger-causality when all quantiles are considered. The proposed test statistic has correct asymptotic size, is consistent against fixed alternatives, and has power against Pitman deviations from the null hypothesis. As the proposed test statistic is asymptotically nonpivotal, we tabulate critical values via a subsampling approach. We present Monte Carlo evidence and an application considering the causal relation between the gold price, the USD/GBP exchange rate, and the oil price.

A Sub-Sampling Approach for Data Acquisition in Gamma Ray Emission Tomography

State of the art data acquisition systems for small animal imaging gamma ray detectors often rely on free running Analog to Digital Converters (ADCs) and high density Field Programmable Gate Arrays (FPGA) devices for digital signal processing. In this work, a sub-sampling acquisition approach, which exploits a priori information regarding the shape of the obtained detector pulses is proposed. Output pulses shape depends on the response of the scintillation crystal, photodetector’s properties and amplifier/shaper operation. Using these known characteristics of the detector pulses prior to digitization, one can model the voltage pulse derived from the shaper (a low-pass filter, last in the front-end electronics chain), in order to reduce the desirable sampling rate of ADCs. Fitting with a small number of measurements, pulse shape estimation is then feasible. In particular, the proposed sub-sampling acquisition approach relies on a bi-exponential modeling of the pulse shape. We show that the properties of the pulse that are relevant for Single Photon Emission Computed Tomography (SPECT) event detection (i.e., position and energy) can be calculated by collecting just a small fraction of the number of samples usually collected in data acquisition systems used so far. Compared to the standard digitization process, the proposed sub-sampling approach allows the use of free running ADCs with sampling rate reduced by a factor of 5. Two small detectors consisting of Cerium doped Gadolinium Aluminum Gallium Garnet (Gd3Al2Ga3O12 : Ce or GAGG:Ce) pixelated arrays (array elements: $2\times 2\times 5~\mathrm {mm}^{3}$ and $1\times 1\times 10~\mathrm {mm}^{3}$ respectively) coupled to a Position Sensitive Photomultiplier Tube (PSPMT) were used for experimental evaluation. The two detectors were used to obtain raw images and energy histograms under 140 keV and 661.7 keV irradiation respectively. The sub-sampling acquisition technique (10 MHz sampling rate) was compared with a standard acquisition method (52 MHz sampling rate), in terms of energy resolution and image signal to noise ratio for both gamma ray energies. The Levenberg-Marquardt (LM) non-linear least-squares algorithm was used, in post processing, in order to fit the acquired data with the proposed model. The results showed that analog pulses prior to digitization are being estimated with high accuracy after fitting with the bi-exponential model.

Sub-Sampling in OFDM with Constant Time Signal Recovery

Abstract The sub-sampling method for Orthogonal Frequency Division Multiplexing proposed recently, has been extended in this paper allowing the Analog-to-Digital Converter on the receiver side to operate in low power mode, up to 3/4 of the time. The predictability of the parity patterns generated by the Forward Error Correction encoder of the transmitter, when sparse data are exchanged, is exploited in order to define appropriate Inverse Fast Fourier Transform input symbol arrangements. These symbol arrangements allow the substitution of a number of samples by others that have already been received. Moreover, several operations of the Fast Fourier Transform can be omitted because their result is zero when identical values appear at its input. The advantages of the proposed method are: low power, higher speed and fewer memory resources. Despite other iterative sub-sampling approaches like Compressive Sampling, the proposed method is not iterative and thus it can be implemented with very low complexity hardware. The simulation results show that full input signal recovery or at least a very low Bit Error Rate is achieved in most of the cases that have been tested.

Environmental drivers of crocodyliform extinction across the Jurassic/Cretaceous transition

Crocodyliforms have a much richer evolutionary history than represented by their extant descendants, including several independent marine and terrestrial radiations during the Mesozoic. However, heterogeneous sampling of their fossil record has obscured their macroevolutionary dynamics, and obfuscated attempts to reconcile external drivers of these patterns. Here, we present a comprehensive analysis of crocodyliform biodiversity through the Jurassic/Cretaceous (J/K) transition using subsampling and phylogenetic approaches and apply maximum-likelihood methods to fit models of extrinsic variables to assess what mediated these patterns. A combination of fluctuations in sea-level and episodic perturbations to the carbon and sulfur cycles was primarily responsible for both a marine and non-marine crocodyliform biodiversity decline through the J/K boundary, primarily documented in Europe. This was tracked by high extinction rates at the boundary and suppressed origination rates throughout the Early Cretaceous. The diversification of Eusuchia and Notosuchia likely emanated from the easing of ecological pressure resulting from the biodiversity decline, which also culminated in the extinction of the marine thalattosuchians in the late Early Cretaceous. Through application of rigorous techniques for estimating biodiversity, our results demonstrate that it is possible to tease apart the complex array of controls on diversification patterns in major archosaur clades.

The Selection of Quantification Pipelines for Illumina RNA-seq Data Using a Subsampling Approach.

RNA sequencing, or (RNA-seq for short,, is a widely applied technology that for extractings gene and transcript expression from biological samples. Given numerous quantification pipelines for RNA-seq data, one fundamental challenge is to determine identify a pipeline that can produce the most accurate estimate the most accurate gene and/or transcript expression. Exploring all available pipelines requires tremendous extensive computational resources, so. Therefore, we propose to use a subsampling approach that can improve speed up the pipeline evaluation and selection the efficiency process of pipeline performance evaluation for a given RNA-seq dataset. We applied our approach to one simulated and two real RNA-seq datasets and found that expression estimates derived from subsampled data are close surrogates for those derived from original data. In addition, the ranking of quantification pipelines based on the subsampled data was highly correlated concordant with that based on the original data. Therefore, we conclude that subsampling is a valid approach to facilitating efficient quantification pipeline selection using RNA-seq data.

Heterogeneous Ensemble Combination Search Using Genetic Algorithm for Class Imbalanced Data Classification.

Classification of datasets with imbalanced sample distributions has always been a challenge. In general, a popular approach for enhancing classification performance is the construction of an ensemble of classifiers. However, the performance of an ensemble is dependent on the choice of constituent base classifiers. Therefore, we propose a genetic algorithm-based search method for finding the optimum combination from a pool of base classifiers to form a heterogeneous ensemble. The algorithm, called GA-EoC, utilises 10 fold-cross validation on training data for evaluating the quality of each candidate ensembles. In order to combine the base classifiers decision into ensemble’s output, we used the simple and widely used majority voting approach. The proposed algorithm, along with the random sub-sampling approach to balance the class distribution, has been used for classifying class-imbalanced datasets. Additionally, if a feature set was not available, we used the (α, β) − k Feature Set method to select a better subset of features for classification. We have tested GA-EoC with three benchmarking datasets from the UCI-Machine Learning repository, one Alzheimer’s disease dataset and a subset of the PubFig database of Columbia University. In general, the performance of the proposed method on the chosen datasets is robust and better than that of the constituent base classifiers and many other well-known ensembles. Based on our empirical study we claim that a genetic algorithm is a superior and reliable approach to heterogeneous ensemble construction and we expect that the proposed GA-EoC would perform consistently in other cases.