Simple Averaging Research Articles

Improved Information-Theoretic Generalization Bounds for Distributed, Federated, and Iterative Learning.

We consider information-theoretic bounds on the expected generalization error for statistical learning problems in a network setting. In this setting, there are K nodes, each with its own independent dataset, and the models from the K nodes have to be aggregated into a final centralized model. We consider both simple averaging of the models as well as more complicated multi-round algorithms. We give upper bounds on the expected generalization error for a variety of problems, such as those with Bregman divergence or Lipschitz continuous losses, that demonstrate an improved dependence of on the number of nodes. These “per node” bounds are in terms of the mutual information between the training dataset and the trained weights at each node and are therefore useful in describing the generalization properties inherent to having communication or privacy constraints at each node.

Respiratory Rate Estimation Combining Autocorrelation Function-Based Power Spectral Feature Extraction with Gradient Boosting Algorithm

Various machine learning models have been used in the biomedical engineering field, but only a small number of studies have been conducted on respiratory rate estimation. Unlike ensemble models using simple averages of basic learners such as bagging, random forest, and boosting, the gradient boosting algorithm is based on effective iteration strategies. This gradient boosting algorithm is just beginning to be used for respiratory rate estimation. Based on this, we propose a novel methodology combining an autocorrelation function-based power spectral feature extraction process with the gradient boosting algorithm to estimate respiratory rate since we acquire the respiration frequency using the autocorrelation function-based power spectral feature extraction that finds the time domain’s periodicity. The proposed methodology solves overfitting for the training datasets because we obtain the data dimension by applying autocorrelation function-based power spectral feature extraction and then split the long-resampled wave signal to increase the number of input data samples. The proposed model provides accurate respiratory rate estimates and offers a solution for reliably managing the estimation uncertainty. In addition, the proposed method presents a more precise estimate than conventional respiratory rate measurement techniques.

Multi-model ensemble approaches for simulation of evapotranspiration of karst agroforestry ecosystems

Water shortages frequently occur in karst areas, and there is an urgent need to quantify water fluxes to provide information for sustainable management of water resources. Thus, a variety of models have been developed to simulate the water balance process, including actual evapotranspiration (ETc), which is a key variable for linking water and energy cycles. However, high heterogeneity of the land surface makes it hard to get precise complete set of parameters for single model, and a single model often has uncertainties in simulating evapotranspiration in karst regions. Therefore, this study integrated three well-known individual models (Penman-Monteith, PM; Priestley and Taylor, PT; and Shuttleworth-Wallace, SW) with two multi-model ensemble approaches (Bayesian model averaging, BMA; and simple model average, SA) to enhance ETc modeling in a subtropical humid karst catchment. Results show that: 1) The individual models show different strengths for different ecosystems, which could be attributed to differences in the underlying landscape surface characteristics; 2) individual models exhibited seasonal uncertainties. For example, simulated ETc (ETs) by the PM and PT model was lower than ETo (observed ETc) during November-March but higher than during April-October for forest-grass mixed and grass ecosystems; 3) Two multi-model ensemble approaches (R2 ≥ 0.85) performed better than any individual model (R2 ≤ 0.85) most likely because multi-model ensemble approaches reduce model uncertainties by weakening the bias of individual models.

Extracting the collective wisdom in probabilistic judgments

How should we combine disagreeing expert judgments on the likelihood of an event? A common solution is simple averaging, which allows independent individual errors to cancel out. However, judgments can be correlated due to an overlap in their information, resulting in a miscalibration in the simple average. Optimal weights for weighted averaging are typically unknown and require past data to estimate reliably. This paper proposes an algorithm to aggregate probabilistic judgments under shared information. Experts are asked to report a prediction and a meta-prediction. The latter is an estimate of the average of other individuals’ predictions. In a Bayesian setup, I show that if average prediction is a consistent estimator, the percentage of predictions and meta-predictions that exceed the average prediction should be the same. An “overshoot surprise” occurs when the two measures differ. The Surprising Overshoot algorithm uses the information revealed in an overshoot surprise to correct for miscalibration in the average prediction. Experimental evidence suggests that the algorithm performs well in moderate to large samples and in aggregation problems where individuals disagree in their predictions.

Single or Combine? Tourism Demand Volatility Forecasting with Exponential Weighting and Smooth Transition Combining Methods

Tourism forecasting has garnered considerable interest. However, integrating tourism forecasting with volatility is significantly less typical. This study investigates the performance of both the single models and their combinations for forecasting the volatility of tourism demand. The seasonal autoregressive integrated moving average (SARIMA) model is used to construct the mean equation, and three single models, namely the generalized autoregressive conditional heteroscedasticity (GARCH) family models, the error-trend-seasonal exponential smoothing (ETS-ES) model, and the innovative smooth transition exponential smoothing (STES) model, are employed to estimate the volatility of monthly tourist arrivals into Malaysia. This study also assesses the accuracy of forecasts using simple average (SA), minimum variance (MV), and novel smooth transition (ST). STES performs the best of the single models for forecasting the out-of-sample of tourism demand volatility, followed closely by ETS-ES. In contrast, the ST combining method surpasses SA and MV. Interestingly, forecast combining methods do not always outperform the best single model, but they consistently outperform the worst single model. The MCS and DM tests confirm the aforementioned findings. This article merits consideration for future forecasting research on tourism demand volatility.

Forecast combination-based forecast reconciliation: Insights and extensions

In this paper, we build upon a recently proposed forecast combination-based approach to the reconciliation of a simple hierarchy (Hollyman R., Petropoulos F., Tipping M.E., Understanding forecast reconciliation, European Journal of Operational Research, 2021, 294, 149–160) and extend it in some new directions. In particular, we provide insights into the nature and mathematical derivation of the level-l conditional coherent (LlCC) point forecast reconciliation procedure for an elementary two-level hierarchy. We show that: (i) the LlCC procedure is the result of a linearly constrained minimization of a quadratic loss function, with an exogenous constraint given by the base forecast of the top level series of the hierarchy, which is not revised; and (ii) endogenous constraints may also be considered in the same framework, thereby resulting in level conditional reconciled forecasts where both the top and the bottom level time series forecasts are coherently revised. In addition, we show that the LlCC procedure (i.e., with exogenous constraints but the result also holds in the endogenous case) does not guarantee the non-negativity of the reconciled forecasts, which can be an issue in cases when non-negativity is a natural attribute of the variables that need to be forecast (e.g., sales and tourism flows). Finally, we consider two forecasting experiments to evaluate the performance of various cross-sectional forecast combination-based point forecast reconciliation procedures (vis-à-vis the state-of-the-art procedures) in a fair setting. In this framework, due to the crucial role played by the (possibly different) models used to compute the base forecasts, we re-interpret the combined conditional coherent reconciliation procedure (CCCH) of Hollyman et al. (2021) as a forecast pooling approach, and show that accuracy improvements may be obtained by adopting a simple forecast averaging strategy.

A Model Stacking Approach for Forecasting Mortality

This article adopts a machine learning method called stacked generalization for forecasting mortality. The main idea is to combine the forecasts from different projection models or algorithms in a certain way in order to increase the prediction accuracy. In particular, the article considers not just the traditionally used mortality projection models, such as the Lee–Carter and CBD models and their extensions, but also some learning algorithms called feedforward and recurrent neural networks that are starting to gain attention in the actuarial literature. For blending the different forecasts, the article examines a number of choices, including simple averaging, weighted averaging, linear regression, and neural network. Using U.S. mortality data, it is found that the proposed stacking approach often outperforms the cases where a projection model or algorithm is applied individually, and that neural networks tend to generate better results than many of the traditional models.

An integrated batting performance analytics model for women’s cricket using Principal Component Analysis and Gini scores

Over the years, women cricketers have garnered little media or societal attention. There has been much research on men’s cricket but relatively little on women’s cricket. This study aims to quantify women’s batting performances in one-day international (ODI) matches. The average batting score has traditionally been used in cricket to determine a batter’s worth. However, ranking by simple average ignores two important factors in ODI matches: consistency and strike rates. To address these issues, we propose a novel methodology for calculating ranks that incorporates Gini-based average scores rather than simple averages and considers batting strike rates in a Principal Component Analysis (PCA) framework. As a result, PCA combined with Gini scores can assist cricket fans, coaches, and managers in better understanding a player’s performance.

HSI model for early life stages of anchovy considering transport processes in Laizhou Bay

Marine fishes are sensitive to the environment during their early life stages. This study adopts a habitat suitability index (HSI) model to evaluate the environmental suitability for early stages of anchovy (Engraulis japonicus) in Laizhou Bay. Instead of calculating the suitability of spawning grounds and nursery grounds independently or the simple average of the two, an individual-based model is used to simulate the drifting trajectories of anchovy eggs to establish the link between a spawning ground and its corresponding nursery ground. The HSI of early life habitat is determined by averaging the HSI value of the paired two grounds. The model results suggest that a small patch at eastern Laizhou Bay (near 120.1 E°, 37.6 N°) is the most critical and suitable area for anchovy in early life stages. It can provide an appropriate habitat for anchovy eggs and allow the eggs to migrate to the inside of the bay with plenty of plankton, which would benefit the newly hatching larvae. The results indicate the significant impact of hydrodynamic transport on fishery recruitment process, which should not be neglected in habitat quality evaluation. The model adopted in this study is applied to anchovy as a case study, but it is also exportable to other species of commercial interest.

Modeling the organic matter of water using the decision tree coupled with bootstrap aggregated and least-squares boosting

The purpose of the work is to investigate the use of decision tree (DT) enhanced by bootstrap aggregates (Bag) and least-squares boosting (Lsboost) in modeling the organic matter of water according to its physicochemical parameters. An entire database of 500 samples of 21 physicochemical parameters, including organic matter, was used to build the DT, DT_Bag, and DT_Lsboost models. Training data (364 data points) is resampled using a bootstrap technique to form different training datasets to train different models. The models built were validated by a dataset of 91 samples. The predicted outputs obtained from the developed DT models are then combined by simple averaging. On the other hand, the data was also boosted with the Lsboost technical aid to increase the strength of a weak learning algorithm. The model trains the first weak learner with equal weight across all data points in the training set, then trains all other weak learners based on the updated weight aimed at the validation result to minimize the squared error medium. Good agreement between the predicted and experimental organic matter concentrations for the DT_Lsboost model was obtained (the correlation coefficient for the validation dataset was 0.9992), followed by the DT-Bag model with a correlation coefficient of 0.9949. The comparison between DT, DT_Bag, and DT_Lsboost revealed the superiority of the DT_Lsboost model (the mean root of the squared errors for the dataset were 0.1295 for the DT_Lsboost, 0.1664 for the DT_Bag, and 0.5444 for the DT). These results show that Lsboost technology dramatically improved the DT model. This result is also confirmed by the results of tests on models (interpolation data of 45 points). It should also be noted that the Bag technique was also very effective in optimizing the DT model, as the results obtained with this technique were very close to the DT_Lsboost model. • The concentration of organic matter in the water was predicted using various models. • The decision tree (DT) model was coupled by bootstrap aggregates (Bag) and least-squares boosting (Lsboost) techniques. • Significant Physico-chemical parameters on the organic matter were identified using the decision tree (DT) and the ensemble trees model (DT_Bag and DT_Lsboost). • The decision of tree (DT) and the ensemble trees model made it possible to highlight the significant interactions. • Bootstrap aggregates (Bag) and least-squares boosting (Lsboost) techniques have improved and developed the decision tree model.

Evaluating Bias-Correction Methods for Seasonal Dynamical Precipitation Forecasts

Abstract Seasonal forecasting of climatological variables is important for water and climatic-related decision-making. Dynamical models provide seasonal forecasts up to one year in advance, but direct outputs from these models need to be bias-corrected prior to application by end users. Here, five bias-correction methods are applied to precipitation hindcasts from ECMWF’s fifth generation seasonal forecast system (SEAS5). We apply each method in two distinct ways; first to the ensemble mean and second to individual ensemble members, before deriving an ensemble mean. The performance of bias-correction methods in both schemes is assessed relative to the simple average of raw ensemble members as a benchmark. Results show that in general, bias correction of individual ensemble members before deriving an ensemble mean (scheme 2) is most skillful for more frequent precipitation values while bias correction of the ensemble mean (scheme 1) performed better for extreme high and low precipitation values. Irrespective of application scheme, all bias-correction methods improved precipitation hindcasts compared to the benchmark method for lead times up to 6 months, with the best performance obtained at one month lead time in winter.

From Many to One: Consensus Inference in a MIP

AbstractA Model Intercomparison Project (MIP) consists of teams who estimate the same underlying quantity (e.g., temperature projections to the year 2070). A simple average of the ensemble of the teams' outputs gives a consensus estimate, but it does not recognize that some outputs are more variable than others. Statistical analysis of variance (ANOVA) models offer a way to obtain a weighted frequentist consensus estimate of outputs with a variance that is the smallest possible. Modulo dependence between MIP outputs, the ANOVA approach weights a team's output inversely proportional to its variance, from which optimally weighted estimates follow. ANOVA weights can also provide a prior distribution for Bayesian Model Averaging of the MIP outputs when external evaluation data are available. We use a MIP of carbon‐dioxide‐flux inversions to illustrate the ANOVA‐based weighting and subsequent frequentist consensus inferences.

Author Response: Effect of Levetiracetam Use Duration on Overall Survival of Isocitrate Dehydrogenase Wild-Type Glioblastoma in Adults: An Observational Study.

Average leverage is often used as a measure of risk. However, average leverage in a limited liability context should not be computed as a simple arithmetic average of the underlying constituents. In fact, using a simple arithmetic average can give misleading results. For example, the simple arithmetic average leverage may give results which run counter to the actual risk exposure for certain portfolios. This article introduces a new measure, Limited Liability Leverage (<i>L</i>³), which corrects the simple average for the limited liability framework. This new measure is discussed in the context of a portfolio of hedge funds and compared to a multi-strategy hedge fund structure, where trading units do not have limited liability. This perspective can also be extended to reflect the lower risk of a financial system with many small institutions relative to a system with large, “too-big-to-fail” institutions. <b>TOPICS:</b>Real assets/alternative investments/private equity, legal/regulatory/public policy, risk management, portfolio construction

Multi-Expert Deep Networks for Multi-Disease Detection in Retinal Fundus Images.

Automatic diagnosis of eye diseases from retinal fundus images is quite challenging. Common public datasets include images of subjects with multiple diseases with uneven distribution of labels. Rare diseases are especially challenging due to their under-representation in such datasets. In this paper, we propose a training pipeline for the multi-labeled classification with uneven distribution of the sample size and sample difficulty. First, we guide the training of the initial model by weighing the training loss using an inverse-frequency for each class. This will balance the training on over-represented and under-represented samples. We then adjust the class weights using the aggregated loss for each class, and train for more iterations. In this way, the model at each iteration will focus more on difficult samples and cover the shortcomings of the previous model. Finally, we ensemble together all the models using out proposed Heuristic Stacking algorithm for improving multi-label predictions beyond simple averaging. Our experimental results on the Retinal Image Analysis for Multi-Disease Detection(RIADD)-2021 challenge dataset show that the proposed approach achieves a 88.24 % accuracy score, which is competitive with the top three ranked methods of the competition. Furthermore, we perform ablation study to stress-test our Heuristic Stacking ensemble methods versus classical methods such as bagging n multi-label classification problems.

The false aperture problem: Global motion perception without integration of local motion signals.

Early direction-selective neurons in the primary visual cortex are widely considered to be the main neural basis underlying motion perception even though motion perception can also rely on attentively tracking the position of objects. Because of their small receptive fields, early direction-selective neurons suffer from the aperture problem, which is assumed to be overcome by integrating inputs from many early direction-selective neurons. Because the perceived motion of objects sometimes depends on static form information and does not always match the mean direction of local motion signals, the general consensus is that motion integration is form dependent and complex. Based on the fact that early direction-selective neurons respond to motion only within a short temporal window, the present study used stroboscopic motion to test their contribution to motion perception of objects. For conditions under which the perceived motion was impaired by stroboscopic motion, the perceived motion matched the mean direction of local motion signals and was form independent. For classic conditions under which the perceived motion could not be explained by a simple form independent averaging of local motion signals, neutralizing the contribution of early direction-selective neurons using stroboscopic motion had little impact on the perceived motion, which demonstrates that the perceived motion relied on position tracking, not on early direction-selective neurons. When the perceived motion relies on position tracking, assuming that motion perception relies on early direction-selective neurons can lead to erroneously postulate the existence of complex or form-dependent integration of inputs from early direction-selective neurons. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

A systematic review of single-case experimental design meta-analyses: characteristics of study designs, data, and analyses

Given the increasing interest in meta-analyses of Single-Case Experimental Design (SCED) studies mainly in the fields of behavioral, communication disorders, educational, and rehabilitation research, the aim of the present review is to determine the general characteristics of these meta-analyses, namely design characteristics, the kind of data provided in the primary studies and the ones included in meta-analyses, and the type of analyses that were conducted. In this review, 178 meta-analyses were examined for these characteristics. The results indicate that the number of SCED meta-analyses has increased remarkably in recent years. The most frequently used effect size metric was the percentage of non-overlapping data (PND) and the most commonly utilized analysis for synthesizing the results of primary SCEDs was a simple average of effect sizes. The current study provides insights in the characteristics of primary SCED studies and SCED meta-analyses, and therefore can help in further developing methodological techniques and in evaluating whether the currently used techniques are in line with the methodological advancements.

Proximal and remote sensor data fusion for 3D imaging of infertile and acidic soil

Soil cation exchange capacity (CEC) and pH affect the condition of soil. To improve soil capability in sugarcane growing areas, Sugar Research Australia introduced the Six-Easy-Steps Nutrient Guidelines based on CEC and pH of topsoil (0–0.3 m). A three-dimensional digital soil mapping (DSM) framework has been used to predict CEC and pH by fitting equal-area splines to four depth intervals (i.e., topsoil, subsurface [0.3–0.6 m], shallow [0.6–0.9 m], and deep subsoil [0.9–1.2 m]) to resample soil data at 0.01 m increments. A single quantile regression forest (QRF) was calibrated to model the relationship between spline-fitted soil data and individual digital data. These included proximal soil sensing (PSS) data such as electromagnetic (EM) induction and gamma-ray (γ-ray) spectrometry, remote sensing (RS) Sentinel-2 imagery, a light detection and ranging (LiDAR) based digital elevation model (DEM), and soil depth. Various data fusion methods and minimum calibration size have been evaluated, including concatenation and model averaging approaches, namely, simple averaging (SA), Bates-Granger averaging (BGA), Granger-Ramanathan averaging (GRA), and bias-corrected eigenvector averaging (BC-EA). In all cases, an independent validation was used to assess prediction agreement (Lin's concordance correlation coefficient—LCCC) and accuracy (ratio of performance to deviation—RPD). For CEC, γ-ray (LCCC = 0.82) was the best, with EM (0.78) and Sentinel-2 (0.77) producing similar agreement, whereas DEM (0.64) had worst performance. For pH, EM, γ-ray, and Sentinel-2 were similar (0.69, 0.73, and 0.77, respectively), and DEM poor (0.48). Optimum results were achieved when PSS, Sentinel-2, and DEM were fused using GRA; CEC agreement (0.88) and accuracy (RPD = 2.14) were strong, while for pH, concatenation had good agreement (0.79) and accuracy (1.59). Neither agreement nor accuracy varied among sample size, with a minimum of 30 (CEC) and 80 (pH) sites necessary (0.4 and 1.1 sampling sites ha−1, respectively). The final DSM for topsoil CEC and pH, were useful for lime application; the northern fields required 2.5 t ha−1 of lime, whereas the southern fields required variable rates (4 and 5 t ha−1).

Simulation study on 3D convolutional neural networks for time-of-flight prediction in monolithic PET detectors using digitized waveforms

Objective. We investigate the use of 3D convolutional neural networks for gamma arrival time estimation in monolithic scintillation detectors. Approach. The required data is obtained by Monte Carlo simulation in GATE v8.2, based on a 50 × 50 × 16 mm3 monolithic LYSO crystal coupled to an 8 × 8 readout array of silicon photomultipliers (SiPMs). The electronic signals are simulated as a sum of bi-exponentional functions centered around the scintillation photon detection times. We include various effects of statistical fluctuations present in non-ideal SiPMs, such as dark counts and limited photon detection efficiency. The data was simulated for two distinct overvoltages of the SensL J-Series 60 035 SiPMs, in order to test the effects of different SiPM parameters. The neural network uses the array of detector waveforms, digitized at 10 GS s−1, to predict the time at which the gamma arrived at the crystal. Main results. Best results were achieved for an overvoltage of +6 V, at which point the SiPM reaches its optimal photon detection efficiency, resulting in a coincidence time resolution (CTR) of 141 ps full width at half maximum (FWHM). It is a 26% improvement compared to a simple averaging of the first few SiPM timestamps obtained by leading edge discrimination, which in comparison produced a CTR of 177 ps FWHM. In addition, better detector uniformity was achieved, although some degradation near the corners did remain. Significance. These improvements in time resolution can lead to higher signal-to-noise ratios in time-of-flight positron emission tomography, ultimately resulting in better diagnostic capabilities.

Evaluation of Different Interpolation Techniques in GIS for Rainfall Data in Sri Lanka (2013-2018) and Identification of the Validation of the Techniques

Geographic Information Systems (GIS) and modelling are becoming powerful tools in geographical and agricultural research. Most data for environmental variables are collected from point sources. The spatial array of these data may enable a more precise estimation of the value of properties at unsampled sites than simple averaging between sampled points. Therefore, the ArcGIS software for interpolation technique was used to identify those differences in terms of rainfall variations. The main objective of this study is to identify the different interpolation techniques for rainfall data and evaluate the most accurate method for Sri Lanka. This study mainly collected rainfall data for weather stations in Sri Lanka. That data was collected in different categories. In this study, only 23 minor meteorological observatories were used for the accuracy assessment of the interpolation methods. For use, all stations are increasing time and cost, and data collection is very difficult. Therefore, 23 minor meteorological observatories were selected randomly from all over the study area. Five interpolation techniques were used. Researcher mainly used the Cross-Validation Method to identify the most suitable interpolation method for rainfall data in Sri Lanka. The main station’s data helped predict rainfall all over the study area, and deleted locations were used to extract estimated rainfall data. Finally, all estimated rainfall data was compared using their actual rainfall values to determine the accuracy of interpolation methods, and the statistical correlation method was used to determine the appropriate interpolation technique for the rainfall data. All estimated values are extracted from rainfall surfaces using an ArcGIS tool called “Extract Values from Points”. Those values are compared with actual observed rainfall values for these sub-stations for the same period. According to this method, then used the correlation statistical (F test) method to reveal the variation of both data sets. F tests were done using SPSS and F values. According to the correlation analysis, the suitable interpolation surfaces are the Spline and Kriging. Consideration of the other four methods (IDW, Kriging (Ordinary), Spline, and Natural Neighbour) shows some similarities. However, finally, researcher identified that the Spline method shows an R value of 0.99 while others show low values. Therefore, the Spline method was found to have the greatest efficiency and be the best method of all five.&#x0D; Keywords: ArcGIS, Inverse distance weighted, Interpolation, Kriging, Spline

Sire evaluation using conventional methods and animal models in Sahiwal cattle

Sire evaluation is one of the most important aspects of dairy cattle genetic improvement programme which involves the estimation of breeding value of the bulls on the basis of first lactation 305-day milk yield. The present study was undertaken to evaluate the Sahiwal sires on the basis of observed and predicted first lactation 305-days milk yield. The study was conducted utilizing 19 Sahiwal sires with three or more daughters per sire which were evaluated and ranked on the basis of first lactation 305-day milk yield. Three different sire evaluation methods, viz. Simple daughter average, Least squares method (LSM), Best linear unbiased prediction method(BLUP) were compared. The BLUP method was found to be superior followed by LSM and Simple Daughter Average Method for evaluating the sires for first lactation 305-day milk yield