Robust Regression Method Research Articles

Anomalous load profile detection in power systems using wavelet transform and robust regression

In modern power systems, a clean database of historical electric loads is crucial for system analysis, planning studies, load forecasting, and decision making. To this end, the clean database should be free of anomalies while preserving the power consumption behavior of special events like holidays. In recent years, model-based anomaly detection methods have been successfully used for anomaly detection and correction in electrical load. In these methods, the collected load data are first compared with the predicted load obtained from a forecasting model; if the difference is greater than a specific limit, the collected load data are replaced with the predicted value. One of the disadvantages of these methods is the consideration of load profiles of the days with higher levels of difficulty in load forecasting, such as holidays, as anomalous load profiles and replacing them with predicted values, which results in fading some important characteristics of the load series. Therefore in this paper, a two-stage anomaly detection method is proposed to alleviate this problem. In the first stage, the wavelet transform is used to identify suspected load profiles. In the second stage, a robust regression method is used to further inspect the suspected load profiles and decide whether they are anomalies or not. By performing experiments on three datasets (a utility of Iran, New York City, and a North American utility) and comparing the results with four other methods, it’s shown that the proposed method decreases false detection of anomalies while accurately correcting anomalous load profiles. Results of load forecasting with the Iranian dataset corrected by the proposed method showed an average of 2.28% and 1.58% error on the holidays and total days, respectively, which is less than the other four methods.

Performance of Contrast Adjustment in Face Recognition with Training Image under Various Lighting Conditions

The lighting factor has a very significant effect on facial recognition performance. To reduce the effect of this lighting factor, at the pre-processing stage the researchers used contrast adjustments to the image to improve facial recognition performance. The histogram equalization technique is generally used for contrast adjustment because of its excellent performance to normalize image illumination which is affected by lighting conditions. In this research, empirical experiments were carried out to determine the effect of contrast adjustment using histogram equalization on face recognition in more detail. This research aims to answer the question whether this technique can be used in all image lighting conditions or not. The Robust Regression method is used in this research to recognize faces, which in many cases have very good performance due to lighting factors. Experiments using images in the AR Face Database related to lighting factors. The testing process is carried out by comparing the results of face recognition using the histogram equalization technique in the pre-processing phase and face recognition without pre-processing in each lighting condition. The experimental results show that the use of the histogram equalization technique in pre-processing gives a better face recognition performance effect in low, medium and high lighting conditions. But in very high (extreme) lighting conditions, the use of the histogram equalization technique in pre-processing turns out to have a worse facial recognition performance effect, with an average accuracy of 93.17%, whereas without pre-processing it produces an average accuracy of 94 , 67%.

ESTIMATING OF PROFIT FUNCTION OF VEGGETABLE CROPS IN ALQOSH REGION FOR THE PRODUCTION SEASON 2019

The research aims to study the profit functions of vegetable crops. Cross-sectional data was used based on a random sample that included 200 farmers in Alqosh region within Nineveh Province for the 2018-2019 agricultural season. The results showed that there are vegetable crops which need a large amount of labor as labor costs amounted to about 71% of the total costs per acre in tomato production. It was also found that total costs were higher in tomato crop cultivation at the dunum level compared to other vegetable crops. In addition, profit function shows that the price of the product has a significant effect on profit compared to the rest of the independent variables in the functions of vegetable crops, as the parameter of tomato crop price was about 51603.22 and it was significant and approved according to the T-test at the level of 1%. The determination coefficient was about 79% in the function estimated by the OLS method. Problem of heteroscedasticity according to White's general test was significant, so the estimation was done by the robust regression method to avoid that problem. That led to a decrease of the determination coefficient to about 55%, While the determinant factor of the cucumber crop reached about 72%, to be reduced to about 56% after addressing the problem of variability instability. The research recommended that farmers should be encouraged to expand tomato cultivation instead of other vegetable crops.

The Unintended Side-Effects of a Major Development Strategy: Commercialization of Smallholder Production and Women Empowerment in Uganda

As many African countries promote commercial agricultural production, it is important to understand how this strategy influences the intra-household balance of power. Commercial crops are traditionally considered the domain of men, and women empowerment may suffer. We use a quasi-experimental design to address the relation between commercial production and women’s voice within the household in rural Uganda. We compare empowerment in households in an area targeted by a large program stimulating rice as a non-traditional cash crop with similar households elsewhere using double robust regression methods. We conclude that the commercialisation program had a significant negative effect on women empowerment in production and women’s control over income, while men’s empowerment in those domains increased. We find only weak effects for social empowerment. Based on these results, we recommend that policies and programs to stimulate commercial agricultural production among smallholder include a strong gender component.

New Robust Regression Method for Outliers and Heavy Sparse Noise Detection via Affine Transformation for Head Pose Estimation and Image Reconstruction in Highly Complex and Correlated Data: Applications in Signal Processing

In this work, we propose a novel method for head pose estimation and face recovery, particularly to solve the potential impacts of noises in signal processing to get an efficient and effective model that is more resilient with annoying effects through adding affine transformation with the low-rank robust subspace regression. Consequently, the corrupted images can be correctly recovered by affine transformations to render more best regression outcomes. Thereby, we need to search so as to get optimal parameters which can be regarded as convex constrained optimization techniques. Afterward, the alternating direction method for multipliers (ADMM) approach is considered and a new set of updated equations is well established so as to update the optimization parameters and affine transformations iteratively in a round-robin manner. Additionally, the convergence of these new updating equations is well scrutinized as well. Thus, the experimental simulations reveal that the proposed method outperforms the state-of-the-art works for head pose estimation and face recovery on some public databases.

Robust regression via error tolerance

Real-world datasets are often characterised by outliers; data items that do not follow the same structure as the rest of the data. These outliers might negatively influence modelling of the data. In data analysis it is, therefore, important to consider methods that are robust to outliers. In this paper we develop a robust regression method that finds the largest subset of data items that can be approximated using a sparse linear model to a given precision. We show that this can yield the best possible robustness to outliers. However, this problem is NP-hard and to solve it we present an efficient approximation algorithm, termed SLISE. Our method extends existing state-of-the-art robust regression methods, especially in terms of speed on high-dimensional datasets. We demonstrate our method by applying it to both synthetic and real-world regression problems.

Robust bootstrap regression testing in the presence of outliers

Bootstrap is one of the random sampling methods with replacement, that was proposed to address the problem of small samples whose distributions are difficult to derive. The distribution of bootstrap samples is empirical or free and due to its random sampling with replacement, the probability of choosing a specific observation may be equal to one. Unfortunately, when the original sample data contains an outlier, there is a serious problem that leads to a breakdown OLS (Ordinary Least Squares) estimator, and robust regression methods should be recommended. It is well known that the best robust regression method has a high breakdown point is not more than 0.50, so the robust regression method would break down when the percentage of outliers in the bootstrap sample exceeds 0.50. It is well known that fixed-x bootstrap is resampled the residuals which probably are having outliers. Moreover, the leverage point(s) is an outlier that occurs in X-direction, so the effects of it on fixed-x bootstrap samples would be existence. However, the decision-making about the null hypothesis of bootstrap regression coefficients could not be reliable. In this paper, we propose using weighted fixed-x bootstrap with a probability approach to guarantee the percentage of outliers in the bootstrap samples will be very low. And then weighted M-estimate should be to tackle the problem of outliers and leverage points and taking a more reliable decision about bootstrap regression coefficients hypothesis test. The performance of the suggested method has been tested with others by using real data and simulation. The results show our proposed method is more efficient and reliable than the others.

Precision Motion Measurement for Linear Motor Based on FNCC and Phase Difference M-Estimator Robust Regression in a VLSM System

This paper investigates a low-cost vision-based line-scan measurement (VLSM) system to achieve the high-precision positioning of linear motors. And an improved two-step phase difference method is performed for detecting subpixel translation of 1-D multi-frame images. In the first step of the algorithm, a fast normalized cross-correlation (FNCC) is adopted for coarse estimation to extract the overlapping portions of the two frames. In the second step, M-Estimator robust regression method is used to estimate the displacement parameters of the phase difference matrix of the overlap further accurately. The simulation cases indicate that the proposed approach outperforms the other existing methods in accuracy and robustness. In addition, the system and proposed algorithm are effectively validated in experiments and achieve a displacement detection of 0.01 mm grade of the mover.

Evaluation of a robust regression method (RoBoost-PLSR) to predict biochemical variables for agronomic applications: Case study of grape berry maturity monitoring

Visible and near infrared spectroscopy (VIS-NIR) is increasingly being transferred from laboratory to industry for in-line and portable applications in various domains. By intensively using VIS-NIR spectroscopy, some abnormal observations may certainly arise. It is then important to properly handle outliers to elaborate effective prediction models. The objective of this study is to investigate the potential of using a robust method called Roboost-PLSR to improve prediction model performances for a viticulture application. This work focuses on a case study to predict sugar content in grape berries of three different grape varieties of Vitis Vinifera in a maturity monitoring context. Hyperspectral images were acquired of grape berries of Syrah, Fer-Servadou and Mauzac varieties. Reference measurements of sugar levels were made in the laboratory by densimetric baths. Performances of RoBoost-PLSR models were compared to performances of reference models using Partial Least Square Regression (PLSR). Reference prediction criteria using PLSR were obtained for all varieties with these following values: Syrah (Rp2 ​= ​0.971; RMSEp ​= ​5.36 ​g/L), Fer-servadou (Rp2 ​= ​0.788; RMSEp ​= ​11.69 ​g/L) and Mauzac (Rp2 ​= ​0.690; RMSEp ​= ​15.61 ​g/L). Prediction qualities are improved with RoBoost-PLSR: Syrah (Rp2 ​= ​0.990; RMSEp ​= ​3.14 ​g/L), Fer-Servadou (Rp2 ​= ​0.848; RMSEp ​= ​10.20 ​g/L) and Mauzac (Rp2 ​= ​0.927; RMSEp ​= ​7.58 ​g/L). Results confirm that Roboost-PLSR method allows a better consideration of outliers within the calibration set.

Online and Distributed Robust Regressions with Extremely Noisy Labels

In today’s era of big data, robust least-squares regression becomes a more challenging problem when considering the extremely corrupted labels along with explosive growth of datasets. Traditional robust methods can handle the noise but suffer from several challenges when applied in huge dataset including (1) computational infeasibility of handling an entire dataset at once, (2) existence of heterogeneously distributed corruption, and (3) difficulty in corruption estimation when data cannot be entirely loaded. This article proposes online and distributed robust regression approaches, both of which can concurrently address all the above challenges. Specifically, the distributed algorithm optimizes the regression coefficients of each data block via heuristic hard thresholding and combines all the estimates in a distributed robust consolidation. In addition, an online version of the distributed algorithm is proposed to incrementally update the existing estimates with new incoming data. Furthermore, a novel online robust regression method is proposed to estimate under a biased-batch corruption. We also prove that our algorithms benefit from strong robustness guarantees in terms of regression coefficient recovery with a constant upper bound on the error of state-of-the-art batch methods. Extensive experiments on synthetic and real datasets demonstrate that our approaches are superior to those of existing methods in effectiveness, with competitive efficiency.

Interval joint robust regression method

Interval-valued data are needed to manage either the uncertainty related to measurements, or the variability inherent to the description of complex objects representing group of individuals. A number of regression methods suitable to interval variables describing variability of complex objects are already available. However, less attention has been given to methods that, simultaneously, take into account the full interval information and are resistant to interval outlier observations, even with the frequent presence of atypical observations on interval-valued data sets. This paper proposes a new robust linear regression method for interval variables, where the presence of outliers either in the center or in the radius penalize both the center and the radius regression models. Moreover, the interval observations with outliers on both center and radius are more penalized than those observations with outliers only in the center (or in the radius). Besides, this paper provides a suitable iterative algorithm to estimate the parameters of the proposed method. The algorithm estimates the parameters of the center (or of the radius) model taking into account both information of the center and the radius. The convergence and time complexity of the iterative algorithm are also presented. Finally, the performance of the new method is compared with some previous robust regression approaches and evaluated on synthetic and real interval-valued data sets.

A new explainable robust high-order intuitionistic fuzzy time-series method

Fuzzy time series, based on type-1 fuzzy sets, continue to have a wide range of use in the literature. These methods use only membership values to determine the fuzzy relations. However, intuitionistic fuzzy time series models use both membership values and non-membership values. So it can be considered that the use of intuitionistic fuzzy time forecasting models will be able to increase the forecasting performance because the intuitionistic fuzzy sets have more information than fuzzy sets. Therefore, intuitionistic fuzzy time series models have started to employ for forecasting the real-life series in the fuzzy time series literature. A novel, explainable, robust high-order intuitionistic fuzzy time series forecasting method is proposed based on a newly defined model. In the proposed method, the intuitionistic fuzzy c-means algorithm is used for the fuzzification of observations, and a robust regression method employed for determining fuzzy relations. With the use of robust regression in determining the fuzzy relationships, all inputs of the proposed method can be explainable and they can be tested and commented on statistically. Applications of this study are made by using energy data of Primary Energy Consumption between the years 1965 and 2016 for 23 countries in the region of Europe-Eurasia. The forecasting performance of the proposed method is compared with the performance of some selected benchmarks, and the obtained results are discussed.

Cyberattack-resilient load forecasting with adaptive robust regression

Cyberattacks in power systems that alter the input data of a load forecasting model have serious, potentially devastating consequences. Existing cyberattack-resilient work focuses mainly on enhancing attack detection. Although some outliers can be easily identified, more carefully designed attacks can escape detection and impact load forecasting. Here, a cyberattack-resilient load forecasting approach based on an adaptive robust regression method is proposed, where the observations are trimmed based on their residuals and the proportion of the trim is adaptively determined by an estimation of the contaminated data proportion. An extensive comparison study shows that the proposed method outperforms the standard robust regression in various settings.

A novel robust PLS regression method inspired from boosting principles: RoBoost-PLSR

The calibration of Partial Least Square regression (PLSR) models can be disturbed by outlying samples in the data. In these cases the models can be unstable and their predictive potential can be depreciated. To address this problem, some robust versions of the PLSR Algorithm were proposed. These algorithms rely on the downweighting of these outliers during calibration. To this end, it is necessary to estimate an inconsistency measurement between the samples and the model. However, this estimation is not trivial in high dimensions. This paper proposes a novel robust PLSR algorithm inspired from the principles of boosting: RoBoost-PLSR. This method consists of realising a series of one latent variable weighted PLSR. RoBoost-PLSR is compared with the PLSR algorithm calibrated with and without outliers and also with Partial Robust M-regression (PRM), a reference robust method. This evaluation is conducted on the basis of three simulated datasets and a real dataset. Finally Roboost-PLSR proves to be resilient to the tested outliers, and can achieve the performances of the reference PLSR calibrated without any outlier.

Association of HIV-1 Infection and Antiretroviral Therapy With Type 2 Diabetes in the Hispanic Population of the Rio Grande Valley, Texas, USA.

The Rio Grande Valley (RGV) in South Texas has one of the highest prevalence of obesity and type 2 diabetes (T2D) in the United States (US). We report for the first time the T2D prevalence in persons with HIV (PWH) in the RGV and the interrelationship between T2D, cardiometabolic risk factors, HIV-related indices, and antiretroviral therapies (ART). The PWH in this study received medical care at Valley AIDS Council (VAC) clinic sites located in Harlingen and McAllen, Texas. Henceforth, this cohort will be referred to as Valley AIDS Council Cohort (VACC). Cross-sectional analyses were conducted using retrospective data obtained from 1,827 registries. It included demographic and anthropometric variables, cardiometabolic traits, and HIV-related virological and immunological indices. For descriptive statistics, we used mean values of the quantitative variables from unbalanced visits across 20 months. Robust regression methods were used to determine the associations. For comparisons, we used cardiometabolic trait data obtained from HIV-uninfected San Antonio Mexican American Family Studies (SAMAFS; N = 2,498), and the Mexican American population in the National Health and Nutrition Examination Survey (HHANES; N = 5,989). The prevalence of T2D in VACC was 51% compared to 27% in SAMAFS and 19% in HHANES, respectively. The PWH with T2D in VACC were younger (4.7 years) and had lower BMI (BMI 2.43 units less) when compared to SAMAFS individuals. In contrast, VACC individuals had increased blood pressure and dyslipidemia. The increased T2D prevalence in VACC was independent of BMI. Within the VACC, ART was associated with viral load and CD4+ T cell counts but not with metabolic dysfunction. Notably, we found that individuals with any INSTI combination had higher T2D risk: OR 2.08 (95%CI 1.67, 2.6; p < 0.001). In summary, our results suggest that VACC individuals may develop T2D at younger ages independent of obesity. The high burden of T2D in these individuals necessitates rigorously designed longitudinal studies to draw potential causal inferences and develop better treatment regimens.

Robust Estimation for Proportional Odds Model through Monte Carlo Simulation

Ordinal regression is used to model the ordinal response variable as functions of several explanatory variables. The most commonly used model for ordinal regression is the proportional odds model (POM). The classical technique for estimating the unknown parameters of this model is the maximum likelihood (ML) estimator. However, this method is not suitable for solving problems with extreme observations. A robust regression method is needed to handle the problem of extreme points in the data. This study proposes Huber M-estimator as a robust method to estimate the parameters of the POM with a logistic link function and polytomous explanatory variables. This study assesses ML estimator performance and the robust method proposed through an extensive Monte Carlo simulation study conducted using statistical software, R. Measurement for comparisons are bias, RMSE, and Lipsitzs' goodness of fit test. Various sample sizes, percentages of contamination, and residual standard deviations are considered in the simulation study. Preliminary results show that Huber estimates provide the best results for parameter estimation and overall model fitting. Huber's estimator has reached a 50% breakdown point for data containing extreme points that are quite far from most points. In addition, the presence of extreme points that have only a distance of two times far from most points has no major impact on ML estimates. This means that the estimates for ML and Huber may yield the same results if the model's residual values are between -2 and 2. This situation may also occur for data with a percentage of contamination below 5%.

Assessing one-minute diffuse fraction models based on worldwide climate features

Despite the variety of irradiance separation models available in the literature, there is not yet a model that performs equally well for every location worldwide. Nevertheless, separation models still represent an interesting approach when only global irradiance is measured. This work presents further developments of the recently proposed Boland-Ridley-Lauret minute model and proposes 1-min diffuse fraction models for each climate zone in the globe. To accomplish this, 1-min worldwide irradiance data from 51 the Baseline Surface Rresearch Network stations and one from Australian Bureau of Meteorology were used. The Köppen-Geiger classification was used to determine the climate zone of each station: both the simple climate classification (A, B, C, D, E) and the complete classification (Aw, Bsh, etc.). Furthermore, a robust nonlinear regression method was used to build the separation models without removing measurement outliers in advance. The climate-specific models proposed herein present better performance than other models from the literature, such as the BRL, Perez and Skartveit models (developed using hourly irradiance data) and the Engerer model (developed using minute data). Generally, the models proposed for climate zones in the complete Köppen classification presented better similitude with the measured data than the models for the simple classification, especially for stations within climate zones B and E.

Sparse Modal Additive Model.

Sparse additive models have been successfully applied to high-dimensional data analysis due to the flexibility and interpretability of their representation. However, the existing methods are often formulated using the least-squares loss with learning the conditional mean, which is sensitive to data with the non-Gaussian noises, e.g., skewed noise, heavy-tailed noise, and outliers. To tackle this problem, we propose a new robust regression method, called as sparse modal additive model (SpMAM), by integrating the modal regression metric, the data-dependent hypothesis space, and the weighted lq,1 -norm regularizer (q ≥ 1) into the additive models. Specifically, the modal regression metric assures the model robustness to complex noises via learning the conditional mode, the data-dependent hypothesis space offers the model adaptivity via sample-based presentation, and the lq,1 -norm regularizer addresses the algorithmic interpretability via sparse variable selection. In theory, the proposed SpMAM enjoys statistical guarantees on asymptotic consistency for regression estimation and variable selection simultaneously. Experimental results on both synthetic and real-world benchmark data sets validate the effectiveness and robustness of the proposed model.

Benchmarking for using an acoustic Doppler current profiler for bathymetric survey.

This research aims to improve data post-processing from an acoustic Doppler current profiler (ADCP) to obtain additional depth information with a high-quality bathymetric result. To validate the depth, dataset in a control area was used a scaled rod, the RTK (Real-Time Kinematic) positioning technique, and a single beam echo sounder (SBES). The developed post-processing and validation in the control area applied to a small region of a water supply reservoir in Brazil. A robust local regression method eliminated outliers from the raw data. Subsequently, a linear regression model was generated for the beams from the ADCP to adjust depths and improve the dataset. The statistical hypothesis test performed before and after the adjustment supported the validation of data processing. The resulting volumes calculated from the ADCP raw data showed a difference of 30% with SBES, which is usually the standard equipment used for bathymetric surveys. The proposed post-processing techniques declined to <1% of the volume discrepancy. The raw dataset standard deviation was 0.15m on average for Doppler beams, and after adjusts, this value dropped to 0.03m. The results showed the necessity of a post-processing method to improve depth data quality from ADCP. Thus, the procedure described in this document can be used for bathymetric surveys using ADCP for analysis concerning the estimation of reservoir volume.

Robust proportional hazard‐based monitoring schemes for reliability data

AbstractReliability of products is a key factor for successful businesses. In general, the existing monitoring schemes have poor performance as reliability data are often censored. Also, the products are manufactured in multistage processes where the outgoing quality gets affected by the previous stage quality. Besides this cascade property, historical data with outliers make the analysis even more complicated. This paper discusses exponentially weighted moving average (EWMA) and cumulative sum (CUSUM) control charts for monitoring a two‐stage dependent process. In particular, the proportional hazard (PH) model is assumed for modeling the relationship of quality characteristics. Furthermore, to remove the detrimental effects of outliers on the results, robust regression method known as the M‐estimation is used. Besides a real case study, the performance of the proposed monitoring approach is assessed through a comprehensive simulation study. The results suggested that the EWMA chart outperforms the CUSUM chart.