Sum Of Absolute Residuals Research Articles

A stable and quantitative method for dimensionality reduction of aortic centerline.

Aortic dissection (AD) is a fatal aortic disease with high mortality. Assessing the morphology of the aorta is critical for diagnostic and surgical decisions. Aortic centerline projection methods have been used to evaluate the morphology of the aorta. However, there is a big difference between the current model of primary plane projection (PPP) and the actual shape of individuals, which is not conducive to morphological statistical analysis. Finding a method to compress the three-dimensional information of the aorta into two dimensions is helpful to clinical decision-making. In this paper, the evaluation parameters, including contour length (CL), enclosure area, and the sum of absolute residuals (SAR), were introduced to objectively evaluate the optimal projection plane rather than artificial subjective judgment. Our results showed that the optimal projection plane could be objectively characterized by the three evaluation parameters. As the morphological criterion, SAR is optimal among the three parameters. Compared to the optimal projection plane selected by traditional PPP, our method has better AD discrimination in the analysis of aortic tortuosity, and is conducive to the clinical operation of AD. Thus, it has application prospects for the preprocessing techniques for the geometric morphology analysis of AD.

Incorporating dosimetric features into the prediction of 3D VMAT dose distributions using deep convolutional neural network

An accurate prediction of achievable dose distribution on a patient specific basis would greatly improve IMRT/VMAT planning in both efficiency and quality. Recently machine learning techniques have been proposed for IMRT dose prediction based on patient’s contour information from planning CT. In these existing prediction models geometric/anatomic features were learned for building the dose prediction models and few features that characterize the dosimetric properties of the patients were utilized. In this study we propose a method to incorporate the dosimetric features in the construction of a more reliable dose prediction model based on the deep convolutional neural network (CNN). In addition to the contour information, the dose distribution from a PTV-only plan (i.e. the plan with the best PTV coverage by sacrificing the OARs sparing) is also employed as the model input to build a deep learning based dose prediction model. A database of 60 volumetric modulated arc therapy (VMAT) plans for the prostate cancer patients was used for training. The trained prediction model was then tested on a cohort of ten cases. Dose difference maps, DVHs, dosimetric endpoints and statistical analysis of the sum of absolute residuals (SARs) were used to evaluate the proposed method. Our results showed that the mean SARs for the PTV, bladder and rectum using our method were 0.007 ± 0.003, 0.035 ± 0.032 and 0.067 ± 0.037 respectively, lower than the SARs obtained with the contours-based method, indicating the potential of the proposed approach in accurately predicting dose distribution.

Dosimetric features-driven machine learning model for DVH prediction in VMAT treatment planning.

Few features characterizing the dosimetric properties of the patients are included in currently available dose-volume histogram (DVH) prediction models, making it intractable to build a correlative relationship between the input and output parameters. Here, we use planning target volume (PTV)-only treatment plans of the patients (i.e., the achievable dose distribution in the absence of organs-at-risk (OAR) constraints) to estimate the potentially achievable quality of treatment plans and establish a machine learning-based DVH prediction framework with the use of the dosimetric metric as model input parameters. A support vector regression (SVR) approach was used as the backbone of our machine learning model. A database containing volumetric modulated arc therapy (VMAT) plans of 63 prostate cancer patients were used. For each patient, the PTV-only plan was generated first. A correlative relationship between the OAR DVH of the PTV-only plan (model input) and the corresponding DVH of the clinical treatment plan (CTP) (model output) was then established with the 53 training cases. The prediction model was tested by the validation cohort of ten cases. For the training cohort, the checks of dosimetric endpoints (DEs) indicated that 52 of 53 plans (98%) were within the 10% error bound for bladder, and 45 of 53 plans (85%) were within the 10% error bound for rectum. In the validation tests, 92% and 96% of the DEs were within the 10% error bounds for bladder and rectum, respectively, and eight of ten validation plans (80%) were within the 10% error bound for both the bladder and rectum. The sum of absolute residuals (SAR) achieved a mean of 0.034±0.028 and 0.046±0.021 for the bladder and rectum, respectively. A novel dosimetric features-driven machine learning model with the use of PTV-only plan has been established for DVH prediction. The framework is capable of efficiently generating best achievable DVHs for VMAT planning.

The importance of calibration parameters on the accuracy of the floods description in the Snyder’s model

Abstract Comparison of quality of Snyder’s model for determination flood waves was examination in this work. Model parameters were calibrated based on objective functions: percentage error in peak flow (PEPF), percentage error in volume (PEV), peak-weighted root mean square error (PWRMSE), sum of absolute residuals (SAR) and sum of squared residuals (SSR). Quality of model was calculating by Nash-Sutcliffe efficiency coefficient E. Additionally sensitivity of a model was characterized by its flexibility. The analyses were performed in the watershed of Grabinka. It has been found that the use PWRMSE as the objective function allows to obtain the best quality results of simulation. Furthermore, Snyder’s model is flexible to the change of Cp coefficient.

Support vector machine identification of a parallel cascade model of human ankle stiffness

Nonlinear systems identification techniques have been used to study the stretch reflex dynamics of the muscles of the human ankle. Kearney and Hunter (1988) suggested a parallel cascade structure consisting of two pathways to represent human ankle stiffness dynamics. The upper pathway contains a linear model that represents the intrinsic stiffness of the ankle while the reflex stiffness, the lower path, is modeled with a Hammerstein cascade. In this work, an algorithm for the identification of the parallel cascade model using SVM regression is developed. The model parameters have been identified by minimizing an epsilon insensitive cost functions based on either the sum of absolute residuals or the sum of square residuals. The proposed algorithm has been validated via simulation.

A fast mutant fault detection method of underwater integrated navigation

The concepts of the mean of residual and the sum of absolute residuals are introduced in this paper. Both of them along with the fault detection function are used to detect mutant fault of the assisted navigation devices in underwater integrated navigation system. (1) The traditional residual χ2 detection method is improved according to the structural characteristics of the underwater navigation system. (2) The mean of residual and the sum of absolute residuals are introduced as the characteristics of mutant faults. (3) The improved residual χ2 detection method is used to make sure of the happening of the mutant fault firstly. Then the residual mean and the sum of residual absolute values are used to distinguish the noise mutant system fault and the information mutant system fault. The results of simulations and the vehicle tests show that: (1) the mutant fault of the sub-system can be detected and the faulty sub-system can be isolated immediately when the fault appears with our novel method; (2) The noise mutant fault and the information mutant fault can be distinguished efficiently according to characteristics of the mean of residuals and the sum of the absolute residuals.

A Fast Gradual Fault Detection Method for Underwater Integrated Navigation Systems

Gradual fault detection is always an important issue in integrated navigation systems, and the gradual fault is the most difficult fault to detect. To detect gradual faults in a timely and precise manner in integrated navigation systems, the statistical concepts of the normalised residual mean and the sum of absolute residuals are introduced according to the characteristics of gradual system failure in this paper. The applicability of the improved residual χ2 detection method is discussed. Then, the gradual fault detection program based on the improved residual χ2 detection method is designed with the criterion of normalised residual mean and the sum of absolute residual. The simulation results and vehicle tests show that: 1) The residual of the failed sub-system can be calculated accurately with the improved residual χ2 detection method, which has strong applicability in gradual fault detection; 2) The gradual fault can be detected in a short time by using the normalised residual mean and the sum of absolute residual.

The importance of the objective functions and flexibility on calibration of parameters of clark instantaneous unit hydrograph

The paper compares the results of automatic calibration of Clark’s synthetic unit hydrographs. Optimal values of model parameters were determined by the objective functions: percentage error in peak flow (PEPF), percentage error in volume (PEV), peak-weighted root mean square error (PWRMSE), sum of absolute residuals (SAR) and sum of squared residuals (SSR). The last part of the analysis assesses the flexibility of studied model. The research was performed in the upland watershed of Grabinka – left tributary of the Wisloka river located in Southern Poland. The analysis reveals that the smallest differences between the maximum flow in the observed and calculated flood culmination were obtained when applying PWRMSE function. This paper also indicates, that Clark’s model was efficient for describing the analyzed floods.

Identification of NARX Hammerstein Models Based on Large Scale Support Vector Machine Regression

Methods for the identification of Hammerstein models consisting of a Support Vector Machine nonlinearity followed by an ARX linear system are developed. The models are identified by minimizing epsilon insensitive cost functions based on either the sum of absolute residuals or the sum of squared residuals. Large scale implementations of these techniques are then derived using subset selection methods, and used to identify a model of the stretch reflex electromyogram from experimental data. The effects of the various cost functions and tuning parameters are demonstrated with the experimental results.

Measuring the Systematic Risk of IPO's Using Empirical Bayes Estimates in the Thinly Traded Istanbul Stock Exchange

The systematic risk of IPO's in the thinly traded Istanbul Stock Exchange (ISE) are estimated using Empirical Bayes Estimators (EBE). The sectors that the firms belong to, provide the priors. Comparisons are made with OLS estimators across different estimation and forecasting periods. Two benchmark criteria are used; sum of squared residuals and sum of absolute residuals. The application requires some complicated manipulation of the theory where some inferiors of the ordinary Bayesian approach are avoided. Results show that using the EBE procedure, betas can be calculated with greater precision than OLS. This enables us to evaluate IPO's on similar intuition with other stocks, i.e. in a portfolio context rather than in isolation.

The historical development of the linear minimax absolute residual estimation procedure 1786–1960

This paper is concerned with the historical development of a traditional procedure for determining appropriate values for the parameters defining a linear relationship. This traditional procedure is variously known as the minimax absolute residual, Chebyshev, or L ∞-norm procedure. Besides being of considerable interest in its own right as one of the earliest objective methods for estimating the parameters of such relationships, this procedure is also closely related to Rousseeuw's least median of squared residuals and to the least sum of absolute residuals or L 1-norm procedures. The minimax absolute residual procedure was first proposed by Laplace in 1786 and developed over the next 40 years by de Prony, Cauchy, Fourier, and Laplace himself. More recent contributions to this traditional literature include those of de la Vallée Poussin and Stiefel. Nowadays, the minimax absolute residual procedure is usually implemented as the solution of a primal or dual linear programming problem. It therefore comes as no surprise to discover that some of the more prominent features of such problems, including early variants of the simplex algorithm are to be found in these contributions. In this paper we re-examine some of the conclusions reached by Grattan-Guinness (1970), Franksen (1985) and Grattan-Guinness (1994) and suggest several amendments to their findings. In particular, we establish the nature of de Prony's geometrical fitting procedure and trace the origins of Fourier's prototype of the simplex algorithm.

On l1 regression coeficients

We propose an alternative method to find the well-known L1 estimators for general regression models. We find that the L1 regression coefficients can be defined in terms of the convergent weighted medians of the slopes from each data point to the point that is assumed to be on a predicted regression line. Since the L1 estimators are obtained by the convergent weighted medians, the L1 estimation method could be regarded as finding the point on a predicted regression line. Moreover, we extend the above method to the multiple regression models. In these cases, the regression coefficients cannot be mentioned as the medians of some slopes, but can be defined in terms of me convergent weighted medians of some slopes. With these situations, we do the analogous argument to find the point on the Lx regression line so that the sum of absolute residuals would be minimized.

Adaptive methods for estimating Arrhenius parameters

In an earlier paper, we presented a comparative study of four methods (linear regression (LR), non-linear regression (NLR), sum of absolute residuals and direct linear plot (DLP)) for estimating the frequency factor and activation energy based on reaction-rate coefficient values as a function of temperature. Five adaptive methods are studied in this paper. The adaptive methods attempt to distinguish the error type (simple or relative) through an appropriate statistical test, and then use LR or median-based DLP if the error type is relative and NLR if the error type is simple. Results of simulation tests to find the relative accuracies of LR, NLR, DLP and the five adaptive methods, are presented and discussed. This work shows that the adaptive methods are practicable and that they, in general, are more accurate than other methods. However, the computational effort involved in any adaptive method is relatively greater.

An Empirical Study of Various Indices for Determining Unidimensionality.

Following a review of indices proposed to assess the unidimensionality of a set of items, Hattie (Note 1) identified 87 indices. The purpose of the present paper is to describe a simulation that determines the adequacy of various indices as decision criteria for assessing unidimensionality. A three-parameter, multivariate, logistic latent-trait model was used to generate item responses. Levels of difficulty, guessing, and discrimination, as well as the number of factors underlying the data, were varied. Many of the indices evaluated were highly intercorrelated. Some resulted in estimates outside their theoretical bounds, and most were particularly sensitive to the intercorrelations between factors. Indices based on answer patterns, reliability, component analysis, linear and nonlinear factor analysis, and on the one-parameter latent trait model were ineffective. Using the sum of absolute residuals from the twoparameter latent trait model, indices were obtained that were able to discriminate between cases with one latent trait and cases with more than one latent trait.

Low Median and Least Absolute Residual Analysis of Two-Way Tables

Abstract Some properties of and extensions to Tukey's method of median polish, an exploratory robust additive decomposition of a two-way table, are presented using the low median. If the table entries are rational numbers, then the iteration process must stop after a finite number of steps. However, even for tables of bounded dimension the number of iterations can be arbitrarily large. For 3 by 3 tables, the sum of absolute residuals is often minimized by median polish. Minimization conditions are identified that are likely to occur in practice. A method to supplement the polishing process by increasing the number of zero residuals is developed.

Low Median and Least Absolute Residual Analysis of Two-Way Tables

Abstract Some properties of and extensions to Tukey's method of median polish, an exploratory robust additive decomposition of a two-way table, are presented using the low median. If the table entries are rational numbers, then the iteration process must stop after a finite number of steps. However, even for tables of bounded dimension the number of iterations can be arbitrarily large. For 3 by 3 tables, the sum of absolute residuals is often minimized by median polish. Minimization conditions are identified that are likely to occur in practice. A method to supplement the polishing process by increasing the number of zero residuals is developed.

A Regression-Based Linear Classification Procedure

A linear regression function is developed for use in a classification procedure. The regression function is chosen to minimize the number of misclassifications and, secondarily, to minimize the sum of absolute residuals. In situations where the categories of classification correspond to ranges of values of a criterion variable in one dimension, this linear classification function is easier to interpret than classical discriminant functions. The procedure is applied to faculty merit review data, resulting in an interpretable regression function and within-sample classifications as good as a four-function discriminant analysis.

Two Linear Programming Algorithms for Unbiased Estimation of Linear Models

Abstract Consider the estimation of in the familiar linear model . It is well-known that the least squares estimation principle yields an un-biased estimator . Two alternative estimation principles sometimes considered are the minimization of the sum of absolute residuals and the minimization of the maximum absolute residual. Since these alternative principles do not usually lead to a unique estimator, the latter depends on the computational algorithm used. We develop two algorithms which are based upon these alternative principles and yield unbiased estimators. The algorithms' essential features are the use of linear programming and an “antisymmetrical” initial estimator.