Mean Absolute Deviation Error Research Articles

LSTM-CNN Tabanlı Derin Öğrenme Tekniği Kullanılarak Küresel Yatay Güneş Radyasyonu ile Hava Durumu Parametrelerinin Tahmini ve Analizi

Predicting global horizontal solar irradiance (GHSI) as well as important climate parameters plays an important role in energy management and resource planning of photovoltaic panels. To further benefit from solar energy, it is necessary to obtain information regarding future values by frequently analyzing and predicting such time series parameter data. Hence, predicting long-term solar irradiance data is a challenging task. For these purposes, in this work, a hybrid method, with modeling of Long Short-Term Memory (LSTM) and Convolutional Neural Network (CNN) deep neural networks, is proposed to ensure the most accurate prediction of such data. The GHSI as well as temperature, relative humidity, and wind speed data obtained in the Jordan valley are used in the forecasting methodology. In the CNN block of the proposed deep architecture, the input parameters are passed through the convolution, pooling, and flattening layers, and the outputs are forwarded to the LSTM data input. With this method, it is aimed to make more effective and accurate estimations. The proposed method has been compared according to Root Mean Square Error (RMSE), Mean Absolute Deviation Error (MADE), and Mean Absolute Percentage Error (MAPE) error performance criteria in order to reveal the difference from other methods. The proposed method produces superior results compared to other algorithms, especially in GHSI estimation.

Total generalized variation denoising of speckled images using a primal-dual algorithm

In this paper, multiplicative noise removal problem is considered. Multiplicative noise is also commonly referred to as speckle. We propose a total generalized variation (TGV) based model which involves the multilook M for multiplicative noise removal. The objective function of our proposed model is strictly convex. Computationally, by using the dual representation of the second-order TGV regularization, our proposed model is transformed into a minimax problem. A first-order primal-dual algorithm is developed to solve the minimax problem and the convergence of the proposed algorithm is strictly proved. At last, compared with several existing methods, experimental results demonstrate the effectiveness of the proposed method, in terms of signal-to-noise ratio, peak signal-to-noise ratio and mean absolute-deviation error.

A random forest partition model for predicting NO2 concentrations from traffic flow and meteorological conditions

High concentrations of nitrogen dioxide in the air, particularly in heavily urbanised areas, have an adverse effect on many aspects of residents' health (short-term and long-term damage, unpleasant odour and other). A method is proposed for modelling atmospheric NO2 concentrations in a conurbation, using a partition model M consisting of two separate models: ML for lower concentration values and MU for upper values. An advanced data mining technique, that of random forests, is used. This is a method based on machine learning, involving the simultaneous compilation of information from multiple random trees. Using the example of data recorded in Wrocław (Poland) in 2015–2017, an iterative method was applied to determine the boundary concentration y˜ for which the mean absolute deviation error for the partition model attained its lowest value. The resulting model had an R2 value of 0.82, compared with 0.60 for a classical random forest model. The importances of the variables in the model ML, similarly as in the classical case, indicate that the greatest influence on NO2 concentrations comes from traffic flow, followed by meteorological factors, in particular the wind direction and speed. In the model MU the importances of the variables are significantly different: while traffic flow still has the greatest impact, the effects of temperature and relative humidity are almost as great. This confirms the justifiability of constructing separate models for low and high pollution concentrations.

Multiplicative noise removal via adaptive learned dictionaries and TV regularization

Multiplicative noise removal is a key issue in image processing problem. While a large amount of literature on this subject are total variation (TV)-based and wavelet-based methods, recently sparse representation of images has shown to be efficient approach for image restoration. TV regularization is efficient to restore cartoon images while dictionaries are well adapted to textures and some tricky structures. Following this idea, in this paper, we propose an approach that combines the advantages of sparse representation over dictionary learning and TV regularization method. The method is proposed to solve multiplicative noise removal problem by minimizing the energy functional, which is composed of the data-fidelity term, a sparse representation prior over adaptive learned dictionaries, and TV regularization term. The optimization problem can be efficiently solved by the split Bregman algorithm. Experimental results validate that the proposed model has a superior performance than many recent methods, in terms of peak signal-to-noise ratio, mean absolute-deviation error, mean structure similarity, and subjective visual quality.

Analytical double-hybrid density functional based on the polynomial series expansion of adiabatic connection: a quadratic approximation.

We present a systematic derivation of double-hybrid density functional (DHDF) based on the polynomial series expansion of adiabatic connection formula in the closed interval λ = [0,1] without a loss of generality. Because of the tendency of Wλ having a small (but not negligible) curvature at equilibrium, we first evaluate the chemical validity of quadratic approximation for Wλ using the large GMTKN30 benchmark database. The resulting functional, obtained analytically and denoted by quadratic adiabatic connection functional-PT2 (QACF-2), is found to be robust and accurate (2.35 kcal/mol of weighted total mean absolute deviation error, WTMAD), comparable or slightly improved compared to other flavors of existing parameter-free DHDFs (2.45 or 3.29 kcal/mol for PBE0-2 or PBE0-DH, respectively). The nonlocal expansion coefficients obtained for the current QACF-2 (aHF = 2/3, aPT2 = 1/3) also offer some interesting observation, in that the latter analytical coefficients are very similar to the empirically optimized coefficients in some of the best DHDFs today with high accuracy (1.5 kcal/mol). Effects of quadratic truncation in QACF-2 have been further assessed and justified by estimating the higher-order corrections to be as much as 0.54 kcal/mol. The present derivation and numerical experiments suggest that the quadratic λ dependence, despite its simplicity, is a surprisingly good approximation to the adiabatic connection that can serve as a good starting point for further development of accurate parameter-free density functionals.

Reference Curves Estimation Using Conditional Quantile and Radial Basis Function Network with Mass Constraint

This paper focuses on the improvement of reference curves building \(Y=q(X)\) using a fast algorithm, robust against outliers. Our method consists in plugging a radial basis function neural network in the local linear quantile regression estimation proposed by Yu and Jones (QYJ). This neural network (QRBFc) is designed with a constructive algorithm, introducing a constraint on its integral over the input space. After explaining the different models and algorithms, we compare the QYJ and QRBFc estimators with the quantile regression neural network (QRNN) implemented by A. J. Cannon through simulations with a known underlying model using the R software. We observe that the QRBFc estimator reduces the mean absolute deviation error obtained with other estimators by about 16 %, the introduction of the constraint allowing to lower the number of neurons and therefore the computation time. Finally, using a database of 416 electroencephalograms recorded on preterm infants, we compare the QYJ, QRBFc and QRNN models for the building of brain maturation curves which are based on the dependence of the mean duration of interburst intervals (called IBIs—periods of quiescence between periods of normal electrical activity) with the age. The pathological infants represent 12 % of the total population. Denoting by \(S_A\) the set of individuals whose coordinates (age, mean IBI length) are above the \(90~\%\)-quantile curve, the QRBFc network improves by \(16.5~\%\) the number of pathological infants in \(S_A\) compared to QYJ, when QRNN proved to be too unstable.

An expanded calibration study of the explicitly correlated CCSD(T)-F12b method using large basis set standard CCSD(T) atomization energies

The effectiveness of the recently developed, explicitly correlated coupled cluster method CCSD(T)-F12b is examined in terms of its ability to reproduce atomization energies derived from complete basis set extrapolations of standard CCSD(T). Most of the standard method findings were obtained with aug-cc-pV7Z or aug-cc-pV8Z basis sets. For a few homonuclear diatomic molecules it was possible to push the basis set to the aug-cc-pV9Z level. F12b calculations were performed with the cc-pVnZ-F12 (n = D, T, Q) basis set sequence and were also extrapolated to the basis set limit using a Schwenke-style, parameterized formula. A systematic bias was observed in the F12b method with the (VTZ-F12/VQZ-F12) basis set combination. This bias resulted in the underestimation of reference values associated with small molecules (valence correlation energies <0.5 E(h)) and an even larger overestimation of atomization energies for bigger systems. Consequently, caution should be exercised in the use of F12b for high accuracy studies. Root mean square and mean absolute deviation error metrics for this basis set combination were comparable to complete basis set values obtained with standard CCSD(T) and the aug-cc-pVDZ through aug-cc-pVQZ basis set sequence. However, the mean signed deviation was an order of magnitude larger. Problems partially due to basis set superposition error were identified with second row compounds which resulted in a weak performance for the smaller VDZ-F12/VTZ-F12 combination of basis sets.

Multiplicative Noise Removal via a Learned Dictionary

Multiplicative noise removal is a challenging image processing problem, and most existing methods are based on the maximum a posteriori formulation and the logarithmic transformation of multiplicative denoising problems into additive denoising problems. Sparse representations of images have shown to be efficient approaches for image recovery. Following this idea, in this paper, we propose to learn a dictionary from the logarithmic transformed image, and then to use it in a variational model built for noise removal. Extensive experimental results suggest that in terms of visual quality, peak signal-to-noise ratio, and mean absolute deviation error, the proposed algorithm outperforms state-of-the-art methods.

Semiparametric ARX neural-network models with an application to forecasting inflation

We examine semiparametric nonlinear autoregressive models with exogenous variables (NLARX) via three classes of artificial neural networks: the first one uses smooth sigmoid activation functions; the second one uses radial basis activation functions; and the third one uses ridgelet activation functions. We provide root mean squared error convergence rates for these ANN estimators of the conditional mean and median functions with stationary beta-mixing data. As an empirical application, we compare the forecasting performance of linear and semiparametric NLARX models of US inflation. We find that all of our semiparametric models outperform a benchmark linear model based on various forecast performance measures. In addition, a semiparametric ridgelet NLARX model which includes various lags of historical inflation and the GDP gap is best in terms of both forecast mean squared error and forecast mean absolute deviation error.

Convergence analysis of the sign algorithm for adaptive filtering

We consider the convergence analysis of the sign algorithm for adaptive filtering when the input processes are uncorrelated and Gaussian and a fixed step size /spl mu/>0 is used. Exact recursive equations for the covariance matrix of the deviation error are established for any step size /spl mu/>0. Asymptotic time-averaged convergence for the mean-absolute deviation error, mean-square deviation error, and for the signal mean-square estimation error are established. These results are shown to hold for arbitrary step size /spl mu/>0. >