Novel robust time series analysis for long-term and short-term prediction

Nonlinear phenomena are universal in ecology. However, their inference and prediction are generally difficult because of autocorrelation and outliers. A traditional least squares method for parameter estimation is capable of improving short-term prediction by estimating autocorrelation, whereas it has weakness to outliers and consequently worse long-term prediction. In contrast, a traditional robust regression approach, such as the least absolute deviations method, alleviates the influence of outliers and has potentially better long-term prediction, whereas it makes accurately estimating autocorrelation difficult and possibly leads to worse short-term prediction. We propose a new robust regression approach that estimates autocorrelation accurately and reduces the influence of outliers. We then compare the new method with the conventional least squares and least absolute deviations methods by using simulated data and real ecological data. Simulations and analysis of real data demonstrate that the new method generally has better long-term and short-term prediction ability for nonlinear estimation problems using spawner–recruitment data. The new method provides nearly unbiased autocorrelation even for highly contaminated simulated data with extreme outliers, whereas other methods fail to estimate autocorrelation accurately.

Algorithms for descent along nodal straight lines in the problem of estimating regression equations using the least absolute deviations method

A problem of estimating linear regression equations by the least absolute deviations method is considered. The exact methods of implementation of the method are significantly inferior in performance to the least square method. The fastest algorithm based on coordinate descent along nodal straight lines has a computational complexity proportional to the square of the number of observations, which limits the practical application of the method to monitoring and diagnostic tasks. The goal of the study is to describe a faster version of the descent along the nodal straight lines, as well as to evaluate the performance. Reduction of the computational costs is achieved due to the fact that instead of calculating the values of the objective function at nodal points, we find the derivative of the objective function in the vicinity of these points along the nodal line. The computational efficiency of gradient descent along nodal straight lines is estimated. For a typical computer, a comparative analysis of the average calculation time for various algorithms of descent along nodal straight lines is performed. A simple example is given to illustrate the implementation of a gradient descent procedure. Along with reduction of the computational costs, we also eliminated the possibility of accumulating computational errors when determining the values of the objective function for large samples. Moreover, gradient descent is quite simple for implementation. This makes it possible to use the method of least absolute deviations as an alternative to the least square method in various practical applications.

Satellite image inpainting with deep generative adversarial neural networks

This work addresses the problem of recovering lost or damaged satellite image pixels (gaps) caused by sensor processing errors or by natural phenomena like cloud presence. Such errors decrease our ability to monitor regions of interest and significantly increase the average revisit time for all satellites. This paper presents a novel neural system based on conditional deep generative adversarial networks (cGAN) optimized to fill satellite imagery gaps using surrounding pixel values and static high-resolution visual priors. Experimental results show that the proposed system outperforms traditional and neural network baselines. It achieves a normalized least absolute deviations error of ( & decrease in error compared with the two baselines) and a mean squared error loss of ( & decrease in error) over the test set. The model can be deployed within a remote sensing data pipeline to reconstruct missing pixel measurements for near-real-time monitoring and inference purposes, thus empowering policymakers and users to make environmentally informed decisions.

Novel Robust Time Series Analysis for Long-term and Short-term Prediction

Nonlinear phenomena are universal in ecology. However, their inference and prediction are generally difficult because of autocorrelation and outliers. A traditional least squares method for parameter estimation is capable of improving short-term prediction by estimating autocorrelation, whereas it has weakness to outliers and consequently worse long-term prediction. In contrast, a traditional robust regression approach, such as the least absolute deviations method, alleviates the influence of outliers and has potentially better long-term prediction, whereas it makes accurately estimating autocorrelation difficult and possibly leads to worse short-term prediction. We propose a new robust regression approach that estimates autocorrelation accurately and reduces the influence of outliers. We then compare the new method with traditional least squares and least absolute deviations methods using simulated data and real ecological data. Simulations and analysis of real data demonstrate that the new method generally has better long-term and short-term prediction ability for nonlinear estimation problems using spawner--recruitment data. The new method provides nearly unbiased autocorrelation even for highly contaminated simulated data with extreme outliers, whereas the other methods fail to estimate autocorrelation accurately.

Robust Bearing-Only Localization Using Total Least Absolute Residuals Optimization

Robust techniques critically improve bearing-only target localization when the relevant measurements are being corrupted by impulsive noise. Resistance to isolated gross errors refers to the conventional least absolute residual (LAR) method, and its estimate can be determined by linear programming when pseudolinear equations are set. The LAR approach, however, cannot reduce the bias attributed to the correlation between system matrices and noise vectors. In the present study, perturbations are introduced into the elements of the system matrix and the data vector simultaneously, and the total optimization problem is formulated based on least absolute deviations. Subsequently, an equivalent form of total least absolute residuals (TLAR) is obtained, and an algorithm is developed to calculate the robust estimate by dual ascent algorithms. Moreover, the performance of the proposed method is verified through the numerical simulations by using two types of localization geometries, i.e., random and linear. As revealed from the results, the TLAR algorithm is capable of exhibiting significantly higher localization accuracy as compared with the LAR method.

Enhancing Satellite Clock Bias Prediction Accuracy in the Case of Jumps with an Improved Grey Model

High accuracy and reliable predictions of the bias of in-orbit atomic clocks are crucial to the application of satellites, while their clocks cannot transfer time information with the earth stations. It brings forward a new short-term, mid-long-term, and long-term prediction approach with the grey predicting model (GM(1, 1)) improved by the least absolute deviations (GM(1, 1)-LAD) when there are abnormal cases (larger fluctuations, jumps, and/or singular points) in SCBs. Firstly, it introduces the basic GM(1, 1) models. As the parameters of the conventional GM(1, 1) model determined by the least squares method (LSM) is not the best in these cases, leading to magnify the fitting errors at the abnormal points, the least absolute deviations (LAD) is used to optimize the conventional GM(1, 1) model. Since the objective function is a nondifferentiable characteristic, some function transformation is inducted. Then, the linear programming and the simplex method are used to solve it. Moreover, to validate the prediction performances of the improved model, six prediction experiments are performed. Compared with those of the conventional GM(1, 1) model and autoregressive moving average (ARMA) model, results indicate that (1) the improved model is more adaptable to SCBs predictions of the abnormal cases; (2) the root mean square (RMS) improvement for the improved model are 5.7%∼81.7% and 6.6%∼88.3%, respectively; (3) the maximum improvement of the pseudorange errors (PE) and mean absolute errors (MAE) for the improved model could reach up to 88.30%, 89.70%, and 87.20%, 85.30%, respectively. These results suggest that our improved method can enhance the prediction accuracy and PE for these abnormal cases in SCBs significantly and effectively and deliver a valuable insight for satellite navigation.

Hybrid Fuzzy Regression Analysis Using the F-Transform

This paper proposes a hybrid estimation algorithm for independently estimating the response function for the center and the response function for the spread in fuzzy regression model. The proposed algorithm combines the least absolute deviations estimation with discriminant analysis. In addition, the F-transform is used to convert spreads of the dependent variable into several groups. Two examples show that our method is superior to the existing methods based on the fuzzy regression model that assumes the same function for spread and center.