A Survey on Machine Learning for Optical Communication [Machine Learning View] <s> G. Regression <s> We introduce low complexity machine learning method method (based on lasso regression, which promotes sparsity, to identify the interaction between symbols in different time slots and to select the minimum number relevant perturbation terms that are employed) for nonlinearity mitigation. The immense intricacy of the problem calls for the development of "smart" methodology, simplifying the analysis without losing the key features that are important for recovery of transmitted data. The proposed sparse identification method for optical systems (SINO) allows to determine the minimal (optimal) number of degrees of freedom required for adaptive mitigation of detrimental nonlinear effects. We demonstrate successful application of the SINO method both for standard fiber communication links (over 3 dB gain) and for few-mode spatial-division-multiplexing systems. <s> BIB001 </s> A Survey on Machine Learning for Optical Communication [Machine Learning View] <s> G. Regression <s> We have developed a low complexity machine learning based nonlinear impairment equalization scheme and demonstrated its successful performance in SDM transmission links achieving compensation of both inter- and intra- channel Kerr-based nonlinear effects. The method operates in one sample per symbol and in one computational step. It is adaptive, i.e. it does not require a knowledge of system parameters, and it is scalable to different power levels and modulation formats. The method can be straightforwardly expanded to multi-channel systems and to any other type of nonlinear impairment. <s> BIB002 </s> A Survey on Machine Learning for Optical Communication [Machine Learning View] <s> G. Regression <s> Using monitored physical parameters in a learning process, we decrease design margins by reducing uncertainties on the input parameters of a Quality of Transmission (QoT) tool, improving the accuracy of the signal-to-noise ratio prediction. <s> BIB003
Definition: Regression is composed of statistical processes for deriving the relationships between variables, and includes several techniques. Actually, it helps better understanding changes of a dependent variable as a response to the variation of one of the independent variables, while fixing other variables. Regression estimates regression function (a function of the independent variables); mostly, it estimates the average of dependent variable while fixing independent variables; sometimes, the focus is on a quantile, or other location parameter of the distribution of the dependent variable while fixing the independent variables. Regression analysis is widely used for prediction and forecasting, where its use has substantial overlap with the field of machine learning. Fig.13. a. LSTM-RNN, b. Bidirectional LSTM-RNN, and c. TDNN. Fiber OC: Least Absolute Shrinkage and Selection Operator (Lasso) regression (Fig.16.a) is a linear regression algorithm, which shrinks data towards a central point, and develops simple, sparse models. In order to identify the interaction between symbols in different time slots and to select the minimum number of relevant employed perturbation terms, sparsity phenomena is required. Considering this scenario, Lasso regression is a good choice for simplifying nonlinearity mitigation analysis without losing the important key features BIB001 BIB002 . Supervised algorithms have a loss function that should be minimized; the Gradient descent is a well-known algorithm for this minimization. It could further extended and used as a learning algorithm, and be used in OC applications (e.g. QoT BIB003 ). Although fiber optic mathematical modeling is hard, some papers deployed some simplified OC models for ML. However, it should be notified that ML has reduced uncertainties on input parameters of these models, by improving the accuracy of the SNR estimation based on a propagation model.