Model structure selection (MSS) is a critical problem in the nonlinear identification field. In the framework of polynomial nonlinear autoregressive [moving average] models with exogenous input variables, it is formulated as the combinatorial problem of finding the subset of regressors that yields optimal model accuracy. Increasing the set of potential model terms improves the flexibility of the model but results in a computational overload and may even jeopardize the ability of the MSS algorithm to find the optimal model. In this work, a distributed optimization scheme is developed to tackle the MSS task for large-sized candidate regressor sets. The regressor set is split among a group of independent processors, and each of them executes an MSS routine on its local subset. Then, the processors exchange information regarding the selected models, and the corresponding regressors are distributed among all the units for a new MSS round. The procedure is repeated until convergence of all processors to the same solution. Besides a drastic reduction in the computational time, thanks to the inherent parallelizability of the algorithm execution, the proposed distributed optimization scheme can also be beneficial in terms of model accuracy, due to a more efficient exploration of the search space.KEYWORDS distributed optimization, model structure selection, nonlinear model identification, parallel processing, polynomial NARX models, randomized algorithms INTRODUCTIONBlack-box identification of nonlinear dynamical models is a challenging problem that has received much attention in the last decades. Since its introduction in the works of Leontaritis and Billings, 1,2 the recursive, input-output models of the nonlinear autoregressive [moving average] with exogenous variables (NAR[MA]X) class have been successfully used in many different application fields because of their flexibility and representative capabilities. In the NARX/NARMAX representation, the system output at a given time is calculated as a nonlinear functional expansion of past input, output, and, possibly, noise terms. In particular, most researchers focused on the polynomial expansion, which provides a very convenient linear-in-the-parameters representation for the NARX case that ultimately amounts to a linear regression.The hardest problem in the polynomial NAR[MA]X model identification, however, is not the estimation of the parameters, but rather the estimation of the correct model structure of the underlying system, which is generally unknown. Model structure selection (MSS) is a combinatorial problem that consists in selecting from a set of candidate regressors the combination of terms that results in the most accurate NARX model. An exhaustive search among all possible

A wearable electromagnetic belt system for the detection of hepatic steatosis (lipid accumulation within the major liver cells, hepatocytes), is proposed. To satisfy the requirements of the belt system, an array of body matched antennas is designed. The belt, which goes around the lower chest and over the liver, requires compact, wideband, unidirectional antennas that operate at low microwave frequencies. To avoid using conventional bulky reflector structures, the designed antenna utilizes the loop-dipole combination concept. To enhance electromagnetic wave penetration, the antenna is designed to match the human body. Thus, thanks to the high dielectric loading from the human body, the dipole element of the antenna is easily miniaturized. Since the same principle does not apply on the loop structure, meandered arc-shapes are employed to increase the effective electrical length of the loop. The final antenna design has a measured wide operating bandwidth of 0.58-1.6 GHz with a compact size of 0.096×0.048×0.048λ 3 . The proposed structure is effective in irradiating the torso, where the signal can reach center of the liver at a depth of 90 mm, with 64% of the peak radiated power. An electromagnetic belt is built using twelve elements of the designed antennas. The belt is then tested on a 3D printed torso phantom that includes models of the lungs and liver. Due to close dielectric properties of the other tissues inside the torso, these are represented using an average tissue mimicking mixture with permittivity of 46. Measured data are analyzed using multivariate energy statistics method. A peak measured dissimilarity of 15.1% between steatotic and healthy liver is attained. These initial tests and obtained results indicate the potential of the proposed system as a method to diagnose hepatic steatosis.INDEX TERMS Body-matched antenna, electromagnetic belt, fatty liver disease, statistical based analysis, wearable system.

We here introduce a novel classification approach adopted from the nonlinear model identification framework, which jointly addresses the feature selection (FS) and classifier design tasks. The classifier is constructed as a polynomial expansion of the original features and a selection process is applied to find the relevant model terms. The selection method progressively refines a probability distribution defined on the model structure space, by extracting sample models from the current distribution and using the aggregate information obtained from the evaluation of the population of models to reinforce the probability of extracting the most important terms. To reduce the initial search space, distance correlation filtering is optionally applied as a preprocessing technique. The proposed method is compared to other well-known FS and classification methods on standard benchmark problems. Besides the favorable properties of the method regarding classification accuracy, the obtained models have a simple structure, easily amenable to interpretation and analysis.

DNA microarray datasets are characterized by a large number of features with very few samples, which is a typical cause of overfitting and poor generalization in the classification task. Here we introduce a novel feature selection (FS) approach which employs the distance correlation (dCor) as a criterion for evaluating the dependence of the class on a given feature subset. The dCor index provides a reliable dependence measure among random vectors of arbitrary dimension, without any assumption on their distribution. Moreover, it is sensitive to the presence of redundant terms. The proposed FS method is based on a probabilistic representation of the feature subset model, which is progressively refined by a repeated process of model extraction and evaluation. A key element of the approach is a distributed optimization scheme based on a vertical partitioning of the dataset, which alleviates the negative effects of its unbalanced dimensions. The proposed method has been tested on several microarray datasets, resulting in quite compact and accurate models obtained at a reasonable computational cost.