Elastic-Net Regularization in Learning Theory

Within the framework of statistical learning theory we analyze in detail the so-called elastic-net regularization scheme proposed by Zou and Hastie for the selection of groups of correlated variables. To investigate on the statistical properties of this scheme and in particular on its consistency properties, we set up a suitable mathematical framework. Our setting is random-design regression where we allow the response variable to be vector-valued and we consider prediction functions which are linear combination of elements ({\em features}) in an infinite-dimensional dictionary. Under the assumption that the regression function admits a sparse representation on the dictionary, we prove that there exists a particular ``{\em elastic-net representation}'' of the regression function such that, if the number of data increases, the elastic-net estimator is consistent not only for prediction but also for variable/feature selection. Our results include finite-sample bounds and an adaptive scheme to select the regularization parameter. Moreover, using convex analysis tools, we derive an iterative thresholding algorithm for computing the elastic-net solution which is different from the optimization procedure originally proposed by Zou and HastieComment: 32 pages, 3 figure

Adaptive Kernel Methods Using the Balancing Principle

The regularization parameter choice is a fundamental problem in supervised learning since the performance of most algorithms crucially depends on the choice of one or more of such parameters. In particular a main theoretical issue regards the amount of prior knowledge on the problem needed to suitably choose the regularization parameter and obtain learning rates. In this paper we present a strategy, the balancing principle, to choose the regularization parameter without knowledge of the regularity of the target function. Such a choice adaptively achieves the best error rate. Our main result applies to regularization algorithms in reproducing kernel Hilbert space with the square loss, though we also study how a similar principle can be used in other situations. As a straightforward corollary we can immediately derive adaptive parameter choice for various kernel methods recently studied. Numerical experiments with the proposed parameter choice rules are also presented

PREDICTION MODELS FOR FREESTYLE PERFORMANCE TIMES IN MASTER SWIMMERS

This study was designed to define the most important factors to predict freestyle performance times in 135 elite master swimmers by prediction models which include age, anthropometric and strength variables. To cross validate these equations found for Elite swimmers, we used a group composed by 126 lower technical level age - and experience - matched master swimmers. Results demonstrated that age, height and hand grip strength were the best predictors in short events, whereas age and height predict middle and long events. The corresponding coefficients of determination (R2) of performance times were 0.84 in 50m, 0.73 in 100m, 0.75 in 200m, 0.66 in 400m and 0.63 in the 800m events. A good correlation have been found when these models have been applied in 126 non-elite master swimmers demonstrating to be useful in all Master swimmers

Understanding neural networks with reproducing kernel Banach spaces

Characterizing the function spaces corresponding to neural networks can provide a way to understand their properties. In this paper we discuss how the theory of reproducing kernel Banach spaces can be used to tackle this challenge. In particular, we prove a representer theorem for a wide class of reproducing kernel Banach spaces that admit a suitable integral representation and include one hidden layer neural networks of possibly infinite width. Further, we show that, for a suitable class of ReLU activation functions, the norm in the corresponding reproducing kernel Banach space can be characterized in terms of the inverse Radon transform of a bounded real measure, with norm given by the total variation norm of the measure. Our analysis simplifies and extends recent results in [43, 34, 35]

Quality of life and psychosocial impacts of the different restrictive measures during one year into the COVID-19 pandemic on patients with cancer in Italy: An ecological study

Background: The aim of the study was to assess the perceived quality of life and the psychosocial impact of the various restrictive measures due to COVID-19 pandemic on cancer patients in Italy, as well as their perception of the relationship with doctors and caregivers. Methods: This study compares three population-based observational studies of patients with cancer carried out in three consecutive time periods characterized by different restrictive measures using a self-administered online questionnaire. Results: Among the basic needs, psychological and medical support appeared to be prevalent; so did the need for safe transportation to reach the treatment facilities. Internet was the main source of information on the coronavirus. Although 74.6% of the total number of patients did not give up hospital therapies, 34.8% complained about variations in the continuity of treatment, with different percentages in the three samples. The majority of the sample (73.8%) was worried of being infected, but 21.9% did not share their anxieties and worries with others. The multivariate regression analysis showed that a pessimistic perception of quality of life was influenced by living in extra-urban areas and alone (OR = 1.4; OR = 2.1); while a perception of a reduced physical function result affected by the state of anxiety and stress (OR = 1.9) and the difficulties in continuity of medical assistance (OR = 2.2). The scoring of the SF-12 in the Physical Component Summary and Mental Component Summary scores showed a fluctuating trend throughout the three periods investigated. Conclusions: It is important for health professionals, caregivers and social workers to identify the new needs in order to enhance home care interventions, personalize and optimize care, ensure continuity of care and guarantee a high quality of life even in a health emergency situation

Thymomas: a review.

Thymomas are neoplasma of thymic epithelial cells. They may be benign or malignant and may associate with locai ìnvasiveness and paraneoplastic diseases. Myasthenia gravis is often associated with thymomas, bui this is not thè rule. Several classifications have been proposed: some of them follow thè histopathological findings (Rosai and Levine, Snover, Marino and Muller- Hermelink classification), other emphasizes thè clinic-pathological stage (Masaoka, Verley and Hollmann stadiation). One third of thymomas is asymptomatic. Diagnosis is made often by plain X-ray and confirmed by Computed Tomography or fine needle biopsy. Surgery is effective in 100% of noninvasive cases and in 58% of invasive ones. Radio and chemotherapy are recommended only in advanced or inoperable stages

Cancer of the Thyroid in patients over the age of fifty.

Aim. The authors performed a retrospective investigation of patients over thè age of 50, in order to detect any peculiarities of cancer of thè thyroid possibly affecting surgical treatment and whether age itself represented an independent prognostic factor. Methods. A total of 152 patients were examined at thè Department of Surgical Science of "La Sapienza" University of Rome with a minimum follow- up of 10 years. The 152 subjects recruited were divided into 3 age groups: from 51 to 60 years, (74 patients); from 61 to 70 years, (57 patients); from 71 to 80 years, (21 patients). Resulti. Relating thè different histologic types to age group, there was found to be a lower incidence of well-differentiated carcinoma and a relative increase in thè epidermoid and undifferentiated forms in older patients. In thè 51-60 age group 80% of thè patients were at stages I and II, while in thè 71-80 age group 56.2% of cases were at stages III and IV. Conclusion. In thè elderly patient undifferentiated, anaplastic or epidermoid forms and those with a higher biologica! aggressiveness are more frequently found. We believe that prompt diagnosis would present thè surgeon with neoplasms at an early stage and with less aggressive histotypes, thus ensuring greater scope for radicai surgical treatment and appreciably enhancing prognosis

Measuring the magnetic axis alignment during solenoids working

A method for monitoring the misalignment of the magnetic axis in solenoids is proposed. This method requires only a few measurements of the magnetic field at fixed positions inside the magnet aperture, and thus overcomes the main drawback of sturdy moving mechanics of other Hall sensor-based methods. Conversely to state-of-the-art axis determination, the proposed method can be applied also during magnet operations, when the axis region and almost the whole remaining magnet aperture are not accessible. Moreover, only a few measurements of the magnetic field at fixed positions inside the magnet aperture are required: thus a slow process such as the mapping of the whole aperture of a magnet by means of moving stages is not necessary. The mathematical formulation of the method is explained, and a case study on a model of a multi–layer solenoid is presented. For this case study, the uncertainty is assessed and the optimal placement of the Hall transducers is derived

Predictive equations not always overestimate the resting energy expenditure in amyotrophic lateral sclerosis patients

Fil: Libere, Guillermo P.. Centro del Parque; ArgentinaFil: Guastavino, Sabrina. Centro del Parque; ArgentinaFil: Escobar, Miguel A.. Centro del Parque; ArgentinaFil: de Vito, Eduardo. Centro del Parque; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Houssay; Argentin