In this paper, we provide explicit upper bounds on some distances between the (law of the) output of a random Gaussian neural network and (the law of) a random Gaussian vector. Our main results concern deep random Gaussian neural networks with a rather general activation function. The upper bounds show how the widths of the layers, the activation function, and other architecture parameters affect the Gaussian approximation of the output. Our techniques, relying on Stein's method and integration by parts formulas for the Gaussian law, yield estimates on distances that are indeed integral probability metrics and include the convex distance. This latter metric is defined by testing against indicator functions of measurable convex sets and so allows for accurate estimates of the probability that the output is localized in some region of the space, which is an aspect of a significant interest both from a practitioner's and a theorist's perspective. We illustrated our results by some numerical examples.

We investigate the consistency and the rate of convergence of the adaptive Lasso estimator for the parameters of linear AR(p) time series with a white noise which is a strictly stationary and ergodic martingale difference. Roughly speaking, we prove that (i) If the white noise has a finite second moment, then the adaptive Lasso estimator is almost sure consistent (ii) If the white noise has a finite fourth moment, then the error estimate converges to zero with the same rate as the regularizing parameters of the adaptive Lasso estimator. Such theoretical findings are applied to estimate the parameters of INAR(p) time series and to estimate the fertility function of Hawkes processes. The results are validated by some numerical simulations, which show that the adaptive Lasso estimator allows for a better balancing between bias and variance with respect to the Conditional Least Square estimator and the classical Lasso estimator.

We propose AFTNet, a novel network-constraint survival analysis method based on the Weibull accelerated failure time (AFT) model solved by a penalized likelihood approach for variable selection and estimation. When using the log-linear representation, the inference problem becomes a structured sparse regression problem for which we explicitly incorporate the correlation patterns among predictors using a double penalty that promotes both sparsity and grouping effect. Moreover, we establish the theoretical consistency for the AFTNet estimator and present an efficient iterative computational algorithm based on the proximal gradient descent method. Finally, we evaluate AFTNet performance both on synthetic and real data examples.

Food allergy (FA) affects approximately 6–8% of children worldwide causing a significant impact on the quality of life of children and their families. In past years, the possible role of weaning in the development of FA has been studied. According to recent studies, this is still controversial and influenced by several factors, such as the type of food, the age at food introduction and family history. In this narrative review, we aimed to collect the most recent evidence about weaning and its role in FA development, organizing the gathered data based on both the type of study and the food. As shown in most of the studies included in this review, early food introduction did not show a potential protective role against FA development, and we conclude that further evidence is needed from future clinical trials.

In this talk we provide explicit upper bounds on some distances between the (law of the) output of a random Gaussian neural network and (the law of) a random Gaussian vector. Our main results concern deep random Gaussian neural networks, with a rather general activation function. The upper bounds show how the widths of the layers, the activation function and other architecture parameters affect the Gaussian approximation of the output. Our techniques, relying on Stein's method and integration by parts formulas for the Gaussian law, yield estimates on distances which are indeed integral probability metrics, and include the convex distance. This latter metric is defined by testing against indicator functions of measurable convex sets, and so allows for accurate estimates of the probability that the output is localized in some region of the space. Such estimates have a significant interest both from a practitioner's and a theorist's perspective.

Estimates networks of conditional dependencies (Gaussian graphical models) from multiple classes of data (similar but not exactly, i.e. measurements on different equipment, in different locations or for various sub-types). Package also allows to generate simulation data and evaluate the performance. Implementation of the method described in Angelini, De Canditiis and Plaksienko (2022) <doi:10.3390/math10213983>.

Background: Major Depressive Disorder (MDD) is a psychiatric illness that is often associated with potentially life -threatening physiological changes and increased risk for suicidal behavior. Electroencephalography (EEG) research suggests an association between depression and specific frequency imbalances in the frontal brain re-gion. Further, while recently developed technology has been proposed to simplify EEG data acquisition, more research is still needed to support its use in patients with MDD.Methods: Using the 14-channel EMOTIV EPOC cap, we recorded resting state EEG from 15 MDD patients with suicidal ideation (SI) vs. 12 healthy controls (HC) to investigate putative power spectral density (PSD) between -group differences at the F3 and F4 electrode sites. Specifically, we explored 1) between-group alpha power asymmetries (AA), 2) between-group differences in delta, theta, alpha and beta power, 3) correlations between PSD data and scores in the Beck's Depression Inventory-II (BDI-II), Beck's Anxiety Inventory (BAI), Reasons for Living Inventory (RFL), and Self-Disgust Questionnaire (SDS).Results: When compared to HC, patients had higher scores on the BAI (p = 0.0018), BDI-II (p = 0.0001) or SDS (p = 0.0142) scale and lower scores in the RFL (p = 0.0006) scale. The PSD analysis revealed no between-group difference or correlation with questionnaire scores for any of the measures considered.Conclusions: The present study could not confirm previous research suggesting frequency-specific anomalies in depressed persons with SI but might suggest that frontal EEG imbalances reflect greater anxiety and negative self -referencing. Future studies should confirm these findings in a larger population sample.

In this paper, we extend the result on the probability of (falsely) connecting two distinct components when learning a GGM (Gaussian Graphical Model) by the joint regression based technique. While the classical method of regression based technique learns the neighbours of each node one at a time through a Lasso penalized regression, its joint modification, considered here, learns the neighbours of each node simultaneously through a group Lasso penalized regression.

Given a random sample drawn from a Multivariate Bernoulli Variable (MBV), we consider the problem of estimating the structure of the undirected graph for which the distribution is pairwise Markov and the parameters' vector of its exponential form. We propose a simple method that provides a closed form estimator of the parameters' vector and through its support also provides an estimate of the undirected graph associated with the MBV distribution. The estimator is proved to be asymptotically consistent but it is feasible only in low-dimensional regimes. Synthetic examples illustrate its performance compared with another method that represents state of the art in literature. Finally, the proposed procedure is used to analyze a data set in the pediatric allergology area showing its practical efficiency.

In this work, we propose and explore a novel network-constraint survival methodology considering the Weibull accelerated failure time (AFT) model combined with a penalized likelihood approach for variable selection and estimation [2]. Our estimator explicitly incorporates the correlation patterns among predictors using a double penalty that promotes both sparsity and the grouping effect. In or- der to solve the structured sparse regression problems we present an efficient iterative computational algorithm based on proximal gradient descent method [1]. We establish the theoretical consistency of the proposed estimator and moreover, we evaluate its performance both on synthetic and real data examples.

Estimates networks of conditional dependencies (Gaussian graphical models) from multiple classes of data (similar but not exactly, i.e. measurements on different equipment, in different locations or for various sub-types). Package also allows to generate simulation data and evaluate the performance. Implementation of the method described in Angelini, De Canditiis and Plaksienko (2022)

Background: The oral food challenge test (OFC) represents the gold standard for the diagnosis of food allergy (FA). It is also necessary for the safe reintroduction of the allergen into the diet of the patient. However, it is burdened with serious side effects. We aimed to determine the role of Skin Prick Tests (SPT) and of component resolved diagnosis (CRD) in the decision to perform OFC in patients aged between 0 and 18 years with FA towards tree nuts, peanuts and seeds. Material and Methods: We enrolled 22 patients (mean age of 10.91±4.22 years; 12 males) with a diagnosis of FA towards nuts, peanuts and seeds. A total of 29 OFCs were performed (6 of these patients were tested for more than one allergen at different times) with the following allergens: peanut, hazelnut, walnut, almond, pistachio and sesame. For each patient, were performed SPT and IgE levels through CRDs towards the culprit allergens (ImmunoCAP). In particular, for the first two variables we considered the diameter of the wheels for the allergen tested for OFC (Prick-OFC) and the mean diameter of the wheals for the other untested allergens (Prick-non OFC). For the other two variables, we focused on the IgE towards the CRDs characterizing the allergens of which they were diagnosed and tested at the OFC (CRD-OFC) and the two most cross-reactive CRDs with the first chosen CRD (CRD-cross). We conducted an inferential statistical analysis with the aim of answering the question: is it possible to predict OFC outcome using the values of the four covariates CRD- OFC, CRD-cross, Prick-OFC and Prick-non OFC? The discriminative power of each of the four covariates was first analyzed independently of the others, by performing a T-test on the two groups for each of them (Y=1, OFC positive result and Y=0, OFC negative result), figure 1. Results: The most indicative variables of a possible positive reaction to OFC are the values of the CRD-cross (p =0.01957) and of the Prick-OFC (p=0.046936), while the prick-non OFC (p=0.30857) and CRD-OFC(P=0.24193) variables do not seem to have discriminatory power. Multivariate logistic regression analysis indicates that none of the four variables considered is statistically predictive of test result. Conclusions: These results are unable to quantify the likelihood that a patient will have a positive OFC based on their SPT and IgE assays. However, we can qualitatively say what to expect by considering its CRD-cross and Prick-OFC values rather than those of CRD-OFC and Prick-non OFC.

In this paper, we consider the problem of estimating the graphs of conditional dependencies between variables (i.e., graphical models) from multiple datasets under Gaussian settings. We present jewel 2.0, which improves our previous method jewel 1.0 by modeling commonality and class-specific differences in the graph structures and better estimating graphs with hubs, making this new approach more appealing for biological data applications. We introduce these two improvements by modifying the regression-based problem formulation and the corresponding minimization algorithm. We also present, for the first time in the multiple graphs setting, a stability selection procedure to reduce the number of false positives in the estimated graphs. Finally, we illustrate the performance of jewel 2.0 through simulated and real data examples. The method is implemented in the new version of the R package jewel

Background COVID-19 lockdown caused sudden changes in people's lifestyle, as a consequence of the forced lockdown imposed by governments all over the world. We aimed to evaluate the impact of lockdown on body mass index (BMI) in a cohort of allergic children and adolescents. Methods From the first of June until the end of October 2020, we submitted a written questionnaire to all the patients who, after lockdown, carried out a visit at the Pediatric Allergy Unit of the Department of Mother-Child, Urological Science, Sapienza University of Rome. The questionnaire was composed by 10 questions, referring to the changes in their daily activities. Data were extrapolated from the questionnaire and then analyzed considering six variables: BMI before and BMI after lockdown, sugar intake, sport, screens, sleep, and anxiety. Results One hundred fifty-three patients agreed to answer our questionnaire. Results showed a statistically significant increase in the BMI after lockdown (20.97 kg/m2 ± 2.63) with respect to the BMI before lockdown (19.18 kg/m2 ± 2.70). A multivariate regression analysis showed that the two variables that mostly influenced the increase in BMI were sleep and anxiety. Conclusions For the analyzed cohort of allergic children and adolescents we obtained significant gain in BMI as consequences of lockdown, which can be explained by many factors: high consumption of consolatory food, less sport activities, more time spent in front of screens, sleep alteration associated with increased anxiety. All these factors acted together, although sleep alteration and increased anxiety were the most influential factors that led to the worsening or the onset of weight gain, creating the basis for future health problems.

Cow's milk allergy (CMA) is a common condition in the pediatric population. CMA can induce a diverse range of symptoms of variable intensity. It occurs mainly in the first year of life, and if the child is not breastfed, hypoallergenic formula is the dietary treatment. Extensively hydrolyzed cow's milk formulas (eHF) with documented hypo-allergenicity can be recommended as the first choice, while amino acid-based formulas (AAF) are recommended for patients with more severe symptoms. Hydrolyzed rice-based formulas (HRFs) are a suitable alternative for infants with CMA that cannot tolerate or do not like eHF and in infants with severe forms of CMA. In the present paper, we reviewed the nutritional composition of HRFs as well as studies regarding their efficacy and tolerance in children, and we provided an updated overview of the recent evidence on the use of HRFs in CMA. The available studies provide evidence that HRFs exhibit excellent efficacy and tolerance and seem to be adequate in providing normal growth in healthy children as well as in children with CMA.

Background Diagnosis and treatment of 22q11.2 deletion syndrome (22q11.2DS) have led to improved life expectancy and achievement of adulthood. Limited data on long-term outcomes reported an increased risk of premature death for cardiovascular causes, even without congenital heart disease (CHD). The aim of this study was to assess the cardiac function in adolescents and young adults with 22q11.2DS without CHDs. Methods A total of 32 patients (20M, 12F; mean age 26.00 ± 8.08 years) and a healthy control group underwent transthoracic echocardiography, including Tissue Doppler Imaging (TDI) and 2-dimensional Speckle Tracking Echocardiography (2D-STE). Results Compared to controls, 22q11.2DS patients showed a significant increase of the left ventricle (LV) diastolic and systolic diameters (p = 0.029 and p = 0.035 respectively), interventricular septum thickness (p = 0.005), LV mass index (p < 0.001) and aortic root size (p < 0.001). 2D-STE analysis revealed a significant reduction of LV global longitudinal strain (p < 0.001) in 22q11.2DS than controls. Moreover, several LV diastolic parameters were significantly different between groups. Conclusions Our results suggest that an echocardiographic follow-up in 22q11.2DS patients without CHDs can help to identify subclinical impairment of the LV and evaluate a potential progression of aortic root dilation over time, improving outcomes, reducing long-term complications and allowing for a better prognosis.

We study the consistency and the oracle properties of the adaptive Lasso estimator for the coefficients of a linear AR(p) time series with a strictly stationary white noise (not necessarily described by i.i.d. r.v.'s). We apply the results to INAR(p) time series and to the non-parametric inference of the fertility function of a Hawkes point process. We present some numerical simulations to emphasize the advantages of the proposed procedure with respect to more classical ones and finally we apply it to a set of epidemiological data

We introduce a new methodology for anomaly detection (AD) in multichannel fast oscillating signals based on nonparametric penalized regression. Assuming the signals share similar shapes and characteristics, the estimation procedures are based on the use of the Rational-Dilation Wavelet Transform (RADWT), equipped with a tunable Q-factor able to provide sparse representations of functions with different oscillations persistence. Under the standard hypothesis of Gaussian additive noise, we model the signals by the RADWT and the anomalies as additive in each signal. Then we perform AD imposing a double penalty on the multiple regression model we obtained, promoting group sparsity both on the regression coefficients and on the anomalies. The first constraint preserves a common structure on the underlying signal components; the second one aims to identify the presence/absence of anomalies. Numerical experiments show the performance of the proposed method in different synthetic scenarios as well as in a real case.

In this paper, we consider the problem of estimating multiple Gaussian Graphical Models from high-dimensional datasets. We assume that these datasets are sampled from different distributions with the same conditional independence structure, but not the same precision matrix. We propose jewel, a joint data estimation method that uses a node-wise penalized regression approach. In particular, jewel uses a group Lasso penalty to simultaneously guarantee the resulting adjacency matrix's symmetry and the graphs' joint learning. We solve the minimization problem using the group descend algorithm and propose two procedures for estimating the regularization parameter. Furthermore, we establish the estimator's consistency property. Finally, we illustrate our estimator's performance through simulated and real data examples on gene regulatory networks.