In this article, we deal with the model selection problem for estimating a Gaussian Graphical Model (GGM) by regression based techniques. In fact, although regression based techniques are well understood and have good theoretical properties, it is still not clear which criterion is more appropriate for model selection. In this work we do a comparative study between CV and BIC, obtaining important conclusions that can be of practical interest in different contexts of data analysis. In this article, we deal with the model selection problem for estimating a Gaussian Graphical Model (GGM) by regression based techniques. In fact, although regression based techniques are well understood and have good theoretical properties, it is still not clear which criterion is more appropriate for model selection. In this work we do a comparative study between CV and BIC, obtaining important conclusions that can be of practical interest in different contexts of data analysis.

Background: Probiotics may prevent the allergic response development due to their antiinflammatory and immunomodulatory effects. The aim of this study is to determine if the prophylactic treatment with a mixture of Bifidobacterium animalis subsp. Lactis BB12 and Enterococcus faecium L3 would reduce symptoms and need for drug use in children with allergic rhinitis (AR). Methods: The study included 250 children aged from 6 to 17 years, affected by AR. Patients were randomly assigned to the intervention group (150) or to the placebo group (100). Patients in the intervention group, in addition to conventional therapy (local corticosteroids and/or oral antihistamines), were treated in the 3 months preceding the onset of symptoms related to the presence of the allergen to which the children were most sensitized, with a daily oral administration of a probiotic mixture containing the Bifidobacterium animalis subsp. Lactis BB12 DSM 15954 and the Enterococcus faecium L3 LMG P-27496 strain. We used Nasal Symptoms Score (NSS) to evaluate AR severity before and after the treatment with probiotics or placebo. Results: the patients in the intervention group had a significant reduction in their NSS after probiotic treatment (p-value = 2.2 × 10. Moreover, for the same group of patients, we obtained a significant reduction in the intake of pharmacological therapy. In particular, we obtained a reduction in the use of oral antihistamines (p-value = 2.2 × 10), local corticosteroids (p-value = 2.2 × 10), and of both drugs (p-value 1.5 × 10). Conclusions: When administered as a prophylactic treatment, a mixture of BB12 and L3 statistically decreased signs and symptoms of AR and reduced significantly the need of conventional therapy.

The idea that individuals tend to choose a romantic partner following similarities on personality traits has always attracted much attention in the psychological literature, although results were controversial. We conducted a new data analysis approach to personality traits of 235 newlywed couples. Univariate analysis revealed that a neurotic husband is usually paired with a lesser extrovert and open wife. To figure out if this mating selection pattern may be translated in a mathematical predictive model a twofold approach was employed by using Partial Least Squares regression and machine learning algorithm. The experimental results demonstrate that marital assortment for personality is a multi-trait complementarity process but these data are unable to predict human mating.

Graphical models are well-known mathematical objects for describing conditional dependency relationships between random variables of a complex system. Gaussian graphical models refer to the case of multivariate Gaussian variable for which the graphical model is encoded through the support of corresponding inverse covariance (precision) matrix. We consider a problem of estimating multiple Gaussian graphical models from high- dimensional data sets under the assumption that they share the same conditional independence structure. However, the individual correlation matrices can differ. Such a problem can be motivated by applications where data comes from different sources and can be collected in distinct classes or groups. We propose a joint data estimation that uses a node-wise penalized regression approach. Grouped Lasso penalty simultaneously guarantees the resulting adjacency matrix's symmetry and the joint learning of the graphs. We solve the minimization problem using the group descent algorithm and establish the proposed solution's consistency and sparsity properties. Finally, we show how the regularization parameter can be estimated using cross-validation and BIC. We provide a novel R package jewel with the implementation of the proposed method and illustrate our estimator's performance through simulated and real data examples. We compare the proposed approach with other available alternatives.

A technique for the restoration of low resonance component and high res-onance component of K independently measured signals is presented. The definitionof low and high resonance component is given by the Rational Dilatation WaveletTransform (RADWT), a particular kind of finite frame that provides sparse repre-sentation of functions with different oscillations persistence. It is assumed that thesignals are measured simultaneously on several independent channels and in eachchannel the underlying signal is the sum of two components: the low resonancecomponent and the high resonance component, both sharing some common char-acteristic between the channels. Components restoration is performed by means ofthe lasso-type penalty and back-fitting algorithm. Numerical experiments show theperformance of the proposed method in different synthetic scenarios highlightingthe advantage of estimating the two components separately rather than together.

We consider the problem of learning the link parameters as well as the structure of a binary-valued pairwise Markov model. Under sparsity assumption, we propose a method based on l1-regularized logistic regression, which estimate globally the whole set of edges and link parameters. Unlike the more recent methods discussed in literature that learn the edges and the corresponding link parameters one node at a time, in this work we propose a method that learns all the edges and corresponding link parameters simultaneously for all nodes. The idea behind this proposal is to exploit the reciprocal information of the nodes between each other during the estimation process. Numerical experiments highlight the advantage of this technique and confirm the intuition behind it. (C) 2020 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.

A new technique for nonparametric regression of multichannel signals is presented. The technique is 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. In particular, two different frames are obtained by two RADWT with different Q-factors that give sparse representations of functions with low and high resonance. It is assumed that the signals are measured simultaneously on several independent channels and that they share the low resonance component and the spectral characteristics of the high resonance component. Then, a regression analysis is performed by means of the grouped lasso penalty. Furthermore, a result of asymptotic optimality of the estimator is presented using reasonable assumptions and exploiting recent results on group-lasso like procedures. Numerical experiments show the performance of the proposed method in different synthetic scenarios as well as in a real case example for the analysis and joint detection of sleep spindles and K-complex events for multiple electroencephalogram (EEG) signals. (C) 2018 Elsevier B.V. All rights reserved.

A new technique for nonparametric regression of multichannel signals is presented. The technique is 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. In particular, two different frames are obtained by two RADWT with different Q-factors that give sparse representations of functions with low and high resonance. It is assumed that the signals are measured simultaneously on several independent channels and that they share the low resonance component and the spectral characteristics of the high resonance component. Then, a regression analysis is performed by means of the grouped lasso penalty. Furthermore, a result of asymptotic optimality of the estimator is presented using reasonable assumptions and exploiting recent results on group-lasso like procedures. Numerical experiments show the performance of the proposed method in different synthetic scenarios as well as in a real case example for the analysis and joint detection of sleep spindles and K-complex events for multiple electroencephalogram (EEG) signals.

We consider a general statistical linear inverse problem, where the solution is represented via a known (possibly overcomplete) dictionary that allows its sparse representation. We propose two different approaches. A model selection estimator selects a single model by minimizing the penalized empirical risk over all possible models. By contrast with direct problems, the penalty depends on the model itself rather than on its size only as for complexity penalties. A Q-aggregate estimator averages over the entire collection of estimators with properly chosen weights. Under mild conditions on the dictionary, we establish oracle inequalities both with high probability and in expectation for the two estimators. Moreover, for the latter estimator these inequalities are sharp. The proposed procedures are implemented numerically and their performance is assessed by a simulation study.

This chapter presents the most common and useful tests of hypothesis for bioinformatics applications. The hypothesis tests divide essentially into two categories: parametric and nonparametric. At the first category belong those tests based on the assumption of knowing the distribution of the sampling population(s) and inference is drawn on one or more unknown parameter(s); at the second category belong those tests that are "distribution-free" which generally have much less assumptions. For each test, we will present the mathematical hypothesis under which it is applicable and the statistics used to apply it.

Overcomplete representations such as wavelets and windowed Fourier expansions have become mainstays of modern statistical data analysis. In the present work, in the context of general finite frames, we derive an oracle expression for the mean quadratic risk of a linear diagonal de-noising procedure which immediately yields the optimal linear diagonal estimator. Moreover, we obtain an expression for an unbiased estimator of the risk of any smooth shrinkage rule. This last result motivates a set of practical estimation procedures for general finite frames that can be viewed as the generalization of the classical procedures for orthonormal bases. A simulation study verifies the effectiveness of the proposed procedures with respect to the classical ones and confirms that the correlations induced by frame structure should be explicitly treated to yield an improvement in estimation precision.

In this contribution we deal with the problem of learning an undi- rected graph which encodes the conditional dependence relationship be- tween variables of a complex system, given a set of observations of this system. This is a very central problem of modern data analysis and it comes out every time we want to investigate a deeper relationship be- tween random variables, which is different from the classical dependence usually measured by the covariance. In particular, in this contribution we deal with the case of Gaussian Graphical Models (GGMs) for which the system of variables has a mul- tivariate gaussian distribution. We revise some of the existing techniques for such a problem and propose a smart implementation of the symmetric parallel regression technique which turns out to be very competitive for learning sparse GGMs under high dimensional data regime.

In this paper the Wiener estimator for signal-denoising is generalized to finite frame operators. In particular, a two-stage procedure which results in a non-linear and non-diagonal estimator is proposed. Advantages and disadvantages with respect to the classical Wiener estimator used with orthonormal basis operator are discussed showing results on standard and real test signals.

HVAC systems are the largest energy consumers in a building and a clean HVAC system can get about 11% in energy saving. Moreover, particulate pollution represents one of the main causes of cancer death and several health damages. This paper presents an innovative and not invasive procedure for the automatic indoor air quality assessment that depends on HVAC cleaning conditions. It is based on a mathematical algorithm that processes a few on-site physical measurements that are acquired by dedicated sensors at suitable locations with a specif-ic time table. The output of the algorithm is a set of indexes that provide a snapshot of the sys-tem with separated zoom on filters and ducts. The proposed methodology contributes to opti-mize both HVAC maintenance procedures and air quality preservation. Robustness, portability and low implementation costs allow to plan maintenance intervention, limiting it only when standard HVAC working conditions need to be restored.

This paper presents a methodology for assessing and monitoring the cleaning state of a heating, ventilation, and air conditioning (HVAC) system of a building. It consists of a noninvasive method for measuring the amount of dust in the whole ventilation system, that is, the set of filters and air ducts. Specifically, it defines the minimum amount of measurements, their time table, locations, and acquisition conditions. The proposed method promotes early intervention on the system and it guarantees high indoor air quality and proper HVAC working conditions. The effectiveness of the method is proved by some experimental results on different study cases.

In the present paper, we constructed an estimator of a delta contaminated mixing density function $g(\lam)$ of an intensity $\lambda$ of the Poisson distribution. The estimator is based on an expansion of the continuous portion $g_0(\lambda)$ of the unknown pdf over an overcomplete dictionary with the recovery of the coefficients obtained as the solution of an optimization problem with Lasso penalty. In order to apply Lasso technique in the, so called, prediction setting where it requires virtually no assumptions on the dictionary and, moreover, to ensure fast convergence of Lasso estimator, we use a novel formulation of the optimization problem based on the inversion of the dictionary elements. We formulate conditions on the dictionary and the unknown mixing density that yield a sharp oracle inequality for the norm of the difference between $g_0 (\lambda)$ and its estimator and, thus, obtain a smaller error than in a minimax setting. Numerical simulations and comparisons with the Laguerre functions based estimator recently constructed by \cite{Comte} also show advantages of our procedure. At last, we apply the technique developed in the paper to estimation of a delta contaminated mixing density of the Poisson intensity of the Saturn's rings data.

Overcomplete representations such as wavelets and windowed Fourier expansions have become mainstays of modern statistical data analysis. Here we derive expressions for the mean quadratic risk of shrinkage estimators in the context of general finite frames, which include any fullrank linear expansion of vector data in a finite-dimensional setting. We provide several new results and practical estimation procedures that take into account the geometric correlation structure of frame elements. These results motivate aggregation estimators and block thresholding procedures, and reinforce that the correlations induced by frame structure should be explicitly treated to yield improvements in estimation. A simulation study confirms these improvements.

Results: We carried out a simulation study to assess the performance of 5 widely used tools, such as: CEM, Cufflinks, iReckon, RSEM, and SLIDE. All of them have been used with default parameters. In particular, we considered the effect of the following three different scenarios: the availability of complete annotation, incomplete annotation, and no annotation at all. Moreover, comparisons were carried out using the methods in three different modes of action. In the first mode, the methods were forced to only deal with those isoforms that are present in the annotation; in the second mode, they were allowed to detect novel isoforms using the annotation as guide; in the third mode, they were operating in fully data driven way (although with the support of the alignment on the reference genome). In the latter modality, precision and recall are quite poor. On the contrary, results are better with the support of the annotation, even though it is not complete. Finally, abundance estimation error often shows a very skewed distribution. The performance strongly depends on the true real abundance of the isoforms. Lowly (and sometimes also moderately) expressed isoforms are poorly detected and estimated. In particular, lowly expressed isoforms are identified mainly if they are provided in the original annotation as potential isoforms. Background: The main goal of the whole transcriptome analysis is to correctly identify all expressed transcripts within a specific cell/tissue- at a particular stage and condition - to determine their structures and to measure their abundances. RNA-seq data promise to allow identification and quantification of transcriptome at unprecedented level of resolution, accuracy and low cost. Several computational methods have been proposed to achieve such purposes. However, it is still not clear which promises are already met and which challenges are still open and require further methodological developments.

In non-parametric regression analysis the advantage of frames with respect to classical orthonormal bases is that they can furnish an efficient representation of a more broad class of functions. For example, fast oscillating functions as audio, speech, sonar, radar, EEG and stock market are much more well represented by a frame, with similar oscillating characteristic, than by a classical orthonormal basis. In this respect, a new frame based shrinkage estimator is derived as the Empirical Regularized version of the optimal Shrinkage estimator generalized to the frame operator. An analytic expression of it is furnished leading to an efficient implementation. Results on standard and real test functions are shown. © 2014 Elsevier B.V. All rights reserved.