Search results for "Penalized Likelihood"

Model selection for penalized Gaussian Graphical Models

2013

High-dimensional data refers to the case in which the number of parameters is of one or more order greater than the sample size. Penalized Gaussian graphical models can be used to estimate the conditional independence graph in high-dimensional setting. In this setting, the crucial issue is to select the tuning parameter which regulates the sparsity of the graph. In this paper, we focus on estimating the "best" tuning parameter. We propose to select this tuning parameter by minimizing an information criterion based on the generalized information criterion and to use a stability selection approach in order to obtain a more stable graph. The performance of our method is compared with the state…

Inferential tools in penalized logistic regression for small and sparse data: A comparative study.

2016

This paper focuses on inferential tools in the logistic regression model fitted by the Firth penalized likelihood. In this context, the Likelihood Ratio statistic is often reported to be the preferred choice as compared to the ‘traditional’ Wald statistic. In this work, we consider and discuss a wider range of test statistics, including the robust Wald, the Score, and the recently proposed Gradient statistic. We compare all these asymptotically equivalent statistics in terms of interval estimation and hypothesis testing via simulation experiments and analyses of two real datasets. We find out that the Likelihood Ratio statistic does not appear the best inferential device in the Firth penal…

Dynamic factorial graphical models for dynamic networks

2014

Dynamic networks models describe a growing number of important scientific processes, from cell biology and epidemiology to sociology and finance. Estimating dynamic networks from noisy time series data is a difficult task since the number of components involved in the system is very large. As a result, the number of parameters to be estimated is typically larger than the number of observations. However, a characteristic of many real life networks is that they are sparse. For example, the molec- ular structure of genes make interactions with other components a highly-structured and, therefore, a sparse process. Penalized Gaussian graphical models have been used to estimate sparse networks. H…

Penalized inference in multivariate ordered logistic models: theory and applications

2010

Bivariate logistic models for the analysis of the students' University "success"

2012

We analyze the students’ success at University by considering their performance in terms of both “qualitative performance”, measured by their grade average, and “quantitative performance”, measured by University Credits accumulated. To jointly model both marginal and association relationships with covariates, the analysis has been carried out by fitting a bivariate ordered logistic model (BOLM), in a nonparametric fashion, by penalized maximum likelihood estimation. The advantages of such model are in terms of parsimony and parameters interpretation, while preserving goodness-of-fit. The application regards an engineering student (ES) cohort from the University of Palermo.

Sparse model-based network inference using Gaussian graphical models

2010

We consider the problem of estimating a sparse dynamic Gaussian graphical model with L1 penalized maximum likelihood of structured precision matrix. The structure can consist of specific time dynamics, known presence or absence of links in the graphical model or equality constraints on the parameters. The model is defined on the basis of partial correlations, which results in a specific class precision matrices. A priori L1 penalized maximum likelihood estimation in this class is extremely difficult, because of the above mentioned constraints, the computational complexity of the L1 constraint on the side of the usual positive-definite constraint. The implementation is non-trivial, but we sh…

Penalized logistic regression for small or sparse data: interval estimators revisited

2015

This paper focuses on interval estimation in logistic regression models fitted through the Firth penalized log-likelihood. In this context, many authors have claimed superiority of the Likelihood ratio statistic with respect to the (wrong) Wald statistic via simulation evidence. We re-assess such findings by detailing the inferential tools also including in the comparisons the (right) Wald statistic and other statistics neglected in previous literature. In particular, we assess performances of the CIs estimators by simulation and compare them in a real data set. Differently from previous findings, the Likelihood ratio statistic does not appear to be the best inferential device in Firth pena…

A new tuning parameter selector in lasso regression

2019

Penalized regression models are popularly used in high-dimensional data analysis to carry out variable selction and model fitting simultaneously. Whereas success has been widely reported in literature, their performance largely depend on the tuning parameter that balances the trade-off between model fitting and sparsity. In this work we introduce a new tuning parameter selction criterion based on the maximization of the signal-to-noise ratio. To prove its effectiveness we applied it to a real data on prostate cancer disease.

An association model for bivariate data with application to the anlysis of university students' success.

2015

The academic success of students is a priority for all universities. We analyze the students' success at university by considering their performance in terms of both ‘qualitative performance’, measured by their mean grade, and ‘quantitative performance’, measured by university credits accumulated. These data come from an Italian University and concern a cohort of students enrolled at the Faculty of Economics. To jointly model both the marginal relationships and the association structure with covariates, we fit a bivariate ordered logistic model by penalized maximum likelihood estimation. The penalty term we use allows us to smooth the association structure and enlarge the range of possible …

Selecting the tuning parameter in penalized Gaussian graphical models

2019

Penalized inference of Gaussian graphical models is a way to assess the conditional independence structure in multivariate problems. In this setting, the conditional independence structure, corresponding to a graph, is related to the choice of the tuning parameter, which determines the model complexity or degrees of freedom. There has been little research on the degrees of freedom for penalized Gaussian graphical models. In this paper, we propose an estimator of the degrees of freedom in $$\ell _1$$ -penalized Gaussian graphical models. Specifically, we derive an estimator inspired by the generalized information criterion and propose to use this estimator as the bias term for two informatio…