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The Akaike information criterion (AIC) is a model selection criterion widely used in practical applications. The AIC is an estimator of the log-likelihood expected value, and measures the discrepancy between the true model and the estimated…
Regularized m-estimators are widely used due to their ability of recovering a low-dimensional model in high-dimensional scenarios. Some recent efforts on this subject focused on creating a unified framework for establishing oracle bounds,…
Deep learning is renowned for its theory-practice gap, whereby principled theory typically fails to provide much beneficial guidance for implementation in practice. This has been highlighted recently by the benign overfitting phenomenon:…
Model selection is the problem of distinguishing competing models, perhaps featuring different numbers of parameters. The statistics literature contains two distinct sets of tools, those based on information theory such as the Akaike…
Model selection is of fundamental importance to high dimensional modeling featured in many contemporary applications. Classical principles of model selection include the Kullback-Leibler divergence principle and the Bayesian principle,…
We develop an algorithm for model selection which allows for the consideration of a combinatorially large number of candidate models governing a dynamical system. The innovation circumvents a disadvantage of standard model selection which…
In statistical modeling area, the Akaike information criterion AIC, is a widely known and extensively used tool for model choice. The {\phi}-divergence test statistic is a recently developed tool for statistical model selection. The…
AIC is commonly used for model selection but the precise value of AIC has no direct interpretation. We are interested in quantifying a difference of risks between two models. This may be useful for both an explanatory point of view or for…
In the problem of selecting variables in a multivariate linear regression model, we derive new Bayesian information criteria based on a prior mixing a smooth distribution and a delta distribution. Each of them can be interpreted as a fusion…
Model selection is a pivotal process in the quantitative sciences, where researchers must navigate between numerous candidate models of varying complexity. Traditional information criteria, such as the corrected Akaike Information Criterion…
In segmented regression, when the regression function is continuous at the change-points that are the boundaries of the segments, it is also called joinpoint regression, and the analysis package developed by \cite{KimFFM00} has become a…
We introduce a generalized information criterion that contains other well-known information criteria, such as Bayesian information Criterion (BIC) and Akaike information criterion (AIC), as special cases. Furthermore, the proposed spectral…
The Bayesian and Akaike information criteria aim at finding a good balance between under- and over-fitting. They are extensively used every day by practitioners. Yet we contend they suffer from at least two afflictions: their penalty…
Given a random sample from a multivariate population, estimating the number of large eigenvalues of the population covariance matrix is an important problem in Statistics with wide applications in many areas. In the context of Principal…
We investigate the issue of post-selection inference for a fixed and a mixed parameter in a linear mixed model using a conditional Akaike information criterion as a model selection procedure. Within the framework of linear mixed models we…
Bayesian model averaging is a practical method for dealing with uncertainty due to model specification. Use of this technique requires the estimation of model probability weights. In this work, we revisit the derivation of estimators for…
Classical confidence intervals after best subset selection are widely implemented in statistical software and are routinely used to guide practitioners in scientific fields to conclude significance. However, there are increasing concerns in…
The use of Bayesian information criterion (BIC) in the model selection procedure is under the assumption that the observations are independent and identically distributed (i.i.d.). However, in practice, we do not always have i.i.d. samples.…
The information criterion AIC has been used successfully in many areas of statistical modeling, and since it is derived based on the Taylor expansion of the log-likelihood function and the asymptotic distribution of the maximum likelihood…
Regularized models have been applied in lots of areas, with high-dimensional data sets being popular. Because tuning parameter decides the theoretical performance and computational efficiency of the regularized models, tuning parameter…