Related papers: Model selection for dynamical systems via sparse r…
Penalized regression models are popularly used in high-dimensional data analysis to conduct variable selection and model fitting simultaneously. Whereas success has been widely reported in literature, their performances largely depend on…
We consider the problem of model selection and estimation in sparse high dimensional linear regression models with strongly correlated variables. First, we study the theoretical properties of the dual Lasso solution, and we show that joint…
The efficacy of mathematical models heavily depends on the quality of the training data, yet collecting sufficient data is often expensive and challenging. Many modeling applications require inferring parameters only as a means to predict…
In the context of a high-dimensional linear regression model, we propose the use of an empirical correlation-adaptive prior that makes use of information in the observed predictor variable matrix to adaptively address high collinearity,…
Dynamic feature selection, where we sequentially query features to make accurate predictions with a minimal budget, is a promising paradigm to reduce feature acquisition costs and provide transparency into a model's predictions. The problem…
Identifying governing equations from data is a critical step in the modeling and control of complex dynamical systems. Here, we investigate the data-driven identification of nonlinear dynamical systems with inputs and forcing using…
Approximate Bayesian Computation (ABC) methods have gained in their popularity over the last decade because they expand the horizon of Bayesian parameter inference methods to the range of models for which only forward simulation is…
We derive a new Bayesian Information Criterion (BIC) by formulating the problem of estimating the number of clusters in an observed data set as maximization of the posterior probability of the candidate models. Given that some mild…
In this paper we introduce a new feature selection algorithm to remove the irrelevant or redundant features in the data sets. In this algorithm the importance of a feature is based on its fitting to the Catastrophe model. Akaike information…
Datasets encountered when examining deeper issues in ecology and evolution are often complex. This calls for careful strategies for both model building, model selection, and model averaging. Our paper aims at motivating, exhibiting, and…
When performing regression or classification, we are interested in the conditional probability distribution for an outcome or class variable Y given a set of explanatoryor input variables X. We consider Bayesian models for this task. In…
In a typical supervised machine learning setting, the predictions on all test instances are based on a common subset of features discovered during model training. However, using a different subset of features that is most informative for…
The methodology discussed in this paper aims to enhance choice models' comprehensiveness and explanatory power for forecasting choice outcomes. To achieve these, we have developed a data-driven method that leverages machine learning…
In this document, some general results in approximation theory and matrix analysis with applications to sparse identification of time series models and nonlinear discrete-time dynamical systems are presented. The aforementioned theoretical…
We study model selection by the Bayesian information criterion (BIC) in fixed-dimensional exploratory factor analysis over a fixed finite family of compact covariance classes. Our main result shows that the BIC is strongly consistent for…
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…
Variable selection is essential for improving inference and interpretation in multivariate linear regression. Although a number of alternative regressor selection criteria have been suggested, the most prominent and widely used are the…
Multiresponse data with complex group structures in both responses and predictors arises in many fields, yet, due to the difficulty in identifying complex group structures, only a few methods have been studied on this problem. We propose a…
We consider high-dimensional binary classification by sparse logistic regression. We propose a model/feature selection procedure based on penalized maximum likelihood with a complexity penalty on the model size and derive the non-asymptotic…
The Schwarz or Bayesian information criterion (BIC) is one of the most widely used tools for model comparison in social science research. The BIC however is not suitable for evaluating models with order constraints on the parameters of…