arXiv subjects

Laura Vana-Gür

Publications and source records attributed to Laura Vana-Gür.

7 recordsLinked to original sources

arXiv2024

spar: Sparse Projected Averaged Regression in R

Package spar for R builds ensembles of predictive generalized linear models with high-dimensional predictors. It employs an algorithm utilizing variable screening and random projection tools to efficiently handle the computational challenges associated with large sets of predictors. The package is designed with a strong focus on extensibility. Screening and random projection techniques are implemented as S3 classes with user-friendly constructor functions, enabling users to easily integrate and develop new procedures. This design enhances the package's adaptability and makes it a powerful tool for a variety of high-dimensional applications.

stat.CO↗

arXiv2024

A joint model of correlated ordinal and continuous variables

In this paper we build a joint model which can accommodate for binary, ordinal and continuous responses, by assuming that the errors of the continuous variables and the errors underlying the ordinal and binary outcomes follow a multivariate normal distribution. We employ composite likelihood methods to estimate the model parameters and use composite likelihood inference for model comparison and uncertainty quantification. The complimentary R package mvordnorm implements estimation of this model using composite likelihood methods and is available for download from Github. We present two use-cases in the area of risk management to illustrate our approach.

stat.ME↗

arXiv2024

Data-Driven Random Projection and Screening for High-Dimensional Generalized Linear Models

We address the challenge of correlated predictors in high-dimensional GLMs, where regression coefficients range from sparse to dense, by proposing a data-driven random projection method. This is particularly relevant for applications where the number of predictors is (much) larger than the number of observations and the underlying structure -- whether sparse or dense -- is unknown. We achieve this by using ridge-type estimates for variable screening and random projection to incorporate information about the response-predictor relationship when performing dimensionality reduction. We demonstrate that a ridge estimator with a small penalty is effective for random projection and screening, but the penalty value must be carefully selected. Unlike in linear regression, where penalties approaching zero work well, this approach leads to overfitting in non-Gaussian families. Instead, we recommend a data-driven method for penalty selection. This data-driven random projection improves prediction performance over conventional random projections, even surpassing benchmarks like elastic net. Furthermore, an ensemble of multiple such random projections combined with probabilistic variable screening delivers the best aggregated results in prediction and variable ranking across varying sparsity levels in simulations at a rather low computational cost. Finally, three applications with count and binary responses demonstrate the method's advantages in interpretability and prediction accuracy.

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arXiv2024

Cellwise robust and sparse principal component analysis

A first proposal of a sparse and cellwise robust PCA method is presented. Robustness to single outlying cells in the data matrix is achieved by substituting the squared loss function for the approximation error by a robust version. The integration of a sparsity-inducing $L_1$ or elastic net penalty offers additional modeling flexibility. For the resulting challenging optimization problem, an algorithm based on Riemannian stochastic gradient descent is developed, with the advantage of being scalable to high-dimensional data, both in terms of many variables as well as observations. The resulting method is called SCRAMBLE (Sparse Cellwise Robust Algorithm for Manifold-based Learning and Estimation). Simulations reveal the superiority of this approach in comparison to established methods, both in the casewise and cellwise robustness paradigms. Two applications from the field of tribology underline the advantages of a cellwise robust and sparse PCA method.

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arXiv2024

Automated Model Selection for Generalized Linear Models

In this paper, we show how mixed-integer conic optimization can be used to combine feature subset selection with holistic generalized linear models to fully automate the model selection process. Concretely, we directly optimize for the Akaike and Bayesian information criteria while imposing constraints designed to deal with multicollinearity in the feature selection task. Specifically, we propose a novel pairwise correlation constraint that combines the sign coherence constraint with ideas from classical statistical models like Ridge regression and the OSCAR model.

stat.ML↗

arXiv2024

Sparse Data-Driven Random Projection in Regression for High-Dimensional Data

We examine the linear regression problem in a challenging high-dimensional setting with correlated predictors where the vector of coefficients can vary from sparse to dense. In this setting, we propose a combination of probabilistic variable screening with random projection tools as a viable approach. More specifically, we introduce a new data-driven random projection tailored to the problem at hand and derive a theoretical bound on the gain in expected prediction error over conventional random projections. The variables to enter the projection are screened by accounting for predictor correlation. To reduce the dependence on fine-tuning choices, we aggregate over an ensemble of linear models. A thresholding parameter is introduced to obtain a higher degree of sparsity. Both this parameter and the number of models in the ensemble can be chosen by cross-validation. In extensive simulations, we compare the proposed method with other random projection tools and with classical sparse and dense methods and show that it is competitive in terms of prediction across a variety of scenarios with different sparsity and predictor covariance settings. We also show that the method with cross-validation is able to rank the variables satisfactorily. Finally, we showcase the method on two real data applications.

stat.ME↗

arXiv2024

Multivariate ordinal regression for multiple repeated measurements

In this paper we propose a multivariate ordinal regression model which allows the joint modeling of three-dimensional panel data containing both repeated and multiple measurements for a collection of subjects. This is achieved by a multivariate autoregressive structure on the errors of the latent variables underlying the ordinal responses, where we distinguish between the correlations at a single point in time and the persistence over time. The error distribution is assumed to be normal or Student t distributed. The estimation is performed using composite likelihood methods. We perform several simulation exercises to investigate the quality of the estimates in different settings as well as in comparison with a Bayesian approach. The simulation study confirms that the estimation procedure is able to recover the model parameters well and is competitive in terms of computation time. We also introduce R package mvordflex and illustrate how this implementation can be used to estimate the proposed model in a user-friendly, convenient way. Finally, we illustrate the framework on a data set containing firm failure and credit ratings information from the rating agencies S&P and Moody's for US listed companies.

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