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Recently much attention has been devoted to model selection through regularization methods in regression and classification where features are selected by use of a penalty function (e.g. Lasso in Tibshirani, 1996). While the resulting sparsity leads to more interpretable models, one may want to further incorporate natural groupings or hierarchical(More)
Extracting useful information from high-dimensional data is an important focus of today's statistical research and practice. Penalized loss function minimization has been shown to be effective for this task both theoretically and empirically. With the virtues of both regularization and sparsity, the L1-penalized squared error minimization method Lasso has(More)
Given n observations of a p-dimensional random vector, the covariance matrix and its inverse (precision matrix) are needed in a wide range of applications. Sample covariance (e.g. its eigenstructure) can misbehave when p is comparable to the sample size n. Regularization is often used to mitigate the problem. In this paper, we proposed an 1 penalized(More)
Since its early use in least squares regression problems, the ℓ 1-penalization framework for variable selection has been employed in conjunction with a wide range of loss functions encompassing regression, classification and survival analysis. While a well developed theory exists for the ℓ 1-penalized least squares estimates, few results concern the(More)
Since its early use in least squares regression problems, the 1-penalization framework for variable selection has been employed in conjunction with a wide range of loss functions encompassing regression, classification and survival analysis. While a well developed theory exists for the 1-penalized least squares estimates, few results concern the behavior of(More)
Advances in Wireless Sensor Networks (WSN) technology have provided promising possibilities in detecting a change in the state of a structure through monitoring its features estimated using sensor data. The natural vibration properties of the structure are a set of features commonly used for this purpose and are often estimated using a multivariate(More)
The Minimum Description Length (MDL) principle is an important tool for retrieving knowledge from data as it embodies the scientific strife for simplicity in describing the relationship among variables. As MDL and other model selection criteria penalize models on their dimensionality, the estimation problem involves a combinatorial search over subsets of(More)
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