We consider the class of convex minimization problems, composed of a self-concordant function, such as the logdet metric, a convex data fidelity term h(.) and, a regularizing — possibly non-smooth — function g(.). This type of problems have recently attracted a great deal of interest, mainly due to their omnipresence in top-notch applications. Under this locally Lipschitz continuous gradient setting, we analyze the convergence behavior of proximal Newton schemes with the added twist of a probable presence of inexact evaluations. We prove attractive convergence rate guarantees and enhance state-of-the-art optimization schemes to accommodate such developments. Experimental results on sparse covariance estimation show the merits of our algorithm, both in terms of recovery efficiency and complexity.

Mutual information (MI) based approaches are a popular feature selection paradigm. Although the stated goal of MI-based feature selection is to identify a subset of features that share the highest mutual information with the class variable, most current MI-based techniques are greedy methods that make use of low dimensional MI quantities. The reason for using low dimensional approximation has been mostly attributed to the difficulty associated with estimating the high dimensional MI from limited samples. In this paper, we argue a different viewpoint that, given a very large amount of data, the high dimensional MI objective is still problematic to be employed as a meaningful optimization criterion, due to its overfitting nature: the MI almost always increases as more features are added, thus leading to a trivial solution which includes all features. We propose a novel approach to the MI-based feature selection problem, in which the overfitting phenomenon is controlled rigourously by means of a statistical test. We develop local and global optimization algorithms for this new feature selection model, and demonstrate its effectiveness in the applications of explaining variables and objects.

Mutual information (MI) based approaches are a popular feature selection paradigm. Although the stated goal of MI-based feature selection is to identify a subset of features that share the highest mutual information with the class variable, most current MI-based techniques are greedy methods that make use of low dimensional MI quantities. The reason for using low dimensional approximation has been mostly attributed to the difficulty associated with estimating the high dimensional MI from limited samples. In this paper, we argue a different viewpoint that, given a very large amount of data, the high dimensional MI objective is still problematic to be employed as a meaningful optimization criterion, due to its overfitting nature: the MI almost always increases as more features are added, thus leading to a trivial solution which includes all features. We propose a novel approach to the MI-based feature selection problem, in which the overfitting phenomenon is controlled rigourously by means of a statistical test. We develop local and global optimization algorithms for this new feature selection model, and demonstrate its effectiveness in the applications of explaining variables and objects.

Mutual information (MI) based approaches are a popular feature selection paradigm. Although the stated goal of MI-based feature selection is to identify a subset of features that share the highest mutual information with the class variable, most current MI-based techniques are greedy methods that make use of low dimensional MI quantities. The reason for using low dimensional approximation has been mostly attributed to the difficulty associated with estimating the high dimensional MI from limited samples. In this paper, we argue a different viewpoint that, given a very large amount of data, the high dimensional MI objective is still problematic to be employed as a meaningful optimization criterion, due to its overfitting nature: the MI almost always increases as more features are added, thus leading to a trivial solution which includes all features. We propose a novel approach to the MI-based feature selection problem, in which the overfitting phenomenon is controlled rigourously by means of a statistical test. We develop local and global optimization algorithms for this new feature selection model, and demonstrate its effectiveness in the applications of explaining variables and objects.

Mutual information (MI) based approaches are a popular feature selection paradigm. Although the stated goal of MI-based feature selection is to identify a subset of features that share the highest mutual information with the class variable, most current MI-based techniques are greedy methods that make use of low dimensional MI quantities. The reason for using low dimensional approximation has been mostly attributed to the difficulty associated with estimating the high dimensional MI from limited samples. In this paper, we argue a different viewpoint that, given a very large amount of data, the high dimensional MI objective is still problematic to be employed as a meaningful optimization criterion, due to its overfitting nature: the MI almost always increases as more features are added, thus leading to a trivial solution which includes all features. We propose a novel approach to the MI-based feature selection problem, in which the overfitting phenomenon is controlled rigourously by means of a statistical test. We develop local and global optimization algorithms for this new feature selection model, and demonstrate its effectiveness in the applications of explaining variables and objects.

Mutual information (MI) based approaches are a popular feature selection paradigm. Although the stated goal of MI-based feature selection is to identify a subset of features that share the highest mutual information with the class variable, most current MI-based techniques are greedy methods that make use of low dimensional MI quantities. The reason for using low dimensional approximation has been mostly attributed to the difficulty associated with estimating the high dimensional MI from limited samples. In this paper, we argue a different viewpoint that, given a very large amount of data, the high dimensional MI objective is still problematic to be employed as a meaningful optimization criterion, due to its overfitting nature: the MI almost always increases as more features are added, thus leading to a trivial solution which includes all features. We propose a novel approach to the MI-based feature selection problem, in which the overfitting phenomenon is controlled rigourously by means of a statistical test. We develop local and global optimization algorithms for this new feature selection model, and demonstrate its effectiveness in the applications of explaining variables and objects.

Mutual information (MI) based approaches are a popular feature selection paradigm. Although the stated goal of MI-based feature selection is to identify a subset of features that share the highest mutual information with the class variable, most current MI-based techniques are greedy methods that make use of low dimensional MI quantities. The reason for using low dimensional approximation has been mostly attributed to the difficulty associated with estimating the high dimensional MI from limited samples. In this paper, we argue a different viewpoint that, given a very large amount of data, the high dimensional MI objective is still problematic to be employed as a meaningful optimization criterion, due to its overfitting nature: the MI almost always increases as more features are added, thus leading to a trivial solution which includes all features. We propose a novel approach to the MI-based feature selection problem, in which the overfitting phenomenon is controlled rigourously by means of a statistical test. We develop local and global optimization algorithms for this new feature selection model, and demonstrate its effectiveness in the applications of explaining variables and objects.

Mutual information (MI) based approaches are a popular feature selection paradigm. Although the stated goal of MI-based feature selection is to identify a subset of features that share the highest mutual information with the class variable, most current MI-based techniques are greedy methods that make use of low dimensional MI quantities. The reason for using low dimensional approximation has been mostly attributed to the difficulty associated with estimating the high dimensional MI from limited samples. In this paper, we argue a different viewpoint that, given a very large amount of data, the high dimensional MI objective is still problematic to be employed as a meaningful optimization criterion, due to its overfitting nature: the MI almost always increases as more features are added, thus leading to a trivial solution which includes all features. We propose a novel approach to the MI-based feature selection problem, in which the overfitting phenomenon is controlled rigourously by means of a statistical test. We develop local and global optimization algorithms for this new feature selection model, and demonstrate its effectiveness in the applications of explaining variables and objects.

Mutual information (MI) based approaches are a popular feature selection paradigm. Although the stated goal of MI-based feature selection is to identify a subset of features that share the highest mutual information with the class variable, most current MI-based techniques are greedy methods that make use of low dimensional MI quantities. The reason for using low dimensional approximation has been mostly attributed to the difficulty associated with estimating the high dimensional MI from limited samples. In this paper, we argue a different viewpoint that, given a very large amount of data, the high dimensional MI objective is still problematic to be employed as a meaningful optimization criterion, due to its overfitting nature: the MI almost always increases as more features are added, thus leading to a trivial solution which includes all features. We propose a novel approach to the MI-based feature selection problem, in which the overfitting phenomenon is controlled rigourously by means of a statistical test. We develop local and global optimization algorithms for this new feature selection model, and demonstrate its effectiveness in the applications of explaining variables and objects.

Mutual information (MI) based approaches are a popular feature selection paradigm. Although the stated goal of MI-based feature selection is to identify a subset of features that share the highest mutual information with the class variable, most current MI-based techniques are greedy methods that make use of low dimensional MI quantities. The reason for using low dimensional approximation has been mostly attributed to the difficulty associated with estimating the high dimensional MI from limited samples. In this paper, we argue a different viewpoint that, given a very large amount of data, the high dimensional MI objective is still problematic to be employed as a meaningful optimization criterion, due to its overfitting nature: the MI almost always increases as more features are added, thus leading to a trivial solution which includes all features. We propose a novel approach to the MI-based feature selection problem, in which the overfitting phenomenon is controlled rigourously by means of a statistical test. We develop local and global optimization algorithms for this new feature selection model, and demonstrate its effectiveness in the applications of explaining variables and objects.