1,784 research outputs found
HIPAD - A Hybrid Interior-Point Alternating Direction algorithm for knowledge-based SVM and feature selection
We consider classification tasks in the regime of scarce labeled training
data in high dimensional feature space, where specific expert knowledge is also
available. We propose a new hybrid optimization algorithm that solves the
elastic-net support vector machine (SVM) through an alternating direction
method of multipliers in the first phase, followed by an interior-point method
for the classical SVM in the second phase. Both SVM formulations are adapted to
knowledge incorporation. Our proposed algorithm addresses the challenges of
automatic feature selection, high optimization accuracy, and algorithmic
flexibility for taking advantage of prior knowledge. We demonstrate the
effectiveness and efficiency of our algorithm and compare it with existing
methods on a collection of synthetic and real-world data.Comment: Proceedings of 8th Learning and Intelligent OptimizatioN (LION8)
Conference, 201
Sparse Bilinear Logistic Regression
In this paper, we introduce the concept of sparse bilinear logistic
regression for decision problems involving explanatory variables that are
two-dimensional matrices. Such problems are common in computer vision,
brain-computer interfaces, style/content factorization, and parallel factor
analysis. The underlying optimization problem is bi-convex; we study its
solution and develop an efficient algorithm based on block coordinate descent.
We provide a theoretical guarantee for global convergence and estimate the
asymptotical convergence rate using the Kurdyka-{\L}ojasiewicz inequality. A
range of experiments with simulated and real data demonstrate that sparse
bilinear logistic regression outperforms current techniques in several
important applications.Comment: 27 pages, 5 figure
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