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Journals and Conferences
We describe and analyze a simple and effective iterative algorithm for solving the optimization problem cast by Support Vector Machines (SVM). Our method alternates between stochastic gradient descent steps and projection steps. We prove that the number of iterations required to obtain a solution of accuracy ε is Õ(1/ε). In contrast, previous… (More)
We study PCA, PLS, and CCA as stochastic optimization problems, of optimizing a population objective based on a sample. We suggest several stochastic approximation (SA) methods for PCA and PLS, and investigate their empirical performance.
We present a method for efficiently training binary and multiclass kernelized SVMs on a Graphics Processing Unit (GPU). Our methods apply to a broad range of kernels, including the popular Gaus- sian kernel, on datasets as large as the amount of available memory on the graphics card. Our approach is distinguished from earlier work in that it cleanly and… (More)
Mini-batch algorithms have been proposed as a way to speed-up stochastic convex optimization problems. We study how such algorithms can be improved using accelerated gradient methods. We provide a novel analysis, which shows how standard gradient methods may sometimes be insufficient to obtain a significant speed-up and propose a novel accelerated gradient… (More)
We study PCA as a stochastic optimization problem and propose a novel stochas-tic approximation algorithm which we refer to as " Matrix Stochastic Gradient " (MSG), as well as a practical variant, Capped MSG. We study the method both theoretically and empirically.
This paper describes the effect of DEM data resolution on predictions from the SWAT model. Measured hydrologic, meteorological, watershed characteristics and water quality data from Moores Creek watershed (near Lincoln, AR, USA) were used in the simulation. The effect of input data resolution was evaluated by running seven scenarios at increasing DEM grid… (More)
We show how to train SVMs with an optimal guarantee on the number of support vectors (up to constants), and with sample complexity and training runtime bounds matching the best known for kernel SVM optimization (i.e. without any additional asymptotic cost beyond standard SVM training). Our method is simple to implement and works well in practice.
In a <i>well-spaced point set</i>, when there is a bounding hypercube, the Voronoi cells all have bounded aspect ratio, i.e., the distance from the Voronoi site to the farthest point in the Voronoi cell divided by the distance to the nearest neighbor in the set is bounded by a small constant. Well-spaced point sets satisfy some important geometric… (More)
We present a novel approach for training kernel Support Vector Machines, establish learning runtime guarantees for our method that are better then those of any other known kernelized SVM optimization approach, and show that our method works well in practice compared to existing alternatives.
Real-world machine learning applications may require functions to be fast-to-evaluate and interpretable, in particular, guaranteed monotonicity of the learned function can be critical to user trust. We propose meeting these goals for low-dimensional machine learning problems by learning flexible, monotonic functions using calibrated interpolated look-up… (More)