Frank-Wolfe algorithms for convex minimization have recently gained considerable attention from the Optimization and Machine Learning communities, as their properties make them a suitable choice in a variety of applications. However, as each iteration requires to optimize a linear model, a clever implementation is crucial to make such algorithms viable on large-scale datasets. For this purpose, approximation strategies based on a random sampling have been proposed by several researchers. In this work, we perform an experimental study on the effectiveness of these techniques, analyze possible alternatives and provide some guidelines based on our results.

Solving different types of optimization models (including parameters fitting) for support vector machines on large-scale training data is often an expensive computational task. This paper proposes a multilevel algorithmic framework that scales efficiently to very large data sets. Instead of solving the whole training set in one optimization process, the support vectors are obtained and gradually refined at multiple levels of coarseness of the data. The proposed framework includes: (a) construction of hierarchy of large-scale data coarse representations, and (b) a local processing of updating the hyperplane throughout this hierarchy. Our multilevel framework substantially improves the computational time without loosing the quality of classifiers. The algorithms are demonstrated for both regular and weighted support vector machines. Experimental results are presented for balanced and imbalanced classification problems. Quality improvement on several imbalanced data sets has been observed.

We introduce a method called multi-scale local shape analysis, or MLSA, for extracting features that describe the local structure of points within a dataset. The method uses both geometric and topological features at multiple levels of granularity to capture diverse types of local information for subsequent machine learning algorithms operating on the dataset. Using synthetic and real dataset examples, we demonstrate significant performance improvement of classification algorithms constructed for these datasets with correspondingly augmented features.

In this paper, we consider a supervised learning setting where side knowledge is provided about the labels of unlabeled examples. The side knowledge has the effect of reducing the hypothesis space, leading to tighter generalization bounds, and thus possibly better generalization. We consider several types of side knowledge, the first leading to linear and polygonal constraints on the hypothesis space, the second leading to quadratic constraints, and the last leading to conic constraints. We show how different types of domain knowledge can lead directly to these kinds of side knowledge. We prove bounds on complexity measures of the hypothesis space for quadratic and conic side knowledge, and show that these bounds are tight in a specific sense for the quadratic case.

We present an approximation scheme for support vector machine models that use an RBF kernel. A second-order Maclaurin series approximation is used for exponentials of inner products between support vectors and test instances. The approximation is applicable to all kernel methods featuring sums of kernel evaluations and makes no assumptions regarding data normalization. The prediction speed of approximated models no longer relates to the amount of support vectors but is quadratic in terms of the number of input dimensions. If the number of input dimensions is small compared to the amount of support vectors, the approximated model is significantly faster in prediction and has a smaller memory footprint. An optimized C++ implementation was made to assess the gain in prediction speed in a set of practical tests. We additionally provide a method to verify the approximation accuracy, prior to training models or during run-time, to ensure the loss in accuracy remains acceptable and within known bounds.

Classifiers based on sparse representations have recently been shown to provide excellent results in many visual recognition and classification tasks. However, the high cost of computing sparse representations at test time is a major obstacle that limits the applicability of these methods in large-scale problems, or in scenarios where computational power is restricted. We consider in this paper a simple yet efficient alternative to sparse coding for feature extraction. We study a classification scheme that applies the soft-thresholding nonlinear mapping in a dictionary, followed by a linear classifier. A novel supervised dictionary learning algorithm tailored for this low complexity classification architecture is proposed. The dictionary learning problem, which jointly learns the dictionary and linear classifier, is cast as a difference of convex (DC) program and solved efficiently with an iterative DC solver. We conduct experiments on several datasets, and show that our learning algorithm that leverages the structure of the classification problem outperforms generic learning procedures. Our simple classifier based on soft-thresholding also competes with the recent sparse coding classifiers, when the dictionary is learned appropriately. The adopted classification scheme further requires less computational time at the testing stage, compared to other classifiers. The proposed scheme shows the potential of the adequately trained soft-thresholding mapping for classification and paves the way towards the development of very efficient classification methods for vision problems.

Actively sampled data can have very different characteristics than passively sampled data. Therefore, it's promising to investigate using different inference procedures during AL than are used during passive learning (PL). This general idea is explored in detail for the focused case of AL with cost-weighted SVMs for imbalanced data, a situation that arises for many HLT tasks. The key idea behind the proposed InitPA method for addressing imbalance is to base cost models during AL on an estimate of overall corpus imbalance computed via a small unbiased sample rather than the imbalance in the labeled training data, which is the leading method used during PL.

There is a broad range of BioNLP tasks for which active learning (AL) can significantly reduce annotation costs and a specific AL algorithm we have developed is particularly effective in reducing annotation costs for these tasks. We have previously developed an AL algorithm called ClosestInitPA that works best with tasks that have the following characteristics: redundancy in training material, burdensome annotation costs, Support Vector Machines (SVMs) work well for the task, and imbalanced datasets (i.e. when set up as a binary classification problem, one class is substantially rarer than the other). Many BioNLP tasks have these characteristics and thus our AL algorithm is a natural approach to apply to BioNLP tasks.

Global convergence of an online (stochastic) limited memory version of the Broyden-Fletcher- Goldfarb-Shanno (BFGS) quasi-Newton method for solving optimization problems with stochastic objectives that arise in large scale machine learning is established. Lower and upper bounds on the Hessian eigenvalues of the sample functions are shown to suffice to guarantee that the curvature approximation matrices have bounded determinants and traces, which, in turn, permits establishing convergence to optimal arguments with probability 1. Numerical experiments on support vector machines with synthetic data showcase reductions in convergence time relative to stochastic gradient descent algorithms as well as reductions in storage and computation relative to other online quasi-Newton methods. Experimental evaluation on a search engine advertising problem corroborates that these advantages also manifest in practical applications.

The past years have witnessed many dedicated open-source projects that built and maintain implementations of Support Vector Machines (SVM), parallelized for GPU, multi-core CPUs and distributed systems. Up to this point, no comparable effort has been made to parallelize the Elastic Net, despite its popularity in many high impact applications, including genetics, neuroscience and systems biology. The first contribution in this paper is of theoretical nature. We establish a tight link between two seemingly different algorithms and prove that Elastic Net regression can be reduced to SVM with squared hinge loss classification. Our second contribution is to derive a practical algorithm based on this reduction. The reduction enables us to utilize prior efforts in speeding up and parallelizing SVMs to obtain a highly optimized and parallel solver for the Elastic Net and Lasso. With a simple wrapper, consisting of only 11 lines of MATLAB code, we obtain an Elastic Net implementation that naturally utilizes GPU and multi-core CPUs. We demonstrate on twelve real world data sets, that our algorithm yields identical results as the popular (and highly optimized) glmnet implementation but is one or several orders of magnitude faster.