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Numerous machine learning algorithms contain pairwise statistical problems at their core-that is, tasks that require computations over all pairs of input points if implemented naively. Often, tree structures are used to solve these problems efficiently. Dual-tree algorithms can efficiently solve or approximate many of these problems. Using cover trees, rigorous worst-case runtime guarantees have been proven for some of these algorithms. In this paper, we present a problem-independent runtime guarantee for any dual-tree algorithm using the cover tree, separating out the problem-dependent and the problem-independent elements. This allows us to just plug in bounds for the problem-dependent elements to get runtime guarantees for dual-tree algorithms for any pairwise statistical problem without re-deriving the entire proof. We demonstrate this plug-and-play procedure for nearest-neighbor search and approximate kernel density estimation to get improved runtime guarantees. Under mild assumptions, we also present the first linear runtime guarantee for dual-tree based range search. [ABSTRACT FROM AUTHOR]

We consider selective classification, a term we adopt here to refer to 'classification with a reject option.' The essence in selective classification is to trade-off classifier coverage for higher accuracy. We term this trade-off the risk-coverage (RC) trade-off. Our main objective is to characterize this trade-off and to construct algorithms that can optimally or near optimally achieve the best possible trade-offs in a controlled manner. For noise-free models we present in this paper a thorough analysis of selective classification including characterizations of RC trade-offs in various interesting settings. [ABSTRACT FROM AUTHOR]

Linear support vector machines (SVM) are useful for classifying large-scale sparse data. Problems with sparse features are common in applications such as document classification and natural language processing. In this paper, we propose a novel coordinate descent algorithm for training linear SVM with the L2-loss function. At each step, the proposed method minimizes a one-variable sub-problem while fixing other variables. The sub-problem is solved by Newton steps with the line search technique. The procedure globally converges at the linear rate. As each sub-problem involves only values of a corresponding feature, the proposed approach is suitable when accessing a feature is more convenient than accessing an instance. Experiments show that our method is more efficient and stable than state of the art methods such as Pegasos and TRON. [ABSTRACT FROM AUTHOR]

Ensemble learning algorithms such as boosting can achieve better performance by averaging over the predictions of some base hypotheses. Nevertheless, most existing algorithms are limited to combining only a finite number of hypotheses, and the generated ensemble is usually sparse. Thus, it is not clear whether we should construct an ensemble classifier with a larger or even an infinite number of hypotheses. In addition, constructing an infinite ensemble itself is a challenging task. In this paper, we formulate an infinite ensemble learning framework based on the support vector machine (SVM). The framework can output an infinite and nonsparse ensemble through embedding infinitely many hypotheses into an SVM kernel. We use the framework to derive two novel kernels, the stump kernel and the perceptron kernel. The stump kernel embodies infinitely many decision stumps, and the perceptron kernel embodies infinitely many perceptrons. We also show that the Laplacian radial basis function kernel embodies infinitely many decision trees, and can thus be explained through infinite ensemble learning. Experimental results show that SVM with these kernels is superior to boosting with the same base hypothesis set. In addition, SVM with the stump kernel or the perceptron kernel performs similarly to SVM with the Gaussian radial basis function kernel, but enjoys the benefit of faster parameter selection. These properties make the novel kernels favorable choices in practice. [ABSTRACT FROM AUTHOR]

Classifiers favoring sparse solutions, such as support vector machines, relevance vector machines, LASSO-regression based classifiers, etc., provide competitive methods for classification problems in high dimensions. However, current algorithms for training sparse classifiers typically scale quite unfavorably with respect to the number of training examples. This paper proposes online and multi-pass algorithms for training sparse linear classifiers for high dimensional data. These algorithms have computational complexity and memory requirements that make learning on massive data sets feasible. The central idea that makes this possible is a straightforward quadratic approximation to the likelihood function. [ABSTRACT FROM AUTHOR]

One of the most important issues in machine learning is whether one can improve the performance of a supervised learning algorithm by including unlabeled data. Methods that use both labeled and unlabeled data are generally referred to as semi-supervised learning. Although a number of such methods are proposed, at the current stage, we still don't have a complete understanding of their effectiveness. This paper investigates a closely related problem, which leads to a novel approach to semi-supervised learning. Specifically we consider learning predictive structures on hypothesis spaces (that is, what kind of classifiers have good predictive power) from multiple learning tasks. We present a general framework in which the structural learning problem can be formulated and analyzed theoretically, and relate it to learning with unlabeled data. Under this framework, algorithms for structural learning will be proposed, and computational issues will be investigated. Experiments will be given to demonstrate the effectiveness of the proposed algorithms in the semi-supervised learning setting. [ABSTRACT FROM AUTHOR]

Standard SVM training has O(m³) time and O(m²) space complexities, where m is the training set size. It is thus computationally infeasible on very large data sets. By observing that practical SVM implementations only approximate the optimal solution by an iterative strategy, we scale up kernel methods by exploiting such "approximateness" in this paper. We first show that many kernel methods can be equivalently formulated as minimum enclosing ball (MEB) problems in computational geometry. Then, by adopting an efficient approximate MEB algorithm, we obtain provably approximately optimal solutions with the idea of core sets. Our proposed Core Vector Machine (CVM) algorithm can be used with nonlinear kernels and has a time complexity that is linear in m and a space complexity that is independent of m. Experiments on large toy and real-world data sets demonstrate that the CVM is as accurate as existing SVM implementations, but is much faster and can handle much larger data sets than existing scale-up methods. For example, CVM with the Gaussian kernel produces superior results on the KDDCUP-99 intrusion detection data, which has about five million training patterns, in only 1.4 seconds on a 3.2GHz Pentium-4 PC. [ABSTRACT FROM AUTHOR]

Model-based clustering techniques have been widely used and have shown promising results in many applications involving complex data. This paper presents a unified framework for probabilistic model-based clustering based on a bipartite graph view of data and models that highlights the commonalities and differences among existing model-based clustering algorithms. In this view, clusters are represented as probabilistic models in a model space that is conceptually separate from the data space. For partitional clustering, the view is conceptually similar to the ExpectationMaximization (EM) algorithm. For hierarchical clustering, the graph-based view helps to visualize critical/important distinctions between similarity-based approaches and model-based approaches. The framework also suggests several useful variations of existing clustering algorithms. Two new variations—balanced model-based clustering and hybrid model-based clustering—are discussed and empirically evaluated on a variety of data types. [ABSTRACT FROM AUTHOR]