Category: JMLR

Regularized kernel discriminant analysis (RKDA) performs linear discriminant analysis in the feature space via the kernel trick. Its performance depends on the selection of kernels. In this paper, we consider the problem of multiple kernel learning (MKL) for RKDA, in which the optimal kernel matrix is obtained as a linear combination of pre-specified kernel matrices. We show that the kernel learning problem in RKDA can be formulated as convex programs. First, we show that this problem can be formulated as a semidefinite program (SDP). Based on the equivalence relationship between RKDA and least square problems in the binary-class case, we propose a convex quadratically constrained quadratic programming (QCQP) formulation for kernel learning in RKDA. A semi-infinite linear programming (SILP) formulation is derived to further improve the efficiency. We extend these formulations to the multi-class case based on a key result established in this paper. That is, the multi-class RKDA kernel learning problem can be decomposed into a set of binary-class kernel learning problems which are constrained to share a common kernel. Based on this decomposition property, SDP formulations are proposed for the multi-class case. Furthermore, it leads naturally to QCQP and SILP formulations. As the performance of RKDA depends on the regularization parameter, we show that this parameter can also be optimized in a joint framework with the kernel. Extensive experiments have been conducted and analyzed, and connections to other algorithms are discussed.

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.

Multi Agent Reinforcement Learning (MARL) has received continually growing attention in the past decade. Many algorithms that vary in their approaches to the different subtasks of MARL have been developed. However, the theoretical convergence results for these algorithms do not give a clue as to their practical performance nor supply insights to the dynamics of the learning process itself. This work is a comprehensive empirical study conducted on MGS, a simulation system developed for this purpose. It surveys the important algorithms in the field, demonstrates the strengths and weaknesses of the different approaches to MARL through application of FriendQ, OAL, WoLF, FoeQ, Rmax, and other algorithms to a variety of fully cooperative and fully competitive domains in self and heterogeneous play, and supplies an informal analysis of the resulting learning processes. The results can aid in the design of new learning algorithms, in matching existing algorithms to specific tasks, and may guide further research and formal analysis of the learning processes.

Multiple kernel learning (MKL) aims at simultaneously learning a kernel and the associated predictor in supervised learning settings. For the support vector machine, an efficient and general multiple kernel learning algorithm, based on semi-infinite linear programming, has been recently proposed. This approach has opened new perspectives since it makes MKL tractable for large-scale problems, by iteratively using existing support vector machine code. However, it turns out that this iterative algorithm needs numerous iterations for converging towards a reasonable solution. In this paper, we address the MKL problem through a weighted 2-norm regularization formulation with an additional constraint on the weights that encourages sparse kernel combinations. Apart from learning the combination, we solve a standard SVM optimization problem, where the kernel is defined as a linear combination of multiple kernels. We propose an algorithm, named SimpleMKL, for solving this MKL problem and provide a new insight on MKL algorithms based on mixed-norm regularization by showing that the two approaches are equivalent. We show how SimpleMKL can be applied beyond binary classification, for problems like regression, clustering (one-class classification) or multiclass classification. Experimental results show that the proposed algorithm converges rapidly and that its efficiency compares favorably to other MKL algorithms. Finally, we illustrate the usefulness of MKL for some regressors based on wavelet kernels and on some model selection problems related to multiclass classification problems.

We design an online algorithm for Principal Component Analysis. In each trial the current instance is centered and projected into a probabilistically chosen low dimensional subspace. The regret of our online algorithm, that is, the total expected quadratic compression loss of the online algorithm minus the total quadratic compression loss of the batch algorithm, is bounded by a term whose dependence on the dimension of the instances is only logarithmic.

We first develop our methodology in the expert setting of online learning by giving an algorithm for learning as well as the best subset of experts of a certain size. This algorithm is then lifted to the matrix setting where the subsets of experts correspond to subspaces. The algorithm represents the uncertainty over the best subspace as a density matrix whose eigenvalues are bounded. The running time is O(n²) per trial, where n is the dimension of the instances.

We provide a comprehensive overview of many recent algorithms for approximate inference in Gaussian process models for probabilistic binary classification. The relationships between several approaches are elucidated theoretically, and the properties of the different algorithms are corroborated by experimental results. We examine both 1) the quality of the predictive distributions and 2) the suitability of the different marginal likelihood approximations for model selection (selecting hyperparameters) and compare to a gold standard based on MCMC. Interestingly, some methods produce good predictive distributions although their marginal likelihood approximations are poor. Strong conclusions are drawn about the methods: The Expectation Propagation algorithm is almost always the method of choice unless the computational budget is very tight. We also extend existing methods in various ways, and provide unifying code implementing all approaches.

We consider the problem of binary classification where the classifier can, for a particular cost, choose not to classify an observation. Just as in the conventional classification problem, minimization of the sample average of the cost is a difficult optimization problem. As an alternative, we propose the optimization of a certain convex loss function φ, analogous to the hinge loss used in support vector machines (SVMs). Its convexity ensures that the sample average of this surrogate loss can be efficiently minimized. We study its statistical properties. We show that minimizing the expected surrogate loss—the φ-risk—also minimizes the risk. We also study the rate at which the φ-risk approaches its minimum value. We show that fast rates are possible when the conditional probability P(Y=1|X) is unlikely to be close to certain critical values.

Existing template-independent web data extraction approaches adopt highly ineffective decoupled strategies---attempting to do data record detection and attribute labeling in two separate phases. In this paper, we propose an integrated web data extraction paradigm with hierarchical models. The proposed model is called Dynamic Hierarchical Markov Random Fields (DHMRFs). DHMRFs take structural uncertainty into consideration and define a joint distribution of both model structure and class labels. The joint distribution is an exponential family distribution. As a conditional model, DHMRFs relax the independence assumption as made in directed models. Since exact inference is intractable, a variational method is developed to learn the model's parameters and to find the MAP model structure and label assignments. We apply DHMRFs to a real-world web data extraction task. Experimental results show that: (1) integrated web data extraction models can achieve significant improvements on both record detection and attribute labeling compared to decoupled models; (2) in diverse web data extraction DHMRFs can potentially address the blocky artifact issue which is suffered by fixed-structured hierarchical models.