We consider the problem of assigning class labels to an unlabeled test data set, given several labeled training data sets drawn from similar distributions. This problem arises in several applications where data distributions fluctuate because of biological, technical, or other sources of variation. We develop a distribution-free, kernel-based approach to the problem. This approach involves identifying an appropriate reproducing kernel Hilbert space and optimizing a regularized empirical risk over the space. We present generalization error analysis, describe universal kernels, and establish universal consistency of the proposed methodology. Experimental results on flow cytometry data are presented.

We study multi-label prediction for structured output spaces, a problem that occurs, for example, in object detection in images, secondary structure prediction in computational biology, and graph matching with symmetries. Conventional multi-label classification techniques are typically not applicable in this situation, because they require explicit enumeration of the label space, which is infeasible in case of structured outputs. Relying on techniques originally designed for single- label structured prediction, in particular structured support vector machines, results in reduced prediction accuracy, or leads to infeasible optimization problems. In this work we derive a maximum-margin training formulation for multi-label structured prediction that remains computationally tractable while achieving high prediction accuracy. It also shares most beneficial properties with single-label maximum-margin approaches, in particular a formulation as a convex optimization problem, efficient working set training, and PAC-Bayesian generalization bounds.

A scattering transform defines a signal representation which is invariant to translations and Lipschitz continuous relatively to deformations. It is implemented with a non-linear convolution network that iterates over wavelet and modulus operators. Lipschitz continuity locally linearizes deformations. Complex classes of signals and textures can be modeled with low-dimensional affine spaces, computed with a PCA in the scattering domain. Classification is performed with a penalized model selection. State of the art results are obtained for handwritten digit recognition over small training sets, and for texture classification.

Machine learning approaches to multi-label document classification have to date largely relied on discriminative modeling techniques such as support vector machines. A drawback of these approaches is that performance rapidly drops off as the total number of labels and the number of labels per document increase. This problem is amplified when the label frequencies exhibit the type of highly skewed distributions that are often observed in real-world datasets. In this paper we investigate a class of generative statistical topic models for multi-label documents that associate individual word tokens with different labels. We investigate the advantages of this approach relative to discriminative models, particularly with respect to classification problems involving large numbers of relatively rare labels. We compare the performance of generative and discriminative approaches on document labeling tasks ranging from datasets with several thousand labels to datasets with tens of labels. The experimental results indicate that probabilistic generative models can achieve competitive multi-label classification performance compared to discriminative methods, and have advantages for datasets with many labels and skewed label frequencies.

A main goal of regression is to derive statistical conclusions on the conditional distribution of the output variable Y given the input values x. Two of the most important characteristics of a single distribution are location and scale. Support vector machines (SVMs) are well established to estimate location functions like the conditional median or the conditional mean. We investigate the estimation of scale functions by SVMs when the conditional median is unknown, too. Estimation of scale functions is important e.g. to estimate the volatility in finance. We consider the median absolute deviation (MAD) and the interquantile range (IQR) as measures of scale. Our main result shows the consistency of MAD-type SVMs.

It is shown that bootstrap approximations of an estimator which is based on a continuous operator from the set of Borel probability measures defined on a compact metric space into a complete separable metric space is stable in the sense of qualitative robustness. Support vector machines based on shifted loss functions are treated as special cases.

Support vector machines have attracted much attention in theoretical and in applied statistics. Main topics of recent interest are consistency, learning rates and robustness. In this article, it is shown that support vector machines are qualitatively robust. Since support vector machines can be represented by a functional on the set of all probability measures, qualitative robustness is proven by showing that this functional is continuous with respect to the topology generated by weak convergence of probability measures. Combined with the existence and uniqueness of support vector machines, our results show that support vector machines are the solutions of a well-posed mathematical problem in Hadamard's sense.

We revisit the additive model learning literature and adapt a penalized spline formulation due to Eilers and Marx, to train additive classifiers efficiently. We also propose two new embeddings based two classes of orthogonal basis with orthogonal derivatives, which can also be used to efficiently learn additive classifiers. This paper follows the popular theme in the current literature where kernel SVMs are learned much more efficiently using a approximate embedding and linear machine. In this paper we show that spline basis are especially well suited for learning additive models because of their sparsity structure and the ease of computing the embedding which enables one to train these models in an online manner, without incurring the memory overhead of precomputing the storing the embeddings. We show interesting connections between B-Spline basis and histogram intersection kernel and show that for a particular choice of regularization and degree of the B-Splines, our proposed learning algorithm closely approximates the histogram intersection kernel SVM. This enables one to learn additive models with almost no memory overhead compared to fast a linear solver, such as LIBLINEAR, while being only 5-6X slower on average. On two large scale image classification datasets, MNIST and Daimler Chrysler pedestrians, the proposed additive classifiers are as accurate as the kernel SVM, while being two orders of magnitude faster to train.

A nonlinear channel estimator using complex Least Square Support Vector Machines (LS-SVM) is proposed for pilot-aided OFDM system and applied to Long Term Evolution (LTE) downlink under high mobility conditions. The estimation algorithm makes use of the reference signals to estimate the total frequency response of the highly selective multipath channel in the presence of non-Gaussian impulse noise interfering with pilot signals. Thus, the algorithm maps trained data into a high dimensional feature space and uses the structural risk minimization (SRM) principle to carry out the regression estimation for the frequency response function of the highly selective channel. The simulations show the effectiveness of the proposed method which has good performance and high precision to track the variations of the fading channels compared to the conventional LS method and it is robust at high speed mobility.

In this work we present a quadratic programming approximation of the Semi-Supervised Support Vector Machine (S3VM) problem, namely approximate QP-S3VM, that can be efficiently solved using off the shelf optimization packages. We prove that this approximate formulation establishes a relation between the low density separation and the graph-based models of semi-supervised learning (SSL) which is important to develop a unifying framework for semi-supervised learning methods. Furthermore, we propose the novel idea of representing SSL problems as submodular set functions and use efficient submodular optimization algorithms to solve them. Using this new idea we develop a representation of the approximate QP-S3VM as a maximization of a submodular set function which makes it possible to optimize using efficient greedy algorithms. We demonstrate that the proposed methods are accurate and provide significant improvement in time complexity over the state of the art in the literature.