Roy Bar-Haim, Indrajit Bhattacharya, Francesco Dinuzzo, Amrita Saha, Noam Slonim. Proceedings of the 15th Conference of the European Chapter of the Association for Computational Linguistics: Volume 1, Long Papers. 2017.

It is known that the solution of regularization and interpolation problems with Hilbertian penalties can be expressed as a linear combination of the data. This very useful property, called the representer theorem, has been widely studied and applied to machine learning problems. Analogous optimality conditions have appeared in other contexts, notably in matrix regularization. In this paper we propose a unified view, which generalizes the concept of representer theorems and extends necessary and sufficient conditions for such theorems to hold. Our main result shows a close connection between representer theorems and certain classes of regularization penalties, which we call orthomonotone functions. This result not only subsumes previous representer theorems as special cases but also yields a new class of optimality conditions, which goes beyond the classical linear combination of the data. Moreover, orthomonotonicity provides a useful criterion for testing whether a representer theorem holds for a specific regularization problem.

This paper considers the classification problem using support vector (SV) machines and investigates how to maximally reduce the size of the training set without losing information. Under separable data set assumptions, we derive the exact conditions stating which observations can be discarded without diminishing the overall information content. For this purpose, we introduce the concept of potential SVs, i.e., those data that can become SVs when future data become available. To complement this, we also characterize the set of discardable vectors (DVs), i.e., those data that, given the current data set, can never become SVs. Thus, these vectors are useless for future training purposes and can eventually be removed without loss of information. Then, we provide an efficient algorithm based on linear programming that returns the potential and DVs by constructing a simplex tableau. Finally, we compare it with alternative algorithms available in the literature on some synthetic data as well as on data sets from standard repositories.

This paper presents a novel interactive domain-adaptation technique based on active learning for the classification of remote sensing (RS) images. The proposed method aims at adapting the supervised classifier trained on a given RS source image to make it suitable for classifying a different but related target image. The two images can be acquired in different locations and/or at different times, but present the same set of land-cover classes. The proposed approach iteratively selects the most informative samples of the target image to be labeled by the user and included in the training set, while the source-image samples are re-weighted or possibly removed from the training set on the basis of their disagreement with the target image classification problem. In this way, the consistent information available from the source image can be effectively exploited for the classification of a target image and for guiding the user in the selection of the new samples to be labeled, whereas the inconsistent information is automatically detected and removed. Experimental results on a Very High Resolution (VHR) multispectral dataset confirm the effectiveness of the proposed method.

The representer theorem is a property that lies at the foundation of regularization theory and kernel methods. A class of regularization functionals is said to admit a linear representer theorem if every member of the class admits minimizers that lie in the finite dimensional subspace spanned by the representers of the data. A recent characterization states that certain classes of regularization functionals with differentiable regularization term admit a linear representer theorem for any choice of the data if and only if the regularization term is a radial nondecreasing function. In this paper, we extend such result by weakening the assumptions on the regularization term. In particular, the main result of this paper implies that, for a sufficiently large family of regularization functionals, radial nondecreasing functions are the only lower semicontinuous regularization terms that guarantee existence of a representer theorem for any choice of the data.

This paper presents a kernel-based discriminative learning framework on probability measures. Rather than relying on large collections of vectorial training examples, our framework learns using a collection of probability distributions that have been constructed to meaningfully represent training data. By representing these probability distributions as mean embeddings in the reproducing kernel Hilbert space (RKHS), we are able to apply many standard kernel-based learning techniques in straightforward fashion. To accomplish this, we construct a generalization of the support vector machine (SVM) called a support measure machine (SMM). Our analyses of SMMs provides several insights into their relationship to traditional SVMs. Based on such insights, we propose a flexible SVM (Flex-SVM) that places different kernel functions on each training example. Experimental results on both synthetic and real-world data demonstrate the effectiveness of our proposed framework.

In this paper, we analyze the convergence of two general classes of optimization algorithms for regularized kernel methods with convex loss function and quadratic norm regularization. The first methodology is a new class of algorithms based on fixed-point iterations that are well-suited for a parallel implementation and can be used with any convex loss function. The second methodology is based on coordinate descent, and generalizes some techniques previously proposed for linear support vector machines. It exploits the structure of additively separable loss functions to compute solutions of line searches in closed form. The two methodologies are both very easy to implement. In this paper, we also show how to remove non-differentiability of the objective functional by exactly reformulating a convex regularization problem as an unconstrained differentiable stabilization problem.

A client-server architecture to simultaneously solve multiple learning tasks from distributed datasets is described. In such architecture, each client corresponds to an individual learning task and the associated dataset of examples. The goal of the architecture is to perform information fusion from multiple datasets while preserving privacy of individual data. The role of the server is to collect data in real time from the clients and codify the information in a common database. Such information can be used by all the clients to solve their individual learning task, so that each client can exploit the information content of all the datasets without actually having access to private data of others. The proposed algorithmic framework, based on regularization and kernel methods, uses a suitable class of "mixed effect" kernels. The methodology is illustrated through a simulated recommendation system, as well as an experiment involving pharmacological data coming from a multicentric clinical trial.

Standard single-task kernel methods have recently been extended to the case of multitask learning in the context of regularization theory. There are experimental results, especially in biomedicine, showing the benefit of the multitask approach compared to the single-task one. However, a possible drawback is computational complexity. For instance, when regularization networks are used, complexity scales as the cube of the overall number of training data, which may be large when several tasks are involved. The aim of this paper is to derive an efficient computational scheme for an important class of multitask kernels. More precisely, a quadratic loss is assumed and each task consists of the sum of a common term and a task-specific one. Within a Bayesian setting, a recursive online algorithm is obtained, which updates both estimates and confidence intervals as new data become available. The algorithm is tested on two simulated problems and a real data set relative to xenobiotics administration in human patients.