Causal structure-discovery techniques usually assume that all causes of more than one variable are observed. This is the so-called causal sufficiency assumption. In practice, it is untestable, and often violated. In this paper, we present an efficient causal structure-learning algorithm, suited for causally insufficient data. Similar to algorithms such as IC* and FCI, the proposed approach drops the causal sufficiency assumption and learns a structure that indicates (potential) latent causes for pairs of observed variables. Assuming a constant local density of the data-generating graph, our algorithm makes a quadratic number of conditional-independence tests w.r.t. the number of variables. We show with experiments that our algorithm is comparable to the state-of-the-art FCI algorithm in accuracy, while being several orders of magnitude faster on large problems. We conclude that MBCS* makes a new range of causally insufficient problems computationally tractable.

A key issue in supervised protein classification is the representation of input sequencesof amino acids. Recent work using string kernels for protein datahas achieved state-of-the-art classification performance. However, suchrepresentations are based only on labeled data -- examples with known 3D structures, organized into structural classes -- while in practice, unlabeled data is far more plentiful.

We consider the learning problem of finding a dependency between a general class of objects and another, possibly different, general class of objects. The objects can be for example: vectors, images, strings, trees or graphs. Such a task is made possible by employing similarity measures in both input and output spaces using kernel functions, thus embedding the objects into vector spaces. We experimentally validate our approach on several tasks: mapping strings to strings, pattern recognition, and reconstruction from partial images. 1 Introduction In this article we consider the rather general learning problem of finding a dependency between inputs x E X and outputs y E Y given a training set (Xl,yl),...,(xm, Ym) E X x Y This includes conventional pattern recognition and regression estimation. It also encompasses more complex dependency estimation tasks, e.g mapping of a certain class of strings to a certain class of graphs (as in text parsing) or the mapping of text descriptions to images.

Jason Weston, Olivier Chapelle, Andre Elisseeff, Bernhard Scholkopf and Vladimir Vapnik* Max Planck Institute for Biological Cybernetics, 72076 Tubingen, Germany *NEC Research Institute, Princeton, NJ 08540 USA Abstract We consider the learning problem of finding a dependency between a general class of objects and another, possibly different, general class of objects. The objects can be for example: vectors, images, strings, trees or graphs. Such a task is made possible by employing similarity measures in both input and output spaces using kernel functions,thus embedding the objects into vector spaces. We experimentally validate our approach on several tasks: mapping strings to strings, pattern recognition, and reconstruction from partial images. 1 Introduction In this article we consider the rather general learning problem of finding a dependency betweeninputs x E X and outputs y E Y given a training set (Xl,yl), ...,(xm, Ym) This includes conventional pattern recognition and regression estimation. It also encompasses more complex dependency estimation tasks, e.g mapping of a certain class of strings to a certain class of graphs (as in text parsing) or the mapping of text descriptions to images.

This article presents a Support Vector Machine (SVM) like learning system tohandle multi-label problems. Such problems are usually decomposed intomany two-class problems but the expressive power of such a system can be weak [5, 7]. We explore a new direct approach. It is based on a large margin ranking system that shares a lot of common properties withSVMs. We tested it on a Yeast gene functional classification problem with positive results.

We introduce the notion of kernel-alignment, a measure of similarity between two kernel functions or between a kernel and a target function. This quantity captures the degree of agreement between a kernel and a given learning task, and has very natural interpretations in machine learning, leading also to simple algorithms for model selection and learning. We analyse its theoretical properties, proving that it is sharply concentrated around its expected value, and we discuss its relation with other standard measures of performance. Finally we describe some of the algorithms that can be obtained within this framework, giving experimental results showing that adapting the kernel to improve alignment on the labelled data significantly increases the alignment on the test set, giving improved classification accuracy. Hence, the approach provides a principled method of performing transduction.

This article presents a Support Vector Machine (SVM) like learning system to handle multi-label problems. Such problems are usually decomposed into many two-class problems but the expressive power of such a system can be weak [5, 7]. We explore a new direct approach. It is based on a large margin ranking system that shares a lot of common properties with SVMs. We tested it on a Yeast gene functional classification problem with positive results.

We introduce the notion of kernel-alignment, a measure of similarity betweentwo kernel functions or between a kernel and a target function. This quantity captures the degree of agreement between a kernel and a given learning task, and has very natural interpretations inmachine learning, leading also to simple algorithms for model selection and learning.

Until recently, most of the research in that area has focused on uniform a-priori bounds giving a guarantee that the difference between the training error and the test error is uniformly small for any hypothesis in a given class. These bounds are usually expressed in terms of combinatorial quantities such as VCdimension. In the last few years, researchers have tried to use more refined quantities to either estimate the complexity of the search space (e.g.

A stable learner is one for which the learned solution does not change much with small changes in the training set. The bounds we obtain do not depend on any measure of the complexity of the hypothesis space (e.g. VC dimension) but rather depend on how the learning algorithm searches this space, and can thus be applied even when the VC dimension is infinite. We demonstrate that regularization networks possess the required stability property and apply our method to obtain new bounds on their generalization performance.