We present a fast algorithm for the detection of multiple change-points when each is frequently shared by members of a set of co-occurring one-dimensional signals. We give conditions on consistency of the method when the number of signals increases, and provide empirical evidence to support the consistency results.

We propose new methodologies to detect anomalies in discrete-time processes taking values in a probability space. These methods are based on the inference of functionals whose evaluations on successive states visited by the process are stationary and have low autocorrelations. Deviations from this behavior are used to flag anomalies. The candidate functionals are estimated in a subspace of a reproducing kernel Hilbert space associated with the original probability space considered. We provide experimental results on simulated datasets which show that these techniques compare favorably with other algorithms.

In multi-task learning several related tasks are considered simultaneously, with the hope that by an appropriate sharing of information across tasks, each task may benefit from the others. In the context of learning linear functions for supervised classification or regression, this can be achieved by including a priori information about the weight vectors associated with the tasks, and how they are expected to be related to each other. In this paper, we assume that tasks are clustered into groups, which are unknown beforehand, and that tasks within a group have similar weight vectors. We design a new spectral norm that encodes this a priori assumption, without the prior knowledge of the partition of tasks into groups, resulting in a new convex optimization formulation for multi-task learning. We show in simulations on synthetic examples and on the iedb MHC-I binding dataset, that our approach outperforms well-known convex methods for multi-task learning, as well as related non convex methods dedicated to the same problem.

We describe a hierarchy of motif-based kernels for multiple alignments of biological sequences, particularly suitable to process regulatory regions of genes. The kernels incorporate progressively more information, with the most complex kernel accounting for a multiple alignment of orthologous regions, the phylogenetic tree relating the species, and the prior knowledge that relevant sequence patterns occur in conserved motif blocks. These kernels can be used in the presence of a library of known transcription factor binding sites, or de novo by iterating over all k-mers of a given length. In the latter mode, a discriminative classifier built from such a kernel not only recognizes a given class of promoter regions, but as a side effect simultaneously identifies a collection of relevant, discriminative sequence motifs. We demonstrate the utility of the motif-based multiple alignment kernels by using a collection of aligned promoter regions from five yeast species to recognize classes of cell-cycle regulated genes.

We describe a hierarchy of motif-based kernels for multiple alignments of biological sequences, particularly suitable to process regulatory regions ofgenes. The kernels incorporate progressively more information, with the most complex kernel accounting for a multiple alignment of orthologous regions, the phylogenetic tree relating the species, and the prior knowledge that relevant sequence patterns occur in conserved motif blocks.These kernels can be used in the presence of a library of known transcription factor binding sites, or de novo by iterating over all k-mers of a given length. In the latter mode, a discriminative classifier builtfrom such a kernel not only recognizes a given class of promoter regions,but as a side effect simultaneously identifies a collection of relevant, discriminative sequence motifs. We demonstrate the utility of the motif-based multiple alignment kernels by using a collection ofaligned promoter regions from five yeast species to recognize classes of cell-cycle regulated genes.

We determine the asymptotic limit of the function computed by support vector machines (SVM) and related algorithms that minimize a regularized empiricalconvex loss function in the reproducing kernel Hilbert space of the Gaussian RBF kernel, in the situation where the number of examples tends to infinity, the bandwidth of the Gaussian kernel tends to 0, and the regularization parameter is held fixed.

Complex objects can often be conveniently represented by finite sets of simpler components, such as images by sets of patches or texts by bags of words. We study the class of positive definite (p.d.) kernels for two such objects that can be expressed as a function of the merger of their respective sets of components. We prove a general integral representation ofsuch kernels and present two particular examples. One of them leads to a kernel for sets of points living in a space endowed itself with a positive definite kernel. We provide experimental results on a benchmark experiment of handwritten digits image classification which illustrate the validity of the approach.

We formulate the problem of graph inference where part of the graph is known as a supervised learning problem, and propose an algorithm to solve it. The method involves the learning of a mapping of the vertices to a Euclidean space where the graph is easy to infer, and can be formulated asan optimization problem in a reproducing kernel Hilbert space. We report encouraging results on the problem of metabolic network reconstruction fromgenomic data.

We present an algorithm to extract features from high-dimensional gene expression profiles, based on the knowledge of a graph which links together genes known to participate to successive reactions in metabolic pathways. Motivated by the intuition that biologically relevant features are likely to exhibit smoothness with respect to the graph topology, the algorithm involves encoding the graph and the set of expression profiles into kernel functions, and performing a generalized form of canonical correlation analysis in the corresponding reproducible kernel Hilbert spaces. Function prediction experiments for the genes of the yeast S. Cerevisiae validate this approach by showing a consistent increase in performance when a state-of-the-art classifier uses the vector of features instead of the original expression profile to predict the functional class of a gene.

We present an algorithm to extract features from high-dimensional gene expression profiles, based on the knowledge of a graph which links together genes known to participate to successive reactions in metabolic pathways. Motivated by the intuition that biologically relevant features are likely to exhibit smoothness with respect to the graph topology, the algorithm involves encoding the graph and the set of expression profiles into kernel functions, and performing a generalized form of canonical correlation analysis in the corresponding reproducible kernel Hilbert spaces. Function prediction experiments for the genes of the yeast S. Cerevisiae validate this approach by showing a consistent increase in performance when a state-of-the-art classifier uses the vector of features instead of the original expression profile to predict the functional class of a gene.