We present a method for the reconstruction of networks, based on the order of nodes visited by a stochastic branching process. Our algorithm reconstructs a network of minimal size that ensures consistency with the data. Crucially, we show that global consistency with the data can be achieved through purely local considerations, inferring the neighbourhood of each node in turn. The optimisation problem solved for each individual node can be reduced to a Set Covering Problem, which is known to be NP-hard but can be approximated well in practice. We then extend our approach to account for noisy data, based on the Minimum Description Length principle. We demonstrate our algorithms on synthetic data, generated by an SIR-like epidemiological model.

The 2-class transduction problem, as formulated by Vapnik [1], involves finding a separating hyperplane for a labelled data set that is also maximally distant from a given set of unlabelled test points. In this form, the problem has exponential computational complexity in the size of the working set. So far it has been attacked by means of integer programming techniques [2] that do not scale to reasonable problem sizes, or by local search procedures [3]. In this paper we present a relaxation of this task based on semidefinite programming(SDP), resulting in a convex optimization problem that has polynomial complexity in the size of the data set. The results are very encouraging for mid sized data sets, however the cost is still too high for large scale problems, due to the high dimensional searchspace. To this end, we restrict the feasible region by introducing an approximation based on solving an eigenproblem. With this approximation, the computational cost of the algorithm is such that problems with more than 1000 points can be treated.

The problem of learning a semantic representation of a text document from data is addressed, in the situation where a corpus of unlabeled paired documents is available, each pair being formed by a short English document and its French translation. This representation can then be used for any retrieval, categorization or clustering task, both in a standard and in a cross-lingual setting. By using kernel functions, in this case simple bag-of-words inner products, each part of the corpus is mapped to a high-dimensional space. The correlations between the two spaces are then learnt by using kernel Canonical Correlation Analysis. A set of directions is found in the first and in the second space that are maximally correlated. Since we assume the two representations are completely independent apart from the semantic content, any correlation between them should reflect some semantic similarity. Certain patterns of English words that relate to a specific meaning should correlate with certain patterns of French words corresponding to the same meaning, across the corpus. Using the semantic representation obtained in this way we first demonstrate that the correlations detected between the two versions of the corpus are significantly higher than random, and hence that a representation based on such features does capture statistical patterns that should reflect semantic information. Then we use such representation both in cross-language and in single-language retrieval tasks, observing performance that is consistently and significantly superior to LSI on the same data.

The standard representation of text documents as bags of words suffers from well known limitations, mostly due to its inability to exploit semantic similarity between terms. Attempts to incorporate some notion of term similarity include latent semantic indexing [8], the use of semantic networks [9], and probabilistic methods [5]. In this paper we propose two methods for inferring such similarity from a corpus. The first one defines word-similarity based on document-similarity and viceversa, giving rise to a system of equations whose equilibrium point we use to obtain a semantic similarity measure. The second method models semantic relations by means of a diffusion process on a graph defined by lexicon and co-occurrence information.

The standard representation of text documents as bags of words suffers from well known limitations, mostly due to its inability to exploit semantic similarity between terms. Attempts to incorporate somenotion of term similarity include latent semantic indexing [8], the use of semantic networks [9], and probabilistic methods [5]. In this paper we propose two methods for inferring such similarity froma corpus. The first one defines word-similarity based on document-similarity and viceversa, giving rise to a system of equations whose equilibrium point we use to obtain a semantic similarity measure. The second method models semantic relations by means of a diffusion process on a graph defined by lexicon and co-occurrence information.

The problem of learning a semantic representation of a text document from data is addressed, in the situation where a corpus of unlabeled paired documents is available, each pair being formed by a short English documentand its French translation. This representation can then be used for any retrieval, categorization or clustering task, both in a standard andin a cross-lingual setting. By using kernel functions, in this case simple bag-of-words inner products, each part of the corpus is mapped to a high-dimensional space. The correlations between the two spaces are then learnt by using kernel Canonical Correlation Analysis. A set of directions is found in the first and in the second space that are maximally correlated.Since we assume the two representations are completely independentapart from the semantic content, any correlation between them should reflect some semantic similarity. Certain patterns of English words that relate to a specific meaning should correlate with certain patternsof French words corresponding to the same meaning, across the corpus. Using the semantic representation obtained in this way we first demonstrate that the correlations detected between the two versions of the corpus are significantly higher than random, and hence that a representation basedon such features does capture statistical patterns that should reflect semantic information. Then we use such representation both in cross-language and in single-language retrieval tasks, observing performance that is consistently and significantly superior to LSI on the same data.

Note that lEs is the expectation operator under the selection of the sample.

Note that lEs is the expectation operator under the selection of the sample.

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.

Note that lEs is the expectation operator under the selection of the sample.