Given a set of points and a set of prototypes representing them, how to create a graph of the prototypes whose topology accounts for that of the points? This problem had not yet been explored in the framework of statistical learning theory. In this work, we propose a generative model based on the Delaunay graph of the prototypes and the Expectation-Maximization algorithm to learn the parameters. This work is a first step towards the construction of a topological model of a set of points grounded on statistics.

A foundational problem in semi-supervised learning is the construction of a graph underlying the data. We propose to use a method which optimally combines a number of differently constructed graphs.

Many real-world classification problems involve the prediction of multiple interdependent variables forming some structural dependency. Recent progress in machine learning has mainly focused on supervised classification of such structured variables. In this paper, we investigate structured classification in a semi-supervised setting. We present a discriminative approach that utilizes the intrinsic geometry of input patterns revealed by unlabeled data points and we derive a maximum-margin formulation of semi-supervised learning for structured variables. Unlike transductive algorithms, our formulation naturally extends to new test points.

Our understanding of the input-output function of single cells has been substantially advanced by biophysically accurate multi-compartmental models. The large number of parameters needing hand tuning in these models has, however, somewhat hampered their applicability and interpretability. Here we propose a simple and well-founded method for automatic estimation of many of these key parameters: 1) the spatial distribution of channel densities on the cell's membrane; 2) the spatiotemporal pattern of synaptic input; 3) the channels' reversal potentials; 4) the intercompartmental conductances; and 5) the noise level in each compartment. We assume experimental access to: a) the spatiotemporal voltage signal in the dendrite (or some contiguous subpart thereof, e.g.

We propose a simple information-theoretic approach to soft clustering based on maximizing the mutual information I(x, y) between the unknown cluster labels y and the training patterns x with respect to parameters of specifically constrained encoding distributions. The constraints are chosen such that patterns are likely to be clustered similarly if they lie close to specific unknown vectors in the feature space. The method may be conveniently applied to learning the optimal affinity matrix, which corresponds to learning parameters of the kernelized encoder. The procedure does not require computations of eigenvalues of the Gram matrices, which makes it potentially attractive for clustering large data sets.

In this paper we derive an algorithm that computes the entire solution path of the support vector regression, with essentially the same computational cost as fitting one SVR model. We also propose an unbiased estimate for the degrees of freedom of the SVR model, which allows convenient selection of the regularization parameter.

This paper presents a non-asymptotic statistical analysis of Kernel-PCA with a focus different from the one proposed in previous work on this topic. Here instead of considering the reconstruction error of KPCA we are interested in approximation error bounds for the eigenspaces themselves. We prove an upper bound depending on the spacing between eigenvalues but not on the dimensionality of the eigenspace. As a consequence this allows to infer stability results for these estimated spaces.

We propose a fast manifold learning algorithm based on the methodology of domain decomposition. Starting with the set of sample points partitioned into two subdomains, we develop the solution of the interface problem that can glue the embeddings on the two subdomains into an embedding on the whole domain. We provide a detailed analysis to assess the errors produced by the gluing process using matrix perturbation theory. Numerical examples are given to illustrate the efficiency and effectiveness of the proposed methods.

We propose a probabilistic model based on Independent Component Analysis for learning multiple related tasks. In our model the task parameters are assumed to be generated from independent sources which account for the relatedness of the tasks. We use Laplace distributions to model hidden sources which makes it possible to identify the hidden, independent components instead of just modeling correlations. Furthermore, our model enjoys a sparsity property which makes it both parsimonious and robust. We also propose efficient algorithms for both empirical Bayes method and point estimation. Our experimental results on two multi-label text classification data sets show that the proposed approach is promising.

We propose a simple clustering framework on graphs encoding pairwise data similarities. Unlike usual similarity-based methods, the approach softly assigns data to clusters in a probabilistic way. More importantly, a hierarchical clustering is naturally derived in this framework to gradually merge lower-level clusters into higher-level ones. A random walk analysis indicates that the algorithm exposes clustering structures in various resolutions, i.e., a higher level statistically models a longer-term diffusion on graphs and thus discovers a more global clustering structure. Finally we provide very encouraging experimental results.