Driven by a large number of potential applications in areas like bioinformatics, information retrieval and social network analysis, the problem setting of inferring relations between pairs of data objects has recently been investigated quite intensively in the machine learning community. To this end, current approaches typically consider datasets containing crisp relations, so that standard classification methods can be adopted. However, relations between objects like similarities and preferences are often expressed in a graded manner in real-world applications. A general kernel-based framework for learning relations from data is introduced here. It extends existing approaches because both crisp and graded relations are considered, and it unifies existing approaches because different types of graded relations can be modeled, including symmetric and reciprocal relations. This framework establishes important links between recent developments in fuzzy set theory and machine learning. Its usefulness is demonstrated through various experiments on synthetic and real-world data.

The size of 3D models used on the web or stored in databases is becoming increasingly high. Then, an efficient method that allows users to find similar 3D objects for a given 3D model query has become necessary. Keywords and the geometry of a 3D model cannot meet the needs of users' retrieval because they do not include the semantic information. In this paper, a new method has been proposed to 3D models retrieval using semantic concepts combined with shape indexes. To obtain these concepts, we use the machine learning methods to label 3D models by k-means algorithm in measures and shape indexes space. Moreover, semantic concepts have been organized and represented by ontology language OWL and spatial relationships are used to disambiguate among models of similar appearance. The SPARQL query language has been used to question the information displayed in this language and to compute the similarity between two 3D models. We interpret our results using the Princeton Shape Benchmark Database and the results show the performance of the proposed new approach to retrieval 3D models. Keywords: 3D Model, 3D retrieval, measures, shape indexes, semantic, ontology

We describe many vantage points on the Baire metric and its use in clustering data, or its use in preprocessing and structuring data in order to support search and retrieval operations. In some cases, we proceed directly to clusters and do not directly determine the distances. We show how a hierarchical clustering can be read directly from one pass through the data. We offer insights also on practical implications of precision of data measurement. As a mechanism for treating multidimensional data, including very high dimensional data, we use random projections.

We consider a standard binary classification problem. The performance of any binary classifier based on the training data is characterized by the excess risk. We study Bahadur's type exponential bounds on the minimax accuracy confidence function based on the excess risk. We study how this quantity depends on the complexity of the class of distributions characterized by exponents of entropies of the class of regression functions or of the class of Bayes classifiers corresponding to the distributions from the class. We also study its dependence on margin parameters of the classification problem.

Many problems in artificial intelligence require adaptively making a sequence of decisions with uncertain outcomes under partial observability. Solving such stochastic optimization problems is a fundamental but notoriously difficult challenge. In this paper, we introduce the concept of adaptive submodularity, generalizing submodular set functions to adaptive policies. We prove that if a problem satisfies this property, a simple adaptive greedy algorithm is guaranteed to be competitive with the optimal policy. In addition to providing performance guarantees for both stochastic maximization and coverage, adaptive submodularity can be exploited to drastically speed up the greedy algorithm by using lazy evaluations. We illustrate the usefulness of the concept by giving several examples of adaptive submodular objectives arising in diverse AI applications including management of sensing resources, viral marketing and active learning. Proving adaptive submodularity for these problems allows us to recover existing results in these applications as special cases, improve approximation guarantees and handle natural generalizations.

This paper introduces a new specialized algorithm for equilibrium Monte Carlo sampling of binary-valued systems, which allows for large moves in the state space. This is achieved by constructing self-avoiding walks (SAWs) in the state space. As a consequence, many bits are flipped in a single MCMC step. We name the algorithm SARDONICS, an acronym for Self-Avoiding Random Dynamics on Integer Complex Systems. The algorithm has several free parameters, but we show that Bayesian optimization can be used to automatically tune them. SARDONICS performs remarkably well in a broad number of sampling tasks: toroidal ferromagnetic and frustrated Ising models, 3D Ising models, restricted Boltzmann machines and chimera graphs arising in the design of quantum computers.

We information-theoretically reformulate two measures of capacity from statistical learning theory: empirical VC-entropy and empirical Rademacher complexity. We show these capacity measures count the number of hypotheses about a dataset that a learning algorithm falsifies when it finds the classifier in its repertoire minimizing empirical risk. It then follows from that the future performance of predictors on unseen data is controlled in part by how many hypotheses the learner falsifies. As a corollary we show that empirical VC-entropy quantifies the message length of the true hypothesis in the optimal code of a particular probability distribution, the so-called actual repertoire.

Sparse estimation methods are aimed at using or obtaining parsimonious representations of data or models. They were first dedicated to linear variable selection but numerous extensions have now emerged such as structured sparsity or kernel selection. It turns out that many of the related estimation problems can be cast as convex optimization problems by regularizing the empirical risk with appropriate non-smooth norms. The goal of this paper is to present from a general perspective optimization tools and techniques dedicated to such sparsity-inducing penalties. We cover proximal methods, block-coordinate descent, reweighted $\ell_2$-penalized techniques, working-set and homotopy methods, as well as non-convex formulations and extensions, and provide an extensive set of experiments to compare various algorithms from a computational point of view.

Relative to the large literature on upper bounds on complexity of convex optimization, lesser attention has been paid to the fundamental hardness of these problems. Given the extensive use of convex optimization in machine learning and statistics, gaining an understanding of these complexity-theoretic issues is important. In this paper, we study the complexity of stochastic convex optimization in an oracle model of computation. We improve upon known results and obtain tight minimax complexity estimates for various function classes.

We propose a Bayesian nonparametric approach to the problem of jointly modeling multiple related time series. Our approach is based on the discovery of a set of latent, shared dynamical behaviors. Using a beta process prior, the size of the set and the sharing pattern are both inferred from data. We develop efficient Markov chain Monte Carlo methods based on the Indian buffet process representation of the predictive distribution of the beta process, without relying on a truncated model. In particular, our approach uses the sum-product algorithm to efficiently compute Metropolis-Hastings acceptance probabilities, and explores new dynamical behaviors via birth and death proposals. We examine the benefits of our proposed feature-based model on several synthetic datasets, and also demonstrate promising results on unsupervised segmentation of visual motion capture data.