TASK DEFINITION: In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.
PROBLEM: We introduce a copula mixture model to perform dependency-seeking clustering when cooccurring samples from different data sources are available. The model takes advantage of the great flexibility offered by the copulas framework to extend mixtures of Canonical Correlation Analysis to multivariate data with arbitrary continuous marginal densities. We formulate our model as a non-parametric Bayesian mixture, while providing efficient MCMC inference. Experiments on synthetic and real data demonstrate that the increased flexibility of the copula mixture significantly improves the clustering and the interpretability of the results.

SOLUTION: Copula Mixture Model for Dependency-seeking Clustering

PROBLEM: Spectral methods are popular in detecting global structures in the given data that can be represented as a matrix. However when the data matrix is sparse or noisy, classic spectral methods usually fail to work, due to localization of eigenvectors (or singular vectors) induced by the sparsity or noise. In this work, we propose a general method to solve the localization problem by learning a regularization matrix from the localized eigenvectors. Using matrix perturbation analysis, we demonstrate that the learned regularizations suppress down the eigenvalues associated with localized eigenvectors and enable us to recover the informative eigenvectors representing the global structure. We show applications of our method in several inference problems: community detection in networks, clustering from pairwise similarities, rank estimation and matrix completion problems. Using extensive experiments, we illustrate that our method solves the localization problem and works down to the theoretical detectability limits in different kinds of synthetic data. This is in contrast with existing spectral algorithms based on data matrix, non-backtracking matrix, Laplacians and those with rank-one regularizations, which perform poorly in the sparse case with noise.

SOLUTION: Robust Spectral Detection of Global Structures in the Data by Learning a Regularization

PROBLEM: We propose a regularized linear learning algorithm to sequence groups of features, where each group incurs test-time cost or computation. Specifically, we develop a simple extension to Orthogonal Matching Pursuit (OMP) that respects the structure of groups of features with variable costs, and we prove that it achieves nearoptimal anytime linear prediction at each budget threshold where a new group is selected. Our algorithm and analysis extends to generalized linear models with multi-dimensional responses. We demonstrate the scalability of the resulting approach on large real-world data-sets with many feature groups associated with test-time computational costs. Our method improves over Group Lasso and Group OMP in the anytime performance of linear predictions, measured in timeliness[7], an anytime prediction performance metric, while providing rigorous performance guarantees.

SOLUTION:
Efficient Feature Group Sequencing for Anytime Linear Prediction