Learning the Structure for Structured Sparsity

Structured sparsity has recently emerged in statistics, machine learning and signal processing as a promising paradigm for learning in high-dimensional settings. All existing methods for learning under the assumption of structured sparsity rely on prior knowledge on how to weight (or how to penalize) individual subsets of variables during the subset selection process, which is not available in general. Inferring group weights from data is a key open research problem in structured sparsity.In this paper, we propose a Bayesian approach to the problem of group weight learning. We model the group weights as hyperparameters of heavy-tailed priors on groups of variables and derive an approximate inference scheme to infer these hyperparameters. We empirically show that we are able to recover the model hyperparameters when the data are generated from the model, and we demonstrate the utility of learning weights in synthetic and real denoising problems

Online quantum mixture regression for trajectory learning by demonstration

In this work, we present the online Quantum Mixture Model (oQMM), which combines the merits of quantum mechanics and stochastic optimization. More specifically it allows for quantum effects on the mixture states, which in turn become a superposition of conventional mixture states. We propose an efficient stochastic online learning algorithm based on the online Expectation Maximization (EM), as well as a generation and decay scheme for model components. Our method is suitable for complex robotic applications, where data is abundant or where we wish to iteratively refine our model and conduct predictions during the course of learning. With a synthetic example, we show that the algorithm can achieve higher numerical stability. We also empirically demonstrate the efficacy of our method in well-known regression benchmark datasets. Under a trajectory Learning by Demonstration setting we employ a multi-shot learning application in joint angle space, where we observe higher quality of learning and reproduction. We compare against popular and well-established methods, widely adopted across the robotics community

Gibbs Max-margin Topic Models with Data Augmentation

Max-margin learning is a powerful approach to building classifiers and structured output predictors. Recent work on max-margin supervised topic models has successfully integrated it with Bayesian topic models to discover discriminative latent semantic structures and make accurate predictions for unseen testing data. However, the resulting learning problems are usually hard to solve because of the non-smoothness of the margin loss. Existing approaches to building max-margin supervised topic models rely on an iterative procedure to solve multiple latent SVM subproblems with additional mean-field assumptions on the desired posterior distributions. This paper presents an alternative approach by defining a new max-margin loss. Namely, we present Gibbs max-margin supervised topic models, a latent variable Gibbs classifier to discover hidden topic representations for various tasks, including classification, regression and multi-task learning. Gibbs max-margin supervised topic models minimize an expected margin loss, which is an upper bound of the existing margin loss derived from an expected prediction rule. By introducing augmented variables and integrating out the Dirichlet variables analytically by conjugacy, we develop simple Gibbs sampling algorithms with no restricting assumptions and no need to solve SVM subproblems. Furthermore, each step of the "augment-and-collapse" Gibbs sampling algorithms has an analytical conditional distribution, from which samples can be easily drawn. Experimental results demonstrate significant improvements on time efficiency. The classification performance is also significantly improved over competitors on binary, multi-class and multi-label classification tasks.Comment: 35 page