Clustered sparse Bayesian learning

Many machine learning and signal processing tasks involve computing sparse representations using an overcomplete set of features or basis vectors, with compressive sensing-based applications a notable example. While traditionally such problems have been solved individually for different tasks, this strategy ignores strong correlations that may be present in real world data. Consequently there has been a push to exploit these statistical dependencies by jointly solving a series of sparse linear inverse problems. In the majority of the resulting algorithms however, we must a priori decide which tasks can most judiciously be grouped together. In contrast, this paper proposes an integrated Bayesian framework for both clustering tasks together and subsequently learning optimally sparse representations within each cluster. While probabilistic models have been applied previously to solve these types of problems, they typically involve a complex hierarchical Bayesian generative model merged with some type of approximate inference, the combination of which renders rigorous analysis of the underlying behavior virtually impossible. On the other hand, our model subscribes to concrete motivating principles that we carefully evaluate both theoretically and empirically. Importantly, our analyses take into account all approximations that are involved in arriving at the actual cost function to be optimized. Results on synthetic data as well as image recovery from compressive measurements show improved performance over existing methods

A novel prestack sparse azimuthal AVO inversion

In this paper we demonstrate a new algorithm for sparse prestack azimuthal AVO inversion. A novel Euclidean prior model is developed to at once respect sparseness in the layered earth and smoothness in the model of reflectivity. Recognizing that methods of artificial intelligence and Bayesian computation are finding an every increasing role in augmenting the process of interpretation and analysis of geophysical data, we derive a generalized matrix-variate model of reflectivity in terms of orthogonal basis functions, subject to sparse constraints. This supports a direct application of machine learning methods, in a way that can be mapped back onto the physical principles known to govern reflection seismology. As a demonstration we present an application of these methods to the Marcellus shale. Attributes extracted using the azimuthal inversion are clustered using an unsupervised learning algorithm. Interpretation of the clusters is performed in the context of the Ruger model of azimuthal AVO

CAMP: An Algorithm to Recover Sparse Signals with Unknown Clustering Pattern Using Approximate Message Passing

Recovering clustered sparse signals with an unknown sparsity pattern for the single measurement vector (SMV) problems is considered. The notion of sparsity in this context is referred to the signals having very few non-zero elements in some known basis. In the SMV, the objective is to recover a sparse or compressible signal from a small set of linear non-adaptive measurements. The case considered in this paper is that the signal of interest is not only sparse but also has an unknown clustered pattern, which occurs in many practical situations. In this case, we propose a sparse Bayesian learning algorithm simplified by the approximate message passing to reduce the complexity of the algorithm. In order to encourage the probably existing clustered sparsity pattern, we define a prior which provides a measure of contiguity over the supports of the solution. We refer to the proposed algorithm as CAMP, where the letter C stands for clustered sparsity pattern and AMP denotes approximate message passing. Simulation results show an encouraging result