Block-diagonal covariance selection for high-dimensional Gaussian graphical models

Gaussian graphical models are widely utilized to infer and visualize networks of dependencies between continuous variables. However, inferring the graph is difficult when the sample size is small compared to the number of variables. To reduce the number of parameters to estimate in the model, we propose a non-asymptotic model selection procedure supported by strong theoretical guarantees based on an oracle inequality and a minimax lower bound. The covariance matrix of the model is approximated by a block-diagonal matrix. The structure of this matrix is detected by thresholding the sample covariance matrix, where the threshold is selected using the slope heuristic. Based on the block-diagonal structure of the covariance matrix, the estimation problem is divided into several independent problems: subsequently, the network of dependencies between variables is inferred using the graphical lasso algorithm in each block. The performance of the procedure is illustrated on simulated data. An application to a real gene expression dataset with a limited sample size is also presented: the dimension reduction allows attention to be objectively focused on interactions among smaller subsets of genes, leading to a more parsimonious and interpretable modular network.Comment: Accepted in JAS

Calibrating Array Detectors

The development of sensitive large format imaging arrays for the infrared promises to provide revolutionary capabilities for space astronomy. For example, the Infrared Array Camera (IRAC) on SIRTF will use four 256 x 256 arrays to provide background limited high spatial resolution images of the sky in the 3 to 8 micron spectral region. In order to reach the performance limits possible with this generation of sensitive detectors, calibration procedures must be developed so that uncertainties in detector calibration will always be dominated by photon statistics from the dark sky as a major system noise source. In the near infrared, where the faint extragalactic sky is observed through the scattered and reemitted zodiacal light from our solar system, calibration is particularly important. Faint sources must be detected on this brighter local foreground. We present a procedure for calibrating imaging systems and analyzing such data. In our approach, by proper choice of observing strategy, information about detector parameters is encoded in the sky measurements. Proper analysis allows us to simultaneously solve for sky brightness and detector parameters, and provides accurate formal error estimates. This approach allows us to extract the calibration from the observations themselves; little or no additional information is necessary to allow full interpretation of the data. Further, this approach allows refinement and verification of detector parameters during the mission, and thus does not depend on a priori knowledge of the system or ground calibration for interpretation of images.Comment: Scheduled for ApJS, June 2000 (16 pages, 3 JPEG figures

Image formation in synthetic aperture radio telescopes

Next generation radio telescopes will be much larger, more sensitive, have much larger observation bandwidth and will be capable of pointing multiple beams simultaneously. Obtaining the sensitivity, resolution and dynamic range supported by the receivers requires the development of new signal processing techniques for array and atmospheric calibration as well as new imaging techniques that are both more accurate and computationally efficient since data volumes will be much larger. This paper provides a tutorial overview of existing image formation techniques and outlines some of the future directions needed for information extraction from future radio telescopes. We describe the imaging process from measurement equation until deconvolution, both as a Fourier inversion problem and as an array processing estimation problem. The latter formulation enables the development of more advanced techniques based on state of the art array processing. We demonstrate the techniques on simulated and measured radio telescope data.Comment: 12 page

4D Seismic History Matching Incorporating Unsupervised Learning

The work discussed and presented in this paper focuses on the history matching of reservoirs by integrating 4D seismic data into the inversion process using machine learning techniques. A new integrated scheme for the reconstruction of petrophysical properties with a modified Ensemble Smoother with Multiple Data Assimilation (ES-MDA) in a synthetic reservoir is proposed. The permeability field inside the reservoir is parametrised with an unsupervised learning approach, namely K-means with Singular Value Decomposition (K-SVD). This is combined with the Orthogonal Matching Pursuit (OMP) technique which is very typical for sparsity promoting regularisation schemes. Moreover, seismic attributes, in particular, acoustic impedance, are parametrised with the Discrete Cosine Transform (DCT). This novel combination of techniques from machine learning, sparsity regularisation, seismic imaging and history matching aims to address the ill-posedness of the inversion of historical production data efficiently using ES-MDA. In the numerical experiments provided, I demonstrate that these sparse representations of the petrophysical properties and the seismic attributes enables to obtain better production data matches to the true production data and to quantify the propagating waterfront better compared to more traditional methods that do not use comparable parametrisation techniques