Variational Inference of Joint Models using Multivariate Gaussian Convolution Processes

We present a non-parametric prognostic framework for individualized event prediction based on joint modeling of both longitudinal and time-to-event data. Our approach exploits a multivariate Gaussian convolution process (MGCP) to model the evolution of longitudinal signals and a Cox model to map time-to-event data with longitudinal data modeled through the MGCP. Taking advantage of the unique structure imposed by convolved processes, we provide a variational inference framework to simultaneously estimate parameters in the joint MGCP-Cox model. This significantly reduces computational complexity and safeguards against model overfitting. Experiments on synthetic and real world data show that the proposed framework outperforms state-of-the art approaches built on two-stage inference and strong parametric assumptions

Advances in Hyperspectral Image Classification: Earth monitoring with statistical learning methods

Hyperspectral images show similar statistical properties to natural grayscale or color photographic images. However, the classification of hyperspectral images is more challenging because of the very high dimensionality of the pixels and the small number of labeled examples typically available for learning. These peculiarities lead to particular signal processing problems, mainly characterized by indetermination and complex manifolds. The framework of statistical learning has gained popularity in the last decade. New methods have been presented to account for the spatial homogeneity of images, to include user's interaction via active learning, to take advantage of the manifold structure with semisupervised learning, to extract and encode invariances, or to adapt classifiers and image representations to unseen yet similar scenes. This tutuorial reviews the main advances for hyperspectral remote sensing image classification through illustrative examples.Comment: IEEE Signal Processing Magazine, 201

Non-parametric deprojection of NIKA SZ observations: Pressure distribution in the Planck-discovered cluster PSZ1 G045.85+57.71

The determination of the thermodynamic properties of clusters of galaxies at intermediate and high redshift can bring new insights into the formation of large-scale structures. It is essential for a robust calibration of the mass-observable scaling relations and their scatter, which are key ingredients for precise cosmology using cluster statistics. Here we illustrate an application of high resolution $(< 20$ arcsec) thermal Sunyaev-Zel'dovich (tSZ) observations by probing the intracluster medium (ICM) of the \planck-discovered galaxy cluster \psz\ at redshift $z = 0.61$, using tSZ data obtained with the NIKA camera, which is a dual-band (150 and 260~GHz) instrument operated at the IRAM 30-meter telescope. We deproject jointly NIKA and \planck\ data to extract the electronic pressure distribution from the cluster core ($R \sim 0.02\, R_{500}$) to its outskirts ($R \sim 3\, R_{500}$) non-parametrically for the first time at intermediate redshift. The constraints on the resulting pressure profile allow us to reduce the relative uncertainty on the integrated Compton parameter by a factor of two compared to the \planck\ value. Combining the tSZ data and the deprojected electronic density profile from \xmm\ allows us to undertake a hydrostatic mass analysis, for which we study the impact of a spherical model assumption on the total mass estimate. We also investigate the radial temperature and entropy distributions. These data indicate that \psz\ is a massive ($M_{500} \sim 5.5 \times 10^{14}$ M$_{\odot}$) cool-core cluster. This work is part of a pilot study aiming at optimizing the treatment of the NIKA2 tSZ large program dedicated to the follow-up of SZ-discovered clusters at intermediate and high redshifts. (abridged)Comment: 16 pages, 10 figure

Partially-observed models for classifying minerals on Mars

The identification of phyllosilicates by NASA's CRISM (Compact Reconnaissance Imaging Spectrometer for Mars) strongly suggests the presence of water-related geological processes. A variety of water-bearing phyllosilicate minerals have already been identified by several research groups utilizing spectral enrichment techniques and matching phyllosilicate-rich regions on the Martian surface to known spectra of minerals found on earth. However, fully automated analysis of the CRISM data remains a challenge for two main reasons. First, there is significant variability in the spectral signature of the same mineral obtained from different regions on the Martian surface. Second, the list of mineral confirmed to date constituting the set of training classes is not exhaustive. Thus, when classifying new regions, using a classifier trained with selected minerals and chemicals, one must consider the potential presence of unknown materials not represented in the training library. We made an initial attempt to study these problems in the context of our recent work on partially-observed classification models and present results that show the utility of such models in identifying spectra of unknown minerals while simultaneously recognizing spectra of known minerals

Meta learning of bounds on the Bayes classifier error

Meta learning uses information from base learners (e.g. classifiers or estimators) as well as information about the learning problem to improve upon the performance of a single base learner. For example, the Bayes error rate of a given feature space, if known, can be used to aid in choosing a classifier, as well as in feature selection and model selection for the base classifiers and the meta classifier. Recent work in the field of f-divergence functional estimation has led to the development of simple and rapidly converging estimators that can be used to estimate various bounds on the Bayes error. We estimate multiple bounds on the Bayes error using an estimator that applies meta learning to slowly converging plug-in estimators to obtain the parametric convergence rate. We compare the estimated bounds empirically on simulated data and then estimate the tighter bounds on features extracted from an image patch analysis of sunspot continuum and magnetogram images.Comment: 6 pages, 3 figures, to appear in proceedings of 2015 IEEE Signal Processing and SP Education Worksho