Feedforward neural networks based on Rectified linear units (ReLU) cannot efficiently approximate quantile functions which are not bounded, especially in the case of heavy-tailed distributions. We thus propose a new parametrization for the generator of a Generative adversarial network (GAN) adapted to this framework, basing on extreme-value theory. An analysis of the uniform error between the extreme quantile and its GAN approximation is provided: We establish that the rate of convergence of the error is mainly driven by the second-order parameter of the data distribution. The above results are illustrated on simulated data and real financial data. It appears that our approach outperforms the classical GAN in a wide range of situations including high-dimensional and dependent data.

Recent satellite missions have led to a huge amount of Earth observation data, most of them being freely available. In such a context, satellite image time series have been used to study land use and land cover information. However, optical time series, such as Sentinel-2 or Landsat ones, are provided with an irregular time sampling for different spatial locations, and images may contain clouds and shadows. Thus, preprocessing techniques are usually required to properly classify such data. The proposed approach is able to deal with irregular temporal sampling and missing data directly in the classification process. It is based on Gaussian processes and allows to perform jointly the classification of the pixel labels as well as the reconstruction of the pixel time series. The method complexity scales linearly with the number of pixels, making it amenable in large-scale scenarios. Experimental classification and reconstruction results show that the method does not compete yet with state-of-the-art classifiers but yields reconstructions that are robust with respect to the presence of undetected clouds or shadows and does not require any temporal preprocessing.

The connection between Bayesian neural networks and Gaussian processes gained a lot of attention in the last few years. Hidden units are proven to follow a Gaussian process limit when the layer width tends to infinity. Recent work has suggested that finite Bayesian neural networks may outperform their infinite counterparts because they adapt their internal representations flexibly. To establish solid ground for future research on finite-width neural networks, our goal is to study the prior induced on hidden units. Our main result is an accurate description of hidden units tails which shows that unit priors become heavier-tailed going deeper, thanks to the introduced notion of generalized Weibull-tail. This finding sheds light on the behavior of hidden units of finite Bayesian neural networks.

The aim of this study is to build a model suitable to classify grassland management practices using satellite image time series with high spatial resolution. The study site is located in southern France where 52 parcels with three management types were selected. The NDVI computed from a Formosat-2 intra-annual time series of 17 images was used. To work at the parcel scale while accounting for the spectral variability inside the grasslands, the pixels signal distribution is modeled by a Gaussian distribution. To deal with the small ground sample size compared to the large number of variables, a parsimonious Gaussian model is used. A high dimensional symmetrized Kullback-Leibler divergence (KLD) is introduced to compute the similarity between each pair of grasslands. Our proposed model provides better results than the conventional KLD in terms of classification accuracy using SVM.

This paper is concerned with the estimation of a local measure of intrinsic dimensionality (ID) recently proposed by Houle. The local model can be regarded as an extension of Karger and Ruhl's expansion dimension to a statistical setting in which the distribution of distances to a query point is modeled in terms of a continuous random variable. This form of intrinsic dimensionality can be particularly useful in search, classification, outlier detection, and other contexts in machine learning, databases, and data mining, as it has been shown to be equivalent to a measure of the discriminative power of similarity functions. Several estimators of local ID are proposed and analyzed based on extreme value theory, using maximum likelihood estimation (MLE), the method of moments (MoM), probability weighted moments (PWM), and regularly varying functions (RV). An experimental evaluation is also provided, using both real and artificial data.

A family of parsimonious Gaussian process models for classification is proposed in this letter. A subspace assumption is used to build these models in the kernel feature space. By constraining some parameters of the models to be common between classes, parsimony is controlled. Experimental results are given for three real hyperspectral data sets, and comparisons are done with three other classifiers. The proposed models show good results in terms of classification accuracy and processing time.

A family of parsimonious Gaussian process models is presented. They allow to construct a Gaussian mixture model in a kernel feature space by assuming that the data of each class live in a specific subspace. The proposed models are used to build a kernel Markov random field (pGPMRF), which is applied to classify the pixels of a real multivariate remotely sensed image. In terms of classification accuracy, some of the proposed models perform equivalently to a SVM but they perform better than another kernel Gaussian mixture model previously defined in the literature. The pGPMRF provides the best classification accuracy thanks to the spatial regularization.

A fast and accurate statistical method that estimates at gate level the leakage power consumption of CMOS digital circuits is demonstrated. Means, variances and correlations of logic gate leakages are extracted at library characterization step, and used for subsequent circuit statistical computation. In this paper, the methodology is applied to an eleven thousand cells ST test IP. The circuit leakage analysis computation time is 400 times faster than a single fast-Spice corner analysis, while providing coherent results.

We are given a set of points in a space of high dimension. For instance, this set may represent many visual appearances of an object, a face, or a hand. We address the problem of approximating this set by a manifold in order to have a compact representation of the object appearance. When the scattering of this set is approximately an ellipsoid, then the problem has a well-known solution given by principal components analysis (PCA). However, in some situations like object displacement learning or face learning, this linear technique may be ill-adapted and nonlinear approximation has to be introduced. The method we propose can be seen as a nonlinear PCA (NLPCA), the main difficulty being that the data are not ordered. We propose an index which favors the choice of axes preserving the closest point neighborhoods. These axes determine an order for visiting all the points when smoothing. Finally, a new criterion, called "generalization error", is introduced to determine the smoothing rate, that is, the knot number for the spline fitting. Experimental results conclude this paper: The method is tested on artificial data and on two databases used in visual learning.