Modèle linéaire généralisé

En statistiques, le modèle linéaire généralisé (MLG) souvent connu sous les initiales anglaises GLM est une généralisation souple de la régression linéaire. Le GLM généralise la régression linéaire en permettant au modèle linéaire d'être relié à la variable réponse via une fonction lien et en autorisant l'amplitude de la variance de chaque mesure d'être une fonction de sa valeur prévue, en fonction de la loi choisie. Formellement, :\operatorname{E}(Y|\mathbf{X}) = \boldsymbol{\mu} = g^{-1}(\mathbf{X}\boldsymbol{\beta}) où \operatorname{E}(Y|\mathbf{X}) est l'espérance mathématique de Y conditionnelle à \mathbf{X}; \mathbf{X}\boldsymbol{\beta} est le prédicteur linéaire, c'est-à-dire une combinaison linéaire des variables explicatives, et où g est une fonction monotone appelée fonction de lien. De plus : \operatorname{Var}(Y|\mathbf{X}) = \operatorname{V}( \boldsymbol{\mu} ) = \operatorname{V}(g^

A Quasi-Likelihood Approach to Zero-Inflated Spatial Count Data

Anthea Monod

The increased accessibility of data that are geographically referenced and correlated increases the demand for techniques of spatial data analysis. The subset of such data comprised of discrete counts exhibit particular difficulties and the challenges further increase when a large proportion (typically 50% or more) of the counts are zero-valued. Such scenarios arise in many applications in numerous fields of research and it is often desirable to infer on subtleties of the process, despite the lack of substantive information obscuring the underlying stochastic mechanism generating the data. An ecological example provides the impetus for the research in this thesis: when observations for a species are recorded over a spatial region, and many of the counts are zero-valued, are the abundant zeros due to bad luck, or are aspects of the region making it unsuitable for the survival of the species? In the framework of generalized linear models, we first develop a zero-inflated Poisson generalized linear regression model, which explains the variability of the responses given a set of measured covariates, and additionally allows for the distinction of two kinds of zeros: sampling ("bad luck" zeros), and structural (zeros that provide insight into the data-generating process). We then adapt this model to the spatial setting by incorporating dependence within the model via a general, leniently-defined quasi-likelihood strategy, which provides consistent, efficient and asymptotically normal estimators, even under erroneous assumptions of the covariance structure. In addition to this advantage of robustness to dependence misspecification, our quasi-likelihood model overcomes the need for the complete specification of a probability model, thus rendering it very general and relevant to many settings. To complement the developed regression model, we further propose methods for the simulation of zero-inflated spatial stochastic processes. This is done by deconstructing the entire process into a mixed, marked spatial point process: we augment existing algorithms for the simulation of spatial marked point processes to comprise a stochastic mechanism to generate zero-abundant marks (counts) at each location. We propose several such mechanisms, and consider interaction and dependence processes for random locations as well as over a lattice.

EPFL2012

Resolution-robust Large Mask In painting with Fourier Convolutions

Anastasia Remizova

Modern image inpainting systems, despite the significant progress, often struggle with large missing areas, complex geometric structures, and high-resolution images. We find that one of the main reasons for that is the lack of an effective receptive field in both the inpainting network and the loss function. To alleviate this issue, we propose a new method called large mask inpainting (LaMa). LaMa is based on i) a new inpainting network architecture that uses fast Fourier convolutions (FFCs), which have the imagewide receptive field; ii) a high receptive field perceptual loss; iii) large training masks, which unlocks the potential of the first two components. Our inpainting network improves the state-of-the-art across a range of datasets and achieves excellent performance even in challenging scenarios, e.g. completion of periodic structures. Our model generalizes surprisingly well to resolutions that are higher than those seen at train time, and achieves this at lower parameter&time costs than the competitive baselines. The code is available at https://github.com/saic-mdal/lama.

IEEE COMPUTER SOC2022

Linear Recursive State Estimation of Hybrid and Unbalanced AC/DC Micro-Grids using Synchronized Measurements

Willem Lambrichts, Mario Paolone

In this paper, we present an exact (i.e. non-approximated) and linear measurement model for hybrid AC/DC micro-grids for recursive state estimation (SE). More specifically, an exact linear model of a voltage source converter (VSC) is proposed. It relies on the complex VSC modulation index to relate the quantities at the converters DC side to the phasors at the AC side. The VSC model is derived from a transformer-like representation and accounts for the VSC conduction and switching losses. In the case of three-phase unbalanced grids, the measurement model is extended using the symmetrical component decomposition where each sequence individually affects the DC quantities. Synchronized measurements are provided by phasor measurement units and DC measurement units in the DC system. To make the SE more resilient to vive step changes in the grid states, an adaptive Kalman Filter that uses an approximation of the prediction-error covariance estimation method is proposed. This approximation reduces the computational speed significantly with only a limited reduction in the SE performance. The hybrid SE is validated in an EMTP-RV time-domain simulation of the CIGRE AC benchmark micro-grid that is connected to a DC grid using 4 VSCs. Bad data detection and identification using the largest normalised residual is assessed with respect to such a system. Furthermore, the proposed method is compared with a non-linear weighted least squares SE in terms of accuracy and computational time.

2022

A Quasi-Likelihood Approach to Zero-Inflated Spatial Count Data

Anthea Monod

EPFL2012