10 research outputs found
Tensor Regression
Regression analysis is a key area of interest in the field of data analysis
and machine learning which is devoted to exploring the dependencies between
variables, often using vectors. The emergence of high dimensional data in
technologies such as neuroimaging, computer vision, climatology and social
networks, has brought challenges to traditional data representation methods.
Tensors, as high dimensional extensions of vectors, are considered as natural
representations of high dimensional data. In this book, the authors provide a
systematic study and analysis of tensor-based regression models and their
applications in recent years. It groups and illustrates the existing
tensor-based regression methods and covers the basics, core ideas, and
theoretical characteristics of most tensor-based regression methods. In
addition, readers can learn how to use existing tensor-based regression methods
to solve specific regression tasks with multiway data, what datasets can be
selected, and what software packages are available to start related work as
soon as possible. Tensor Regression is the first thorough overview of the
fundamentals, motivations, popular algorithms, strategies for efficient
implementation, related applications, available datasets, and software
resources for tensor-based regression analysis. It is essential reading for all
students, researchers and practitioners of working on high dimensional data.Comment: 187 pages, 32 figures, 10 table
A comparison of the CAR and DAGAR spatial random effects models with an application to diabetics rate estimation in Belgium
When hierarchically modelling an epidemiological phenomenon on a finite collection of sites in space, one must always take a latent spatial effect into account in order to capture the correlation structure that links the phenomenon to the territory. In this work, we compare two autoregressive spatial models that can be used for this purpose: the classical CAR model and the more recent DAGAR model. Differently from the former, the latter has a desirable property: its ρ parameter can be naturally interpreted as the average neighbor pair correlation and, in addition, this parameter can be directly estimated when the effect is modelled using a DAGAR rather than a CAR structure. As an application, we model the diabetics rate in Belgium in 2014 and show the adequacy of these models in predicting the response variable when no covariates are available
A Statistical Approach to the Alignment of fMRI Data
Multi-subject functional Magnetic Resonance Image studies are critical. The anatomical and functional structure varies across subjects, so the image alignment is necessary. We define a probabilistic model to describe functional alignment. Imposing a prior distribution, as the matrix Fisher Von Mises distribution, of the orthogonal transformation parameter, the anatomical information is embedded in the estimation of the parameters, i.e., penalizing the combination of spatially distant voxels. Real applications show an improvement in the classification and interpretability of the results compared to various functional alignment methods