Related papers: Scale Invariant Correspondence Analysis
Shuffled regression concerns settings in which covariates and responses are observed without their correct pairing. In dependent-data problems, a second form of missing correspondence can arise when responses are also detached from the…
Spatial fields in the Earth and environmental sciences are often available at multiple scales or resolutions. While coarse-scale data (e.g., from global circulation models) are often abundant, they lack the local detail provided by…
All networks can be analyzed at multiple scales. A higher scale of a network is made up of macro-nodes: subgraphs that have been grouped into individual nodes. Recasting a network at higher scales can have useful effects, such as decreasing…
Traditional methods for the analysis of compositional data consider the log-ratios between all different pairs of variables with equal weight, typically in the form of aggregated contributions. This is not meaningful in contexts where it is…
A modified interaction representation for the master field describing connected $SU(N)$-invariant Wightman's functions in the large $N$ limit of matrix fields is constructed. This construction is based on the representation of the master…
Reduced Rank Regression (RRR) is a widely used method for multi-response regression. However, RRR assumes a linear relationship between features and responses. While linear models are useful and often provide a good approximation, many…
Since the introduction of the lasso in regression, various sparse methods have been developed in an unsupervised context like sparse principal component analysis (s-PCA), sparse canonical correlation analysis (s-CCA) and sparse singular…
Researchers in the biological sciences nowadays often encounter the curse of high-dimensionality, which many previously developed statistical models fail to overcome. To tackle this problem, sufficient dimension reduction aims to estimate…
Pooled imaging data from multiple sources is subject to bias from each source. Studies that do not correct for these scanner/site biases at best lose statistical power, and at worst leave spurious correlations in their data. Estimation of…
Sufficient dimension reduction [J. Amer. Statist. Assoc. 86 (1991) 316-342] has long been a prominent issue in multivariate nonparametric regression analysis. To uncover the central dimension reduction space, we propose in this paper an…
Linear regression without correspondences concerns the recovery of a signal in the linear regression setting, where the correspondences between the observations and the linear functionals are unknown. The associated maximum likelihood…
Bayesian inverse problems use observed data to update a prior probability distribution for an unknown state or parameter of a scientific system to a posterior distribution conditioned on the data. In many applications, the unknown parameter…
On the verge of the centenary of dimensional analysis (DA), we present a generalisation of the theory and a methodology for the discovery of empirical laws from observational data. It is well known that DA: a) reduces the number of free…
Contrastive dimension reduction methods have been developed for case-control study data to identify variation that is enriched in the foreground (case) data X relative to the background (control) data Y. Here, we develop contrastive…
Modal regression has emerged as a flexible alternative to classical regression models when the conditional mean or median are unable to adequately capture the underlying relation between a response and a predictor variable. This approach is…
This book deals with functions allowing to express the dissimilarity (discrepancy) between two data fields or ''divergence functions'' with the aim of applications to linear inverse problems. Most of the divergences found in the litterature…
Sparse Inverse Covariance Estimation (SICE) is useful in many practical data analyses. Recovering the connectivity, non-connectivity graph of covariates is classified amongst the most important data mining and learning problems. In this…
We provide new theoretical results in the field of inverse regression methods for dimension reduction. Our approach is based on the study of some empirical processes that lie close to a certain dimension reduction subspace, called the…
The Monte Carlo toy model of Bose-Einstein correlations is considered to make a best choice from different reference distributions. It occurs that the minimal bias in the Bose-Einstein correlation parameters estimation is provided by the…
Inline holographic imaging presents an ill-posed inverse problem of reconstructing objects' complex amplitude from recorded diffraction patterns. Although recent deep learning approaches have shown promise over classical phase retrieval…