Related papers: Scale Invariant Correspondence Analysis
The development and use of dimension reduction methods is prevalent in modern statistical literature. This paper reviews a class of dimension reduction techniques which aim to simultaneously select relevant predictors and find clusters…
This paper studies the inference of the regression coefficient matrix under multivariate response linear regressions in the presence of hidden variables. A novel procedure for constructing confidence intervals of entries of the coefficient…
Data-driven reduced order models (ROMs) recently emerged as powerful tool for the solution of inverse scattering problems. The main drawback of this approach is that it was limited to the measurement arrays with reciprocally collocated…
Tomograms, a generalization of the Radon transform to arbitrary pairs of non-commuting operators, are positive bilinear transforms with a rigorous probabilistic interpretation which provide a full characterization of the signal and are…
Data matrix having different sets of entities in its rows and columns are known as two mode data or affiliation data. Many practical problems require to find relationships between the two modes by simultaneously clustering the rows and…
This paper proposes two distinct contributions to econometric analysis of large information sets and structural instabilities. First, it treats a regression model with time-varying coefficients, stochastic volatility and exogenous…
Collins' (2002) statement "correspondence analysis makes you blind" followed after his seriation like description of a brand attribute count data set analyzed by Whitlark and Smith (2001), who applied correspondence analysis. In this essay…
Stochastic differential equations have been an important tool in modeling complex financial relations, equipped with the possibility of being multidimensional to better oversee complexities inherent in finance. This multidimensionality,…
We introduce a flexible framework for high-dimensional matrix estimation to incorporate side information for both rows and columns. Existing approaches, such as inductive matrix completion, often impose restrictive structure-for example, an…
Biclustering is an unsupervised data mining technique that aims to unveil patterns (biclusters) from gene expression data matrices. In the framework of this thesis, we propose new biclustering algorithms for microarray data. The latter is…
The conventional classification schemes -- notably multinomial logistic regression -- used in conjunction with convolutional networks (convnets) are classical in statistics, designed without consideration for the usual coupling with…
To date, testing interactions in high dimensions has been a challenging task. Existing methods often have issues with sensitivity to modeling assumptions and heavily asymptotic nominal p-values. To help alleviate these issues, we propose a…
This article is concerned with simultaneous tests on linear regression coefficients in high-dimensional settings. When the dimensionality is larger than the sample size, the classic $F$-test is not applicable since the sample covariance…
Preprocessing data is an important step before any data analysis. In this paper, we focus on one particular aspect, namely scaling or normalization. We analyze various scaling methods in common use and study their effects on different…
We present a new deep learning approach for matching deformable shapes by introducing {\it Shape Deformation Networks} which jointly encode 3D shapes and correspondences. This is achieved by factoring the surface representation into (i) a…
Canonical correlation analysis is a classic well-known multivariate statistical method focusing on the relationships between two sets of variables. The visualisation of those relationships can be achieved by means of a biplot of the…
A data matrix may be seen simply as a means of organizing observations into rows ( e.g., by measured object) and into columns ( e.g., by measured variable) so that the observations can be analyzed with mathematical tools. As a mathematical…
A new, coordinate-free (geometric) approach to multivariate statistical analysis. General multivariate linear models and linear hypotheses are defined in geometric form. A method of constructing statistical criteria is defined for linear…
It is time to renew old ways of thinking about dimensional analysis. Specifically, more than $n-r$ invariants and more than one functional relation between invariants need to be considered simultaneously. Thus generalized, dimensional…
Symmetry transformations induce invariances which are frequently described with deep latent variable models. In many complex domains, such as the chemical space, invariances can be observed, yet the corresponding symmetry transformation…