Related papers: Applications of Multivariate Statistical Methods a…
Spectral clustering is one of the most widely used techniques for extracting the underlying global structure of a data set. Compressed sensing and matrix completion have emerged as prevailing methods for efficiently recovering sparse and…
Modern data-driven and distributed learning frameworks deal with diverse massive data generated by clients spread across heterogeneous environments. Indeed, data heterogeneity is a major bottleneck in scaling up many distributed learning…
The general method to obtain solutions of the Maxwellian equations from scalar representatives is developed and applied to the diffraction of electromagnetic waves. Kirchhoff's integral is modified to provide explicit expressions for these…
The eigenvalue decomposition (EVD) parameters of the second order statistics are ubiquitous in statistical analysis and signal processing. Notably, the EVD of robust scatter $M$-estimators is a popular choice to perform robust probabilistic…
High-fidelity electron microscopy simulations required for quantitative crystal structure refinements face a fundamental challenge: while physical interactions are well-described theoretically, real-world experimental effects are…
State-space mixed-frequency vector autoregressions are now widely used for nowcasting. Despite their popularity, estimating such models can be computationally intensive, especially for large systems with stochastic volatility. To tackle the…
Molecular dynamics simulations produce huge datasets of temporal sequences of molecules. It is of interest to summarize the shape evolution of the molecules in a succinct, low-dimensional representation. However, Euclidean techniques such…
Atomic scale simulations are a key element of modern science in that they allow to understand, and even predict, complex physical or chemical phenomena on the basis of the fundamental laws of nature. Among the different existing atomic…
Divergence is not only an important mathematical concept in information theory, but also applied to machine learning problems such as low-dimensional embedding, manifold learning, clustering, classification, and anomaly detection. We…
In this paper we consider a variety of procedures for numerical statistical inference in the family of univariate and multivariate stable distributions. In connection with univariate distributions (i) we provide approximations by finite…
In this paper, we outline the use of Mixture Models in density estimation of large astronomical databases. This method of density estimation has been known in Statistics for some time but has not been implemented because of the large…
Since Estimation of Distribution Algorithms (EDA) were proposed, many attempts have been made to improve EDAs' performance in the context of global optimization. So far, the studies or applications of multivariate probabilistic model based…
An influential step in weather forecasting was the introduction of ensemble forecasts in operational use due to their capability to account for the uncertainties in the future state of the atmosphere. However, ensemble weather forecasts are…
We introduce Multivariate Circulant Singular Spectrum Analysis (M-CiSSA) to provide a comprehensive framework to analyze fluctuations, extracting the underlying components of a set of time series, disentangling their sources of variation…
We seek a generalization of regression and principle component analysis (PCA) in a metric space where data points are distributions metrized by the Wasserstein metric. We recast these analyses as multimarginal optimal transport problems.…
We introduce principal differences analysis (PDA) for analyzing differences between high-dimensional distributions. The method operates by finding the projection that maximizes the Wasserstein divergence between the resulting univariate…
Multimodal sentiment analysis (MSA) aims to understand human sentiment through multimodal data. In real-world scenarios, practical factors often lead to uncertain modality missingness. Existing methods for handling modality missingness are…
Principal component analysis (PCA) is a classical dimension reduction method which projects data onto the principal subspace spanned by the leading eigenvectors of the covariance matrix. However, it behaves poorly when the number of…
Multiple clustering has gathered significant attention in recent years due to its potential to reveal multiple hidden structures of the data from different perspectives. Most of multiple clustering methods first derive feature…
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…