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The emergent dynamics of complex systems often arise from the internal dynamical interactions among different elements and hence is to be modeled using multiple variables that represent the different dynamical processes. When such systems…
Data quality (DQ) remains a fundamental concern in big data pipelines, especially when aggregations occur at multiple hierarchical levels. Traditional DQ validation rules often fail to scale or generalize across dimensions such as user…
Functional principal component analysis (FPCA) is an important technique for dimension reduction in functional data analysis (FDA). Classical FPCA method is based on the Karhunen-Lo\`{e}ve expansion, which assumes a linear structure of the…
The recently established RPCA method provides us a convenient way to restore low-rank matrices from grossly corrupted observations. While elegant in theory and powerful in reality, RPCA may be not an ultimate solution to the low-rank matrix…
Regularized Generalized Canonical Correlation Analysis (RGCCA) is a general statistical framework for multi-block data analysis. RGCCA enables deciphering relationships between several sets of variables and subsumes many well-known…
Recent studies proposed the use of Total Correlation to describe functional connectivity among brain regions as a multivariate alternative to conventional pair-wise measures such as correlation or mutual information. In this work we build…
Existing approaches for multivariate functional principal component analysis are restricted to data on the same one-dimensional interval. The presented approach focuses on multivariate functional data on different domains that may differ in…
Canonical Correlation Analysis (CCA) is a widely used statistical tool with both well established theory and favorable performance for a wide range of machine learning problems. However, computing CCA for huge datasets can be very slow…
Principal Component Analysis (PCA) is a fundamental tool for data visualization, denoising, and dimensionality reduction. It is widely popular in Statistics, Machine Learning, Computer Vision, and related fields. However, PCA is well-known…
We investigate the identifiability of nonlinear Canonical Correlation Analysis (CCA) in a multi-view setup, where each view is generated by an unknown nonlinear map applied to a linear mixture of shared latents and view-private noise.…
Causal mediation analysis usually requires strong assumptions, such as ignorability of the mediator, which may not hold in many social and scientific studies. Motivated by a multilevel randomized treatment experiment using functional…
Of particular interest is to discover useful representations solely from observations in an unsupervised generative manner. However, the question of whether existing normalizing flows provide effective representations for downstream tasks…
Relations between categorical variables can be analyzed conveniently by multiple correspondence analysis (MCA). %It is well suited to discover relations that may exist between categories of different variables. The graphical representation…
We propose generalized additive partial linear models for complex data which allow one to capture nonlinear patterns of some covariates, in the presence of linear components. The proposed method improves estimation efficiency and increases…
Recently proposed automatic pathological speech detection approaches rely on spectrogram input representations or wav2vec2 embeddings. These representations may contain pathology irrelevant uncorrelated information, such as changing…
We propose a novel algorithm - Multifractal Cross-Correlation Analysis (MFCCA) - that constitutes a consistent extension of the Detrended Cross-Correlation Analysis (DCCA) and is able to properly identify and quantify subtle characteristics…
Compositional data (i.e., data comprising random variables that sum up to a constant) arises in many applications including microbiome studies, chemical ecology, political science, and experimental designs. Yet when compositional data serve…
In microbiome and genomic studies, the regression of compositional data has been a crucial tool for identifying microbial taxa or genes that are associated with clinical phenotypes. To account for the variation in sequencing depth, the…
Correlated pattern mining has increasingly become an important task in data mining since these patterns allow conveying knowledge about meaningful and surprising relations among data. Frequent correlated patterns were thoroughly studied in…
Independent component analysis (ICA) is a powerful computational tool for separating independent source signals from their linear mixtures. ICA has been widely applied in neuroimaging studies to identify and characterize underlying brain…