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The generalized singular value decomposition (GSVD) is a valuable tool that has many applications in computational science. However, computing the GSVD for large-scale problems is challenging. Motivated by applications in hyper-differential…
The generalized singular value decomposition (GSVD, a.k.a. "SVD triplet", "duality diagram" approach) provides a unified strategy and basis to perform nearly all of the most common multivariate analyses (e.g., principal components,…
This paper presents approaches to compute sparse solutions of Generalized Singular Value Problem (GSVP). The GSVP is regularized by $\ell_1$-norm and $\ell_q$-penalty for $0<q<1$, resulting in the $\ell_1$-GSVP and $\ell_q$-GSVP…
Variables in many massive high-dimensional data sets are structured, arising for example from measurements on a regular grid as in imaging and time series or from spatial-temporal measurements as in climate studies. Classical multivariate…
We address the problem of defining a group sparse formulation for Principal Components Analysis (PCA) - or its equivalent formulations as Low Rank approximation or Dictionary Learning problems - which achieves a compromise between…
Multivariate regression techniques are commonly applied to explore the associations between large numbers of outcomes and predictors. In real-world applications, the outcomes are often of mixed types, including continuous measurements,…
Sparse modelling or model selection with categorical data is challenging even for a moderate number of variables, because one parameter is roughly needed to encode one category or level. The Group Lasso is a well known efficient algorithm…
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…
Sparse Singular Value Decomposition (SVD) models have been proposed for biclustering high dimensional gene expression data to identify block patterns with similar expressions. However, these models do not take into account prior group…
Geometry-grounded learning asks models to respect structure in the problem domain rather than treating observations as arbitrary vectors. Motivated by this view, we revisit a classical but underused primitive for comparing datasets: linear…
Many problems require the selection of a subset of variables from a full set of optimization variables. The computational complexity of an exhaustive search over all possible subsets of variables is, however, prohibitively expensive,…
We study the problem of multivariate regression where the data are naturally grouped, and a regression matrix is to be estimated for each group. We propose an approach in which a dictionary of low rank parameter matrices is estimated across…
Structured sparsity is an important modeling tool that expands the applicability of convex formulations for data analysis, however it also creates significant challenges for efficient algorithm design. In this paper we investigate the…
We introduce Group Spike-and-slab Variational Bayes (GSVB), a scalable method for group sparse regression. A fast co-ordinate ascent variational inference (CAVI) algorithm is developed for several common model families including Gaussian,…
In this paper, we consider a new variant for principal component analysis (PCA), aiming to capture the grouping and/or sparse structures of factor loadings simultaneously. To achieve these goals, we employ a non-convex truncated…
For the computation of the generalized singular value decomposition (GSVD) of a large matrix pair $(A,B)$ of full column rank, the GSVD is commonly formulated as two mathematically equivalent generalized eigenvalue problems, so that a…
The higher-order generalized singular value decomposition (HO-GSVD) is a matrix factorization technique that extends the GSVD to $N \ge 2$ data matrices, and can be used to identify shared subspaces in multiple large-scale datasets with…
In many biomedical research, multiple views of data (e.g., genomics, proteomics) are available, and a particular interest might be the detection of sample subgroups characterized by specific groups of variables. Biclustering methods are…
This paper proposes a new algorithm for multiple sparse regression in high dimensions, where the task is to estimate the support and values of several (typically related) sparse vectors from a few noisy linear measurements. Our algorithm is…
Many modern big data applications feature large scale in both numbers of responses and predictors. Better statistical efficiency and scientific insights can be enabled by understanding the large-scale response-predictor association network…