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This paper deals with the estimation of a high-dimensional covariance with a conditional sparsity structure and fast-diverging eigenvalues. By assuming sparse error covariance matrix in an approximate factor model, we allow for the presence…
Multimodal data, where different types of data are collected from the same subjects, are fast emerging in a large variety of scientific applications. Factor analysis is commonly used in integrative analysis of multimodal data, and is…
The sparse factorization of a large matrix is fundamental in modern statistical learning. In particular, the sparse singular value decomposition and its variants have been utilized in multivariate regression, factor analysis, biclustering,…
Factor models are widely used to reduce dimensionality in modeling high-dimensional data. However, there remains a need for models that can be reliably fit in modest sample sizes and are identifiable, interpretable, and flexible. To address…
Single-cell gene expression data are often characterized by large matrices, where the number of cells may be lower than the number of genes of interest. Factorization models have emerged as powerful tools to condense the available…
A key recent advance in face recognition models a test face image as a sparse linear combination of a set of training face images. The resulting sparse representations have been shown to possess robustness against a variety of distortions…
In high-dimensional linear models, the sparsity assumption is typically made, stating that most of the parameters are equal to zero. Under the sparsity assumption, estimation and, recently, inference have been well studied. However, in…
Parametric system identification methods estimate the parameters of explicitly defined physical systems from data. Yet, they remain constrained by the need to provide an explicit function space, typically through a predefined library of…
We study parameter estimation in Nonlinear Factor Analysis (NFA) where the generative model is parameterized by a deep neural network. Recent work has focused on learning such models using inference (or recognition) networks; we identify a…
We propose a novel bootstrap test of a dense model, namely factor regression, against a sparse plus dense alternative augmenting model with sparse idiosyncratic components. The asymptotic properties of the test are established under time…
The linear model, in which a set of observations is assumed to be given by a linear combination of columns of a matrix, has long been the mainstay of the statistics and signal processing literature. One particular challenge for inference…
Connectivity estimation is challenging in the context of high-dimensional data. A useful preprocessing step is to group variables into clusters, however, it is not always clear how to do so from the perspective of connectivity estimation.…
Sparse coding is a core building block in many data analysis and machine learning pipelines. Typically it is solved by relying on generic optimization techniques, that are optimal in the class of first-order methods for non-smooth, convex…
Its conceptual appeal and effectiveness has made latent factor modeling an indispensable tool for multivariate analysis. Despite its popularity across many fields, there are outstanding methodological challenges that have hampered practical…
A problem of paramount importance in both pure (Restricted Invertibility problem) and applied mathematics (Feature extraction) is the one of selecting a submatrix of a given matrix, such that this submatrix has its smallest singular value…
In finance, economics and many other fields, observations in a matrix form are often observed over time. For example, many economic indicators are obtained in different countries over time. Various financial characteristics of many…
Covariance matrices provide a valuable source of information about complex interactions and dependencies within the data. However, from a clustering perspective, this information has often been underutilized and overlooked. Indeed, commonly…
The uniqueness of sparsest solutions of underdetermined linear systems plays a fundamental role in the newly developed compressed sensing theory. Several new algebraic concepts, including the sub-mutual coherence, scaled mutual coherence,…
Graph matching is a challenging problem with very important applications in a wide range of fields, from image and video analysis to biological and biomedical problems. We propose a robust graph matching algorithm inspired in…
Recent work on overfitting Bayesian mixtures of distributions offers a powerful framework for clustering multivariate data using a latent Gaussian model which resembles the factor analysis model. The flexibility provided by overfitting…