Related papers: Data-fusion using factor analysis and low-rank mat…
Principal component analysis and factor analysis are fundamental multivariate analysis methods. In this paper a unified framework to connect them is introduced. Under a general latent variable model, we present matrix optimization problems…
Factor Analysis is a widely used modeling technique for stationary time series which achieves dimensionality reduction by revealing a hidden low-rank plus sparse structure of the covariance matrix. Such an idea of parsimonious modeling has…
Consider a linear model $y = X \beta + z$, $z \sim N(0, \sigma^2 I_n)$. The Gram matrix $\Theta = \frac{1}{n} X'X$ is non-sparse, but it is approximately the sum of two components, a low-rank matrix and a sparse matrix, where neither…
Multivariate spatially-oriented data sets are prevalent in the environmental and physical sciences. Scientists seek to jointly model multiple variables, each indexed by a spatial location, to capture any underlying spatial association for…
Data quality is fundamentally important to ensure the reliability of data for stakeholders to make decisions. In real world applications, such as scientific exploration of extreme environments, it is unrealistic to require raw data…
Estimating large covariance and precision matrices are fundamental in modern multivariate analysis. The problems arise from statistical analysis of large panel economics and finance data. The covariance matrix reveals marginal correlations…
Latent factor models that integrate data from multiple sources/studies or modalities have garnered considerable attention across various disciplines. However, existing methods predominantly focus either on multi-study integration or…
We consider multilevel low rank (MLR) matrices, defined as a row and column permutation of a sum of matrices, each one a block diagonal refinement of the previous one, with all blocks low rank given in factored form. MLR matrices extend low…
Factor analysis (FA) or principal component analysis (PCA) models the covariance matrix of the observed data as R = SS' + {\Sigma}, where SS' is the low-rank covariance matrix of the factors (aka latent variables) and {\Sigma} is the…
Identifying discrete patterns in binary data is an important dimensionality reduction tool in machine learning and data mining. In this paper, we consider the problem of low-rank binary matrix factorisation (BMF) under Boolean arithmetic.…
Constrained low-rank matrix approximations have been known for decades as powerful linear dimensionality reduction techniques to be able to extract the information contained in large data sets in a relevant way. However, such low-rank…
Matrix completion aims to estimate missing entries in a data matrix, using the assumption of a low-complexity structure (e.g., low rank) so that imputation is possible. While many effective estimation algorithms exist in the literature,…
Factor models are widely used for dimension reduction in the analysis of multivariate data. This is achieved through decomposition of a p x p covariance matrix into the sum of two components. Through a latent factor representation, they can…
High-dimensional matrix-variate time series data are becoming widely available in many scientific fields, such as economics, biology, and meteorology. To achieve significant dimension reduction while preserving the intrinsic matrix…
We address one of the important problems in Big Data, namely how to combine estimators from different subsamples by robust fusion procedures, when we are unable to deal with the whole sample. We propose a general framework based on the…
In recent years, researchers pay growing attention to the few-shot learning (FSL) task to address the data-scarce problem. A standard FSL framework is composed of two components: i) Pre-train. Employ the base data to generate a CNN-based…
Supervised classification and representation learning are two widely used classes of methods to analyze multivariate images. Although complementary, these methods have been scarcely considered jointly in a hierarchical modeling. In this…
Current statistical inference problems in areas like astronomy, genomics, and marketing routinely involve the simultaneous testing of thousands -- even millions -- of null hypotheses. For high-dimensional multivariate distributions, these…
Completing multidimensional tensor-structured data with missing entries is a fundamental task for many real-world applications involving incomplete or corrupted datasets. For data with spatial or temporal side information, low-rank…
This paper develops a novel hybrid approach for estimating the mixture model of $t$-factor analyzers (MtFA) that employs multivariate $t$-distribution and factor model to cluster and characterize grouped data. The traditional estimation…