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This letter extends the exactly sparse Gaussian variational inference (ESGVI) algorithm for state estimation in two complementary directions. First, ESGVI is generalized to operate on matrix Lie groups, enabling the estimation of states…

In this paper, we set up the theoretical foundations for a high-dimensional functional factor model approach in the analysis of large cross-sections (panels) of functional time series (FTS). We first establish a representation result…

Nowadays an increasing amount of data is available and we have to deal with models in high dimension (number of covariates much larger than the sample size). Under sparsity assumption it is reasonable to hope that we can make a good…

Motivated by modern applications in which one constructs graphical models based on a very large number of features, this paper introduces a new class of cluster-based graphical models, in which variable clustering is applied as an initial…

A novel unsupervised learning method is proposed in this paper for biclustering large-dimensional matrix-valued time series based on an entirely new latent two-way factor structure. Each block cluster is characterized by its own row and…

Determining the number of factors in high-dimensional factor models remains a fundamental challenge, particularly when data are incomplete. This paper introduces the concept of identifiable factors, those that can be reliably recovered…

In the context of confirmatory factor analysis, the independent clusters model has been found to be overly restrictive in several research contexts. Therefore, a less restrictive criterion for parsimony of non-salient loadings in…

Efficient training and inference algorithms, such as low-rank adaption and model pruning, have shown impressive performance for learning Transformer-based large foundation models. However, due to the technical challenges of the non-convex…

Factor analysis or sometimes referred to as variable analysis has been extensively used in classification problems for identifying specific factors that are significant to particular classes. This type of analysis has been widely used in…

In this paper, we study transfer learning for high-dimensional factor-augmented sparse linear models, motivated by applications in economics and finance where strongly correlated predictors and latent factor structures pose major challenges…

Large-dimensional factor model has drawn much attention in the big-data era, in order to reduce the dimensionality and extract underlying features using a few latent common factors. Conventional methods for estimating the factor model…

As a popular tool for producing meaningful and interpretable models, large-scale sparse learning works efficiently when the underlying structures are indeed or close to sparse. However, naively applying the existing regularization methods…

Approximations to Gaussian processes based on inducing variables, combined with variational inference techniques, enable state-of-the-art sparse approaches to infer GPs at scale through mini batch-based learning. In this work, we address…

Factor analysis is a widely used statistical tool in many scientific disciplines, such as psychology, economics, and sociology. As observations linked by networks become increasingly common, incorporating network structures into factor…

Sparse model estimation is a topic of high importance in modern data analysis due to the increasing availability of data sets with a large number of variables. Another common problem in applied statistics is the presence of outliers in the…

We develop an automated variational method for inference in models with Gaussian process (GP) priors and general likelihoods. The method supports multiple outputs and multiple latent functions and does not require detailed knowledge of the…

In genomics, differential abundance and expression analyses are complicated by the compositional nature of sequence count data, which reflect only relative-not absolute-abundances or expression levels. Many existing methods attempt to…

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…

This paper develops the inferential theory for latent factor models estimated from large dimensional panel data with missing observations. We propose an easy-to-use all-purpose estimator for a latent factor model by applying principal…

Latent factor models are widely used to discover and adjust for hidden variation in modern applications. However, most methods do not fully account for uncertainty in the latent factors, which can lead to miscalibrated inferences such as…