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We consider a statistical model for matrix factorization in a regime where the rank of the two hidden matrix factors grows linearly with their dimension and their product is corrupted by additive noise. Despite various approaches,…
We consider the problem of sparse estimation in a factor analysis model. A traditional estimation procedure in use is the following two-step approach: the model is estimated by maximum likelihood method and then a rotation technique is…
We consider the classical problem of learning, with arbitrary accuracy, the natural parameters of a $k$-parameter truncated \textit{minimal} exponential family from i.i.d. samples in a computationally and statistically efficient manner. We…
We propose modeling raw functional data as a mixture of a smooth function and a highdimensional factor component. The conventional approach to retrieving the smooth function from the raw data is through various smoothing techniques.…
The current high-dimensional linear factor models fail to account for the different types of variables, while high-dimensional nonlinear factor models often overlook the overdispersion present in mixed-type data. However, overdispersion is…
Probabilistic approach to Boolean matrix factorization can provide solutions robustagainst noise and missing values with linear computational complexity. However,the assumption about latent factors can be problematic in real world…
Variable selection and classification are common objectives in the analysis of high-dimensional data. Most such methods make distributional assumptions that may not be compatible with the diverse families of distributions data can take. A…
The modal factor model represents a new factor model for dimension reduction in high dimensional panel data. Unlike the approximate factor model that targets for the mean factors, it captures factors that influence the conditional mode of…
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…
We address the problem of learning of continuous exponential family distributions with unbounded support. While a lot of progress has been made on learning of Gaussian graphical models, we still lack scalable algorithms for reconstructing…
The mean field methods, which entail approximating intractable probability distributions variationally with distributions from a tractable family, enjoy high efficiency, guaranteed convergence, and provide lower bounds on the true…
Generalized latent factor analysis not only provides a useful latent embedding approach in statistics and machine learning, but also serves as a widely used tool across various scientific fields, such as psychometrics, econometrics, and…
This paper investigates the properties of Quasi Maximum Likelihood estimation of an approximate factor model for an $n$-dimensional vector of stationary time series. We prove that the factor loadings estimated by Quasi Maximum Likelihood…
The mixture of factor analyzers (MFA) model provides a powerful tool for analyzing high-dimensional data as it can reduce the number of free parameters through its factor-analytic representation of the component covariance matrices. This…
Nonnegative matrix factorization (NMF) is a linear dimensionality technique for nonnegative data with applications such as image analysis, text mining, audio source separation and hyperspectral unmixing. Given a data matrix $M$ and a…
Beta process is the standard nonparametric Bayesian prior for latent factor model. In this paper, we derive a structured mean-field variational inference algorithm for a beta process non-negative matrix factorization (NMF) model with…
One of the goals of causal inference is to generalize from past experiments and observational data to novel conditions. While it is in principle possible to eventually learn a mapping from a novel experimental condition to an outcome of…
This paper aims to examine the characteristics of the posterior distribution of covariance/precision matrices in a "large $p$, large $n$" scenario, where $p$ represents the number of variables and $n$ is the sample size. Our analysis…
We present large sample results for partitioning-based least squares nonparametric regression, a popular method for approximating conditional expectation functions in statistics, econometrics, and machine learning. First, we obtain a…
In the following article we provide an exposition of exact computational methods to perform parameter inference from partially observed network models. In particular, we consider the duplication attachment (DA) model which has a likelihood…