Related papers: Algebraic Sparse Factor Analysis
There has been a lot of work fitting Ising models to multivariate binary data in order to understand the conditional dependency relationships between the variables. However, additional covariates are frequently recorded together with the…
For factor model, the involved covariance matrix often has no row sparse structure because the common factors may lead some variables to strongly associate with many others. Under the ultra-high dimensional paradigm, this feature causes…
High-dimensional real-world systems can often be well characterized by a small number of simultaneous low-complexity interactions. The analysis of variance (ANOVA) decomposition and the anchored decomposition are typical techniques to find…
Economists are blessed with a wealth of data for analysis, but more often than not, values in some entries of the data matrix are missing. Various methods have been proposed to handle missing observations in a few variables. We exploit the…
Factor models are a parsimonious way to explain the dependence of variables using several latent variables. In Gaussian 1-factor and structural factor models (such as bi-factor, oblique factor) and their factor copula counterparts, factor…
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…
Methods to identify cause-effect relationships currently mostly assume the variables to be scalar random variables. However, in many fields the objects of interest are vectors or groups of scalar variables. We present a new constraint-based…
Causal representation learning aims at identifying high-level causal variables from perceptual data. Most methods assume that all latent causal variables are captured in the high-dimensional observations. We instead consider a partially…
This paper examines a general class of noisy matrix completion tasks where the goal is to estimate a matrix from observations obtained at a subset of its entries, each of which is subject to random noise or corruption. Our specific focus is…
We propose a novel estimation approach for the covariance matrix based on the $l_1$-regularized approximate factor model. Our sparse approximate factor (SAF) covariance estimator allows for the existence of weak factors and hence relaxes…
In this thesis we discuss machine learning methods performing automated variable selection for learning sparse predictive models. There are multiple reasons for promoting sparsity in the predictive models. By relying on a limited set of…
We present a matrix-factorization algorithm that scales to input matrices with both huge number of rows and columns. Learned factors may be sparse or dense and/or non-negative, which makes our algorithm suitable for dictionary learning,…
In an era of unprecedented deluge of (mostly unstructured) data, graphs are proving more and more useful, across the sciences, as a flexible abstraction to capture complex relationships between complex objects. One of the main challenges…
This paper proposes sparse and easy-to-interpret proximate factors to approximate statistical latent factors. Latent factors in a large-dimensional factor model can be estimated by principal component analysis (PCA), but are usually hard to…
Large-scale association analysis between multivariate responses and predictors is of great practical importance, as exemplified by modern business applications including social media marketing and crisis management. Despite the rapid…
In the framework of Symbolic Data Analysis (SDA), distribution-variables are a particular case of multi-valued variables: each unit is represented by a set of distributions (e.g. histograms, density functions or quantile functions), one for…
This paper deals with the factor modeling for high-dimensional time series based on a dimension-reduction viewpoint. Under stationary settings, the inference is simple in the sense that both the number of factors and the factor loadings are…
It has become routine to collect data that are structured as multiway arrays (tensors). There is an enormous literature on low rank and sparse matrix factorizations, but limited consideration of extensions to the tensor case in statistics.…
Confirmatory Factor Analysis (CFA) is a particular form of factor analysis, most commonly used in social research. In confirmatory factor analysis, the researcher first develops a hypothesis about what factors they believe are underlying…
Factor analysis is a flexible technique for assessment of multivariate dependence and codependence. Besides being an exploratory tool used to reduce the dimensionality of multivariate data, it allows estimation of common factors that often…