Related papers: Identifiable and interpretable nonparametric facto…
Data can be assumed to be continuous functions defined on an infinite-dimensional space for many phenomena. However, the infinite-dimensional data might be driven by a small number of latent variables. Hence, factor models are relevant for…
Semi-Non-negative Matrix Factorization is a technique that learns a low-dimensional representation of a dataset that lends itself to a clustering interpretation. It is possible that the mapping between this new representation and our…
It is now practically the norm for data to be very high dimensional in areas such as genetics, machine vision, image analysis and many others. When analyzing such data, parametric models are often too inflexible while nonparametric…
Deep latent variable models learn condensed representations of data that, hopefully, reflect the inner workings of the studied phenomena. Unfortunately, these latent representations are not statistically identifiable, meaning they cannot be…
Across fields such as machine learning, social science, geography, considerable attention has been given to models that factorize a nonnegative matrix into the product of two or three matrices, subject to nonnegative or row-sum-to-1…
Gaussian process-based latent variable models are flexible and theoretically grounded tools for nonlinear dimension reduction, but generalizing to non-Gaussian data likelihoods within this nonlinear framework is statistically challenging.…
Linear mixture models have proven very useful in a plethora of applications, e.g., topic modeling, clustering, and source separation. As a critical aspect of the linear mixture models, identifiability of the model parameters is…
Nonnegative matrix factorization is a powerful technique to realize dimension reduction and pattern recognition through single-layer data representation learning. Deep learning, however, with its carefully designed hierarchical structure,…
Factor modeling is a powerful statistical technique that permits to capture the common dynamics in a large panel of data with a few latent variables, or factors, thus alleviating the curse of dimensionality. Despite its popularity and…
Integrating various data modalities brings valuable insights into underlying phenomena. Multimodal factor analysis (FA) uncovers shared axes of variation underlying different simple data modalities, where each sample is represented by a…
In this work we perform some mathematical analysis on non-negative matrix factorizations (NMF) and apply NMF to some imaging and inverse problems. We will propose a sparse low-rank approximation of big positive data and images in terms of…
In many applications, particularly in the natural sciences, the available high-dimensional set of features may contain variables that are not correlated with the response under consideration. Such irrelevant features can, in certain cases,…
Unmeasured or latent variables are often the cause of correlations between multivariate measurements, which are studied in a variety of fields such as psychology, ecology, and medicine. For Gaussian measurements, there are classical tools…
Non-negative Matrix Factorization (NMF) is a powerful technique for analyzing regularly-sampled data, i.e., data that can be stored in a matrix. For audio, this has led to numerous applications using time-frequency (TF) representations like…
In this work, we develop a scalable approach for a flexible latent factor model for high-dimensional dynamical systems. Each latent factor process has its own correlation and variance parameters, and the orthogonal factor loading matrix can…
Nonnegative matrix factorization (NMF) is a powerful tool in data exploratory analysis by discovering the hidden features and part-based patterns from high-dimensional data. NMF and its variants have been successfully applied into diverse…
The analysis of clinical questionnaire data comes with many inherent challenges. These challenges include the handling of data with missing fields, as well as the overall interpretation of a dataset with many fields of different scales and…
Confirmatory factor analysis (CFA) is a statistical method for identifying and confirming the presence of latent factors among observed variables through the analysis of their covariance structure. Compared to alternative factor models, CFA…
Modeling and forecasting covariance matrices of asset returns play a crucial role in finance. The availability of high frequency intraday data enables the modeling of the realized covariance matrix directly. However, most models in the…
Frailty models are essential tools in survival analysis for addressing unobserved heterogeneity and random effects in the data. These models incorporate a random effect, the frailty, which is assumed to impact the hazard rate…