Related papers: A Unified Framework for Probabilistic Component An…

Principal component analysis (PCA) is a well-established tool in machine learning and data processing. The principal axes in PCA were shown to be equivalent to the maximum marginal likelihood estimator of the factor loading matrix in a…

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…

Probabilistic Component Latent Analysis (PLCA) is a statistical modeling method for feature extraction from non-negative data. It has been fruitfully applied to various research fields of information retrieval. However, the EM-solved…

Probabilistic Circuits (PCs) have emerged as an efficient framework for representing and learning complex probability distributions. Nevertheless, the existing body of research on PCs predominantly concentrates on data-driven parameter…

Revealing the functional sites of biological sequences, such as evolutionary conserved, structurally interacting or co-evolving protein sites, is a fundamental, and yet challenging task. Different frameworks and models were developed to…

This paper proposes a novel statistical approach to intelligent document retrieval. It seeks to offer a more structured and extensible mathematical approach to the term generalization done in the popular Latent Semantic Analysis (LSA)…

Factor-based forecasting using Principal Component Analysis (PCA) is an effective machine learning tool for dimension reduction with many applications in statistics, economics, and finance. This paper introduces a Supervised Screening and…

Sequential decision making, commonly formalized as optimization of a Markov Decision Process, is a key challenge in artificial intelligence. Two successful approaches to MDP optimization are reinforcement learning and planning, which both…

We propose a unified framework to speed up the existing stochastic matrix factorization (SMF) algorithms via variance reduction. Our framework is general and it subsumes several well-known SMF formulations in the literature. We perform a…

We introduce a new perspective on spectral dimensionality reduction which views these methods as Gaussian Markov random fields (GRFs). Our unifying perspective is based on the maximum entropy principle which is in turn inspired by maximum…

We develop Probabilistic Targeted Factor Analysis (PTFA), a likelihood-based framework for constructing latent factors that are explicitly targeted to variables of economic interest. PTFA provides a probabilistic foundation for Partial…

Principal Component Analysis (PCA) is one of the most important methods to handle high dimensional data. However, most of the studies on PCA aim to minimize the loss after projection, which usually measures the Euclidean distance, though in…

Principal components analysis (PCA) is a well-known technique for approximating a tabular data set by a low rank matrix. Here, we extend the idea of PCA to handle arbitrary data sets consisting of numerical, Boolean, categorical, ordinal,…

Probabilistic principal component analysis (PPCA) is currently one of the most used statistical tools to reduce the ambient dimension of the data. From multidimensional scaling to the imputation of missing data, PPCA has a broad spectrum of…

Principal Component Analysis (PCA) is a very successful dimensionality reduction technique, widely used in predictive modeling. A key factor in its widespread use in this domain is the fact that the projection of a dataset onto its first…

We present an information-based uncertainty quantification method for general Markov Random Fields. Markov Random Fields (MRF) are structured, probabilistic graphical models over undirected graphs, and provide a fundamental unifying…

Probabilistic principal component analysis (PPCA) is a probabilistic reformulation of principal component analysis (PCA), under the framework of a Gaussian latent variable model. To improve the robustness of PPCA, it has been proposed to…

Pair-wise Markov random fields (MRF) are considered for application to the development of low complexity, iterative MIMO detection. Specifically, we consider two types of MRF, namely, the fully-connected and ring-type. For the edge…

Principal component analysis (PCA) is perhaps the most widely used method for data dimensionality reduction. A key question in PCA is deciding how many factors to retain. This manuscript describes a new approach to automatically selecting…

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…