Related papers: Non-Gaussian Component Analysis via Lattice Basis …

Principal Component Analysis (PCA) is the workhorse tool for dimensionality reduction in this era of big data. While often overlooked, the purpose of PCA is not only to reduce data dimensionality, but also to yield features that are…

Independent Component Analysis (ICA) is a fundamental unsupervised learning technique foruncovering latent structure in data by separating mixed signals into their independent sources. While substantial progress has been made in…

Identifying low-dimensional latent structures within high-dimensional data has long been a central topic in the machine learning community, driven by the need for data compression, storage, transmission, and deeper data understanding.…

Despite a lack of theoretical understanding, deep neural networks have achieved unparalleled performance in a wide range of applications. On the other hand, shallow representation learning with component analysis is associated with rich…

Principal component analysis (PCA) is arguably the most popular tool in multivariate exploratory data analysis. In this paper, we consider the question of how to handle heterogeneous variables that include continuous, binary, and ordinal.…

In this paper, we propose a stochastic Gauss-Newton (SGN) algorithm to study the online principal component analysis (OPCA) problem, which is formulated by using the symmetric low-rank product (SLRP) model for dominant eigenspace…

We study the problem of learning a mixture model of non-parametric product distributions. The problem of learning a mixture model is that of finding the component distributions along with the mixing weights using observed samples generated…

Regularized generalized canonical correlation analysis (RGCCA) is a generalization of regularized canonical correlation analysis to three or more sets of variables, which is a component-based approach aiming to study the relationships…

Sampling from the lattice Gaussian distribution has emerged as an important problem in coding, decoding and cryptography. In this paper, lattice reduction technique is adopted to Gibbs sampler for lattice Gaussian sampling. Firstly, with…

Distributed algorithms and theories are called for in this era of big data. Under weaker local signal-to-noise ratios, we improve upon the celebrated one-round distributed principal component analysis (PCA) algorithm designed in the spirit…

Robust Principal Component Analysis (RPCA) is a fundamental technique for decomposing data into low-rank and sparse components, which plays a critical role for applications such as image processing and anomaly detection. Traditional RPCA…

Principal component analysis (PCA) is a widely used technique for data analysis and dimension reduction with numerous applications in science and engineering. However, the standard PCA suffers from the fact that the principal components…

Learning a good distance metric in feature space potentially improves the performance of the KNN classifier and is useful in many real-world applications. Many metric learning algorithms are however based on the point estimation of a…

Describing the dimension reduction (DR) techniques by means of probabilistic models has recently been given special attention. Probabilistic models, in addition to a better interpretability of the DR methods, provide a framework for further…

We decompose the Kullback--Leibler generalization error (GE) -- the expected KL divergence from the data distribution to the trained model -- of unsupervised learning into three non-negative components: model error, data bias, and variance.…

Consider a pair of correlated Gaussian sources (X1,X2). Two separate encoders observe the two components and communicate compressed versions of their observations to a common decoder. The decoder is interested in reconstructing a linear…

We consider independent component analysis of binary data. While fundamental in practice, this case has been much less developed than ICA for continuous data. We start by assuming a linear mixing model in a continuous-valued latent space,…

The basic goal of computer engineering is the analysis of data. Such data are often large data sets distributed according to various distribution models. In this manuscript we focus on the analysis of non-Gaussian distributed data. In the…

Principal Component Analysis (PCA) is a cornerstone of dimensionality reduction, yet its classical formulation relies critically on second-order moments and is therefore fragile in the presence of heavy-tailed data and impulsive noise.…

We revisit the problem of distribution learning within the framework of learning-augmented algorithms. In this setting, we explore the scenario where a probability distribution is provided as potentially inaccurate advice on the true,…