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An improved mixture of probabilistic principal component analysis (PPCA) has been introduced for nonlinear data-driven process monitoring in this paper. To realize this purpose, the technique of a mixture of probabilistic principal…
Recent years have witnessed intense development of randomized methods for low-rank approximation. These methods target principal component analysis (PCA) and the calculation of truncated singular value decompositions (SVD). The present…
Principal component analysis (PCA) is recognised as a quintessential data analysis technique when it comes to describing linear relationships between the features of a dataset. However, the well-known sensitivity of PCA to non-Gaussian…
Deep subspace clustering (DSC) networks based on self-expressive model learn representation matrix, often implemented in terms of fully connected network, in the embedded space. After the learning is finished, representation matrix is used…
We develop techniques to convexify a set that is invariant under permutation and/or change of sign of variables and discuss applications of these results. First, we convexify the intersection of the unit ball of a permutation and…
Several fundamental tasks in data science rely on computing an extremal eigenspace of size $r \ll n$, where $n$ is the underlying problem dimension. For example, spectral clustering and PCA both require the computation of the leading…
Probabilistic Circuits (PCs) are tractable representations of probability distributions allowing for exact and efficient computation of likelihoods and marginals. Recent advancements have improved the scalability of PCs either by leveraging…
Markov Chain Monte Carlo (MCMC) algorithms are often used for approximate inference inside learning, but their slow mixing can be difficult to diagnose and the approximations can seriously degrade learning. To alleviate these issues, we…
Single-cell RNA-seq provides detailed molecular snapshots of individual cells but is notoriously noisy. Variability stems from biological differences and technical factors, such as amplification bias and limited RNA capture efficiency,…
Calibration of individual based models (IBMs), successful in modeling complex ecological dynamical systems, is often performed only ad-hoc. Bayesian inference can be used for both parameter estimation and uncertainty quantification, but its…
Recently popularized randomized methods for principal component analysis (PCA) efficiently and reliably produce nearly optimal accuracy --- even on parallel processors --- unlike the classical (deterministic) alternatives. We adapt one of…
Robust principal component analysis (RPCA) is a widely used tool for dimension reduction. In this work, we propose a novel non-convex algorithm, coined Iterated Robust CUR (IRCUR), for solving RPCA problems, which dramatically improves the…
Principal component analysis (PCA) can be significantly limited when there is too few examples of the target data of interest. We propose a transfer learning approach to PCA (TL-PCA) where knowledge from a related source task is used in…
In this paper, we introduce an algorithm for performing spectral clustering efficiently. Spectral clustering is a powerful clustering algorithm that suffers from high computational complexity, due to eigen decomposition. In this work, we…
Modal analysis techniques are used to identify patterns and develop reduced-order models in a variety of fluid applications. However, experimentally acquired flow fields may be corrupted with incorrect and missing entries, which may degrade…
Multi-block CCA constructs linear relationships explaining coherent variations across multiple blocks of data. We view the multi-block CCA problem as finding leading generalized eigenvectors and propose to solve it via a proximal gradient…
We study efficient algorithms for Sparse PCA in standard statistical models (spiked covariance in its Wishart form). Our goal is to achieve optimal recovery guarantees while being resilient to small perturbations. Despite a long history of…
We propose a general method for deep learning based point cloud analysis, which is invariant to rotation on the inputs. Classical methods are vulnerable to rotation, as they usually take aligned point clouds as input. Principle Component…
Classical methods such as Principal Component Analysis (PCA) and Canonical Correlation Analysis (CCA) are ubiquitous in statistics. However, these techniques are only able to reveal linear relationships in data. Although nonlinear variants…
We present a novel approach to detecting and utilizing symmetries in probabilistic graphical models with two main contributions. First, we present a scalable approach to computing generating sets of permutation groups representing the…