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We propose an extension of non-parametric multivariate finite mixture models by dropping the standard conditional independence assumption and incorporating the independent component analysis (ICA) structure instead. We formulate an…

Unsupervised learning plays an important role in many fields, such as artificial intelligence, machine learning, and neuroscience. Compared to static data, methods for extracting low-dimensional structure for dynamic data are lagging. We…

Two types of spatiotemporal chaos exhibited by ensembles of coupled nonlinear oscillators are analyzed using independent component analysis (ICA). For diffusively coupled complex Ginzburg-Landau oscillators that exhibit smooth amplitude…

Accuracy and generalization capabilities are key objectives when learning dynamical system models. To obtain such models from limited data, current works exploit prior knowledge and assumptions about the system. However, the fusion of…

Bayesian hierarchical models with latent Gaussian layers have proven very flexible in capturing complex stochastic behavior and hierarchical structures in high-dimensional spatial and spatio-temporal data. Whereas simulation-based Bayesian…

Noise subtraction is a crucial process in gravitational wave (GW) data analysis to improve the sensitivity of interferometric detectors. While linear noise coupling has been extensively studied and successfully mitigated using methods such…

We propose a new method of independent component analysis (ICA) in order to extract appropriate features from high-dimensional data. In general, matrix factorization methods including ICA have a problem regarding the interpretability of…

Independent component analysis (ICA) has often been used as a tool to model natural image statistics by separating multivariate signals in the image into components that are assumed to be independent. However, these estimated components…

A key goal of unsupervised representation learning is "inverting" a data generating process to recover its latent properties. Existing work that provably achieves this goal relies on strong assumptions on relationships between the latent…

Dimensionality reduction techniques have found great success in a wide range of fields requiring analysis of high-dimensional datasets. Time-lagged independent components analysis (TICA), which finds independent components (TICs) with…

Principal component analysis (PCA) is widely used for feature extraction and dimensionality reduction, with documented merits in diverse tasks involving high-dimensional data. Standard PCA copes with one dataset at a time, but it is…

Dynamic inner principal component analysis (DiPCA) is a powerful method for the analysis of time-dependent multivariate data. DiPCA extracts dynamic latent variables that capture the most dominant temporal trends by solving a large-scale,…

Learning disentangled representations of data is a fundamental problem in artificial intelligence. Specifically, disentangled latent representations allow generative models to control and compose the disentangled factors in the synthesis…

Integrating high-level context information with low-level details is of central importance in semantic segmentation. Towards this end, most existing segmentation models apply bilinear up-sampling and convolutions to feature maps of…

This article establishes a new and comprehensive estimation and inference theory for principal component analysis (PCA) under the weak factor model that allow for cross-sectional dependent idiosyncratic components under the nearly minimal…

In this work, we establish the sufficient conditions under which nonlinear Canonical Correlation Analysis (CCA) recovers ground-truth latent factors up to an affine transformation. By transporting the analysis from the observation space to…

The identification of a linear system model from data has wide applications in control theory. The existing work that provides finite sample guarantees for linear system identification typically uses data from a single long system…

Linear Independent Component Analysis (ICA) is a blind source separation technique that has been used in various domains to identify independent latent sources from observed signals. In order to obtain a higher signal-to-noise ratio, the…

A novel adaptive identifier is developed for nonlinear time-delay systems composed of linear, Lipschitz and non-Lipschitz components. To begin with, an identifier is designed for uncertain systems with a priori known delay values, and then…

Independent Component Analysis (ICA) - one of the basic tools in data analysis - aims to find a coordinate system in which the components of the data are independent. Most of existing methods are based on the minimization of the function of…