Related papers: GREAT: Grassmannian REcursive Algorithm for Tracki…
Data-driven control methods based on subspace representations are powerful but are often limited to linear time-invariant systems where the model order is known. A key challenge is developing online data-driven control algorithms for…
This work presents GROUSE (Grassmanian Rank-One Update Subspace Estimation), an efficient online algorithm for tracking subspaces from highly incomplete observations. GROUSE requires only basic linear algebraic manipulations at each…
This paper discusses robustness guarantees for online tracking of time-varying subspaces from noisy data. Building on recent work in optimization over a Grassmannian manifold, we introduce a new approach for robust subspace tracking by…
We present a dynamic subspace approach for efficiently approximating large-scale systems by learning time-continuous trajectories on the Grassmannian manifold. By parameterizing a low-dimensional basis as a geodesic path, the method allows…
Online system identification algorithms are widely used for monitoring, diagnostics and control by continuously adapting to time-varying dynamics. Typically, these algorithms consider a model structure that lacks parsimony and offers…
Subspace learning and matrix factorization problems have great many applications in science and engineering, and efficient algorithms are critical as dataset sizes continue to grow. Many relevant problem formulations are non-convex, and in…
This paper presents GRASTA (Grassmannian Robust Adaptive Subspace Tracking Algorithm), an efficient and robust online algorithm for tracking subspaces from highly incomplete information. The algorithm uses a robust $l^1$-norm cost function…
We present a framework for supervised subspace tracking, when there are two time series $x_t$ and $y_t$, one being the high-dimensional predictors and the other being the response variables and the subspace tracking needs to take into…
Learning dynamical models from data is not only fundamental but also holds great promise for advancing principle discovery, time-series prediction, and controller design. Among various approaches, Gaussian Process State-Space Models…
Dynamic subspace estimation, or subspace tracking, is a fundamental problem in statistical signal processing and machine learning. This paper considers a geodesic model for time-varying subspaces. The natural objective function for this…
Online learning algorithms for dynamical systems provide finite time guarantees for control in the presence of sequentially revealed cost functions. We pose the classical linear quadratic tracking problem in the framework of online…
It has been observed in a variety of contexts that gradient descent methods have great success in solving low-rank matrix factorization problems, despite the relevant problem formulation being non-convex. We tackle a particular instance of…
Tracking signals in dynamic environments presents difficulties in both analysis and implementation. In this work, we expand on a class of subspace tracking algorithms which utilize the Grassmann manifold -- the set of linear subspaces of a…
Gaussian Processes (GPs) are powerful kernelized methods for non-parameteric regression used in many applications. However, their use is limited to a few thousand of training samples due to their cubic time complexity. In order to scale GPs…
This paper addresses the problem of identifying a very small subset of data points that belong to a significantly larger massive dataset (i.e., Big Data). The small number of selected data points must adequately represent and faithfully…
Inferring time-varying graph structures from high-dimensional nodal observations is a fundamental problem arising in neuroscience, finance, climatology, and beyond. Two intrinsic challenges govern this problem: maintaining the…
This paper introduces a surrogate modeling scheme based on Grassmannian manifold learning to be used for cost-efficient predictions of high-dimensional stochastic systems. The method exploits subspace-structured features of each solution by…
Exact Gaussian Process (GP) regression has O(N^3) runtime for data size N, making it intractable for large N. Many algorithms for improving GP scaling approximate the covariance with lower rank matrices. Other work has exploited structure…
We extend the recently introduced regularization/Bayesian System Identification procedures to the estimation of time-varying systems. Specifically, we consider an online setting, in which new data become available at given time steps. The…
Change points in real-world systems mark significant regime shifts in system dynamics, possibly triggered by exogenous or endogenous factors. These points define regimes for the time evolution of the system and are crucial for understanding…