Related papers: Sparse Linear Dynamical System with Its Applicatio…
In this paper we revisit random linear under-determined systems with sparse solutions. We consider $\ell_1$ optimization heuristic known to work very well when used to solve these systems. A collection of fundamental results that relate to…
Latent linear dynamical systems with Bernoulli observations provide a powerful modeling framework for identifying the temporal dynamics underlying binary time series data, which arise in a variety of contexts such as binary decision-making…
Temporal variations in biological systems and more generally in natural sciences are typically modelled as a set of Ordinary, Partial, or Stochastic Differential or Difference Equations. Algorithms for learning the structure and the…
Sparse linear regression (SLR) is a well-studied problem in statistics where one is given a design matrix $X\in\mathbb{R}^{m\times n}$ and a response vector $y=X\theta^*+w$ for a $k$-sparse vector $\theta^*$ (that is, $\|\theta^*\|_0\leq…
We present the first provable method for identifying symmetric linear dynamical systems (LDS) with accuracy guarantees that are independent of the systems' state dimension or effective memory. Our approach builds upon recent work that…
It is widely believed that sparse supervision is worse than dense supervision in the field of depth completion, but the underlying reasons for this are rarely discussed. To this end, we revisit the task of radar-camera depth completion and…
Linear dynamical systems are a fundamental and powerful parametric model class. However, identifying the parameters of a linear dynamical system is a venerable task, permitting provably efficient solutions only in special cases. This work…
Sparsity constraints on the control inputs of a linear dynamical system naturally arise in several practical applications such as networked control, computer vision, seismic signal processing, and cyber-physical systems. In this work, we…
This paper proposes a fast and accurate method for sparse regression in the presence of missing data. The underlying statistical model encapsulates the low-dimensional structure of the incomplete data matrix and the sparsity of the…
Understanding how the collective activity of neural populations relates to computation and ultimately behavior is a key goal in neuroscience. To this end, statistical methods which describe high-dimensional neural time series in terms of…
Multidimensional scaling (MDS) is a popular dimensionality reduction techniques that has been widely used for network visualization and cooperative localization. However, the traditional stress minimization formulation of MDS necessitates…
This technical note considers the identification of nonlinear discrete-time systems with additive process noise but without measurement noise. In particular, we propose a method and its associated algorithm to identify the system nonlinear…
We propose data-driven nonlinear smoother (DNS) to estimate a hidden state sequence of a complex dynamical process from a noisy, linear measurement sequence. The dynamical process is model-free, that is, we do not have any knowledge of the…
Sparse sampling schemes have the potential to dramatically reduce image acquisition time while simultaneously reducing radiation damage to samples. However, for a sparse sampling scheme to be useful it is important that we are able to…
This paper investigates the problem of identifying state-dependent switching systems, a class of hybrid dynamical systems that combine multiple linear or nonlinear modes. We propose two broad classes of switching systems: switching linear…
Sparse regression has emerged as a popular technique for learning dynamical systems from temporal data, beginning with the SINDy (Sparse Identification of Nonlinear Dynamics) framework proposed by arXiv:1509.03580. Quantifying the…
The concepts of sparsity, and regularised estimation, have proven useful in many high-dimensional statistical applications. Dynamic factor models (DFMs) provide a parsimonious approach to modelling high-dimensional time series, however, it…
Discrete-time linear time-varying (LTV) systems form a powerful class of models to approximate complex dynamical systems with nonlinear dynamics for the purpose of analysis, design and control. Motivated by inference of spatio-temporal…
In applications of nonlinear and complex dynamical systems, a common situation is that the system can be measured but its structure and the detailed rules of dynamical evolution are unknown. The inverse problem is to determine the system…
Generally, discretization of partial differential equations (PDEs) creates a sequence of linear systems $A_k x_k = b_k, k = 0, 1, 2, ..., N$ with well-known and structured sparsity patterns. Preconditioners are often necessary to achieve…