Related papers: Robust reconstruction of sparse network dynamics
Dynamic network reconstruction has been shown to be challenging due to the requirements on sparse network structures and network identifiability. The direct parametric method (e.g., using ARX models) requires a large amount of parameters in…
Reconstructing complex networks from measurable data is a fundamental problem for understanding and controlling collective dynamics of complex networked systems. However, a significant challenge arises when we attempt to decode structural…
Performing multiple experiments is common when learning internal mechanisms of complex systems. These experiments can include perturbations to parameters or external disturbances. A challenging problem is to efficiently incorporate all…
We propose a new method for reconstruction of sparse signals with and without noisy perturbations, termed the subspace pursuit algorithm. The algorithm has two important characteristics: low computational complexity, comparable to that of…
Complex networks hosting binary-state dynamics arise in a variety of contexts. In spite of previous works, to fully reconstruct the network structure from observed binary data remains to be challenging. We articulate a statistical inference…
An important problem in many areas of science is that of recovering interaction networks from simultaneous time-series of many interacting dynamical processes. A common approach is to use the elements of the correlation matrix or its…
While deep neural networks are sensitive to adversarial noise, sparse coding using the Basis Pursuit (BP) method is robust against such attacks, including its multi-layer extensions. We prove that the stability theorem of BP holds upon the…
We present a method for the reconstruction of networks, based on the order of nodes visited by a stochastic branching process. Our algorithm reconstructs a network of minimal size that ensures consistency with the data. Crucially, we show…
We consider the problem of recovering equations of motion from multivariate time series of oscillators interacting on sparse networks. We reconstruct the network from an initial guess which can include expert knowledge about the system such…
We propose a new iterative greedy algorithm for reconstructions of sparse signals with or without noisy perturbations in compressed sensing. The proposed algorithm, called \emph{subspace thresholding pursuit} (STP) in this paper, is a…
We present a data-driven model to reconstruct nonlinear dynamics from a very sparse times series data, which relies on the strength of the echo state network (ESN) in learning nonlinear representation of data. With an assumption of the…
An important problem of reconstruction of diffusion network and transmission probabilities from the data has attracted a considerable attention in the past several years. A number of recent papers introduced efficient algorithms for the…
We propose and analyze an online algorithm for reconstructing a sequence of signals from a limited number of linear measurements. The signals are assumed sparse, with unknown support, and evolve over time according to a generic nonlinear…
Sparse recovery can recover sparse signals from a set of underdetermined linear measurements. Motivated by the need to monitor large-scale networks from a limited number of measurements, this paper addresses the problem of recovering sparse…
Recently, it has been observed that a sparse trigonometric polynomial, i.e. having only a small number of non-zero coefficients, can be reconstructed exactly from a small number of random samples using Basis Pursuit (BP) or Orthogonal…
Reconstructing the equation of motion and thus the network topology of a system from time series is a very important problem. Although many powerful methods have been developed, it remains a great challenge to deal with systems in high…
The problem of reconstructing and identifying intracellular protein signaling and biochemical networks is of critical importance in biology today. We sought to develop a mathematical approach to this problem using, as a test case, one of…
In this article, we discuss a novel greedy algorithm for the recovery of compressive sampled signals under noisy conditions. Most of the greedy recovery algorithms proposed in the literature require sparsity of the signal to be known or…
Novel method of reconstructing dynamical networks from empirically measured time series is proposed. By examining the variable--derivative correlation of network node pairs, we derive a simple equation that directly yields the adjacency…
Recent interest has developed around the problem of dynamic compressed sensing, or the recovery of time-varying, sparse signals from limited observations. In this paper, we study how the dynamics of recurrent networks, formulated as general…